# If the Sun got larger, but maintained its luminosity, would the Earth get hotter or colder?

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A recent question If the Sun were bigger but colder, Earth would be hotter or colder? asked - if the Sun got bigger and cooler, would the Earth heat up or cool down. I think the answer to that is mainly that it depends on the final luminosity.

However, what I want to know here (hypothetically), is if the Sun got larger and it's effective temperature decreased such that it's luminosity was unchanged; how would that affect the equilibrium temperature of the Earth? I suspect the answer may involve the wavelength dependence of the albedo, emissivity and atmospheric absorption of the Earth.

Another, less hypothetical, way of asking this is, if you put an Earth-like planet at different distances from stars with a variety of temperatures, such that the total flux incident at the top of the atmosphere was identical, how would the temperatures of those planets compare?

To a first approximation if the Sun got bigger (by a relatively small factor, say a few times) but maintained its present luminosity, as the Earth would still be intercepting the same total energy per unit time the temperature would stay the same. Constant luminosity gives a constant intensity at the Earth's distance from the Sun (intensity is the energy crossing unit area in unit time) which would mean that the total solar energy intercepted by the Earth would remain the same.

However in this scenario the colour of the sun would change and we would get secondary effects due to the reflectivity of the Earth being frequency dependent so the fraction of the incident energy reflected rather than absorbed would change, which would result in a change in temperature. Which direction this would go in is difficult to say as an increase in temperature should result in more cloud which would increase reflectivity…

The key issue is the opacity of the atmosphere, because I presume the question is about the temperature at the solid surface of the Earth. The atmospheric opacity can be seen from https://physics.stackexchange.com/questions/135260/can-someone-explain-to-me-the-concept-of-atmosphere-opacity, where you can see that the "rainbow" of maximum heat flux from the Sun happens to hit a kind of hole in atmospheric opacity. That has a significant warming effect on the Earth, and is exacerbated by the Greenhouse effect. If sunlight was further into the infrared, the graph shows that much more of it would be intercepted in the atmosphere. That would make the surface significantly colder, though certainly not a factor of 2 colder.

No doubt the question is of more than passing interest, because M dwarfs are the most numerous main-sequence stars and are therefore interesting for life. To have life near an M dwarf, the planet would need to be closer than Earth is to the Sun, but the effect of moving the planet closer and shrinking and cooling the star would be similar to leaving Earth where it is and making the star cooler and larger. So the nature of atmospheric opacity for wet atmospheres must be of great significance for understanding the prospects for life around M dwarfs.

## Faint young Sun paradox

The faint young Sun paradox or faint young Sun problem describes the apparent contradiction between observations of liquid water early in Earth's history and the astrophysical expectation that the Sun's output would be only 70 percent as intense during that epoch as it is during the modern epoch. [1] The paradox is this: With the young sun's output at only 70 percent of its current output, the early earth would be expected to be completely frozen but the early earth seems to have had liquid water.

The issue was raised by astronomers Carl Sagan and George Mullen in 1972. [2] Proposed resolutions of this paradox have taken into account greenhouse effects, changes to planetary albedo, astrophysical influences, or combinations of these suggestions.

An unresolved question is how a climate suitable for life was maintained on Earth over the long timescale despite the variable solar output and wide range of terrestrial conditions. [3]

## If the Sun got larger, but maintained its luminosity, would the Earth get hotter or colder? - Astronomy

Write your name at the top of this quiz as well as on your answer sheet. WRITE YOUR VERSION ON YOUR ANSWER SHEET. Feel free to write or draw on the quiz.

Please put away all electronic devices. You will not need a calculator for this quiz.

SELECT THE BEST ANSWER TO EACH PROBLEM.

1. Neutral helium lines are strongest in the spectra of:
a) F stars.
b) G stars.
c) M stars.
d) K stars.
e) B stars.

e) B stars.

2. Which of the following types of stars have spectra that peak in the UV, according to Wien's Law?
a) M.
b) G.
c) K.
d) O.
e) both K and M.

d) O.

3. If a hydrogen atom has an electron in its ground energy level, what kind of photon is needed to ionize it?
a) ultraviolet.
b) red.
c) blue.
d) infrared.
e) radio.

a) ultraviolet.

4. What is Ejnar Hertzsprung known for?
a) Pioneering the use of plots of luminosity vs. temperature for stars.
b) Re-organizing the spectral sequence ABCDEF. to the sequence used today.
c) Determining that the acceleration of an object is inversely proportional to its mass.
d) Determining that the gravitational force between two objects is inversely proportional to the square of the distance apart.
e) Determining that stars are made up of mostly hydrogen and helium.

a) Pioneering the use of plots of luminosity vs. temperature for stars.

5. A period of 5 - 10 minutes is:
a) Approximately the lifetime of a sunspot.
b) Approximately the lifetime of a granule on the Sun's surface.
c) Approximately the time it takes the Sun to spin once on its axis.
d) Approximately how often the overall magnetic polarity of the Sun reverses.
e) Approximately how often the overall magnetic polarity of the Earth reverses.

b) Approximately the lifetime of a granule on the Sun's surface.

6. Which of the following stars has the coldest photosphere?
a) Pollux (type K0III)
b) Arctaurus (type K2III)
c) 42 Draco (between type K1III and type K2III)
d) Formalhaut (type A3V).
e) Aldebaran (type K5III)

e) Aldebaran (type K5III)

7. In Astronomy, the term spicule' refers to:
a) The strong red emission line of hydrogen.
b) A very low mass neutral particle created by nuclear reactions in the core of the Sun.
c) Short-lived jets of gas above the photosphere of the Sun.
d) The force that holds the nuclei of atoms together.
e) The shift in the wavelength of light due to the relative motion of the source of light and the observer.

c) Short-lived jets of gas above the photosphere of the Sun.

8. By accurately measuring the positions of stars in the sky over and over again, Astronomers can sometimes determine which property of some stars?
a) distance.
b) velocity through space in the plane of the sky.
c) whether the star is part of a binary star.
d) all of the above.
e) none of the above.

d) all of the above.

9. The Super Kamiokande experiment beneath a mountain in Japan was designed to detect what kind of particle produced in the Sun?
a) Neutrons.
b) Neutrinos.
c) Protons.
d) Positrons.
e) Gamma ray photons.

b) Neutrinos.

10. Stefan's Law (the Stefan-Boltzmann Law) describes:
a) The back-and-forth shift of a star on the sky, due to the Earth's orbit around the Sun.
b) The shift in the position of a star on the sky relative to background stars, due to a true motion of the star through space.
c) For a hot solid or hot dense gas, the increase in the wavelength of the peak of the spectrum with decreasing temperature.
d) An increase in the luminosity of an star due to an increase in its temperature and/or radius.
e) The shifting of the wavelength of the light seen by an observer, due to the relative motion of the observer and the source of light.

d) An increase in the luminosity of an star due to an increase in its temperature and/or radius.

11. Giant stars like Capella (a yellow star about ten times the radius of the Sun) are classified as Luminosity Class:
a) III.
b) I.
c) V.
d) X.
e) XXX.

a) III.

12. An M2I star is:
a) hotter and larger than the Sun.
b) hotter but smaller than the Sun.
c) colder and larger than the Sun.
d) colder and smaller than the Sun.
e) the same temperature as the Sun, but larger.

c) colder and larger than the Sun.

13. The ancient Greek Astronomer Hipparchus:
a) Came up with the formula F = GM(1)M(2)/R 2 to describe the gravitational force.
b) Invented the magnitude system we use today.
c) Was the first person to plot the luminosity of stars vs. their temperatures.
d) Invented the sequence of stellar spectral types that we use today in modern Astronomy.
e) Was the first person to realize that the acceleration of an object is equal to the force applied to it, divided by its mass.

b) Invented the magnitude system we use today.

14. Which of the following spectral types of stars are colder than type G stars?
a) K,M.
b) O,B.
c) B,F.
d) A,B,O.
e) A,B.

a) K,M.

15. Which of the following is a white dwarf?
a) Proxima Cen.
b) alpha Cen B.
c) the Sun.
d) Sirius B.
e) All of the above.

d) Sirius B.

16. What is the equation lambda(max) = 0.0029/T called?
a) Stefan's Law.
b) Wien's Law.
c) The parallax law.
d) Newton's Second Law.
e) The inverse Square Law of Light.

b) Wien's Law.

17. What's the difference between acceleration and velocity?
a) Acceleration is a change in velocity with time.
b) Acceleration has a direction associated with it, velocity does not.
c) Velocity has a direction associated with it, acceleration does not.
d) Acceleration has units of distance per time, while velocity has units of distance per time 2 .
e) Acceleration and velocity are the same thing.

a) Acceleration is a change in velocity with time.

18. Why does it take so long for the energy produced in the core of the Sun to make its way out of the Sun?
a) The convective cells in the convective layer move very slowly, transporting the energy very slowly.
b) The speed of light is very low in the interior of the Sun because of the strong gravity.
c) Photons do not travel very far without being absorbed, and when they are re-emitted, it is in a random direction.
d) Millions of small black holes throughout the Sun trap the energy.
e) The nuclear reactions in the core produce mostly radio waves, which travel very slowly.

c) Photons do not travel very far without being absorbed, and when they are re-emitted, it is in a random direction.

19. Star A has a magnitude of 1. If Star B has a brightness 100 times less than Star A (i.e., the brightness of Star B is 1/100 times that of Star A), what is the magnitude of Star B?
a) 2.
b) 3.
c) 6.
d) -4.
e) 0.

c) 6.

20. Which layer of the Sun is the thinnest, in kilometers?
a) The radiative zone.
b) The convective zone.
c) The corona.
d) The chromosphere.
e) The photosphere.

e) The photosphere.

## If the Sun got larger, but maintained its luminosity, would the Earth get hotter or colder? - Astronomy

hot incandescent sphere of gas, held together by its own gravitation gravitation,
the attractive force existing between any two particles of matter. The Law of Universal Gravitation

Since the gravitational force is experienced by all matter in the universe, from the largest galaxies down to the smallest particles, it is often called
. Click the link for more information. , and emitting light and other forms of electromagnetic radiation electromagnetic radiation,
energy radiated in the form of a wave as a result of the motion of electric charges. A moving charge gives rise to a magnetic field, and if the motion is changing (accelerated), then the magnetic field varies and in turn produces an electric field.
. Click the link for more information. whose ultimate source is nuclear energy nuclear energy,
the energy stored in the nucleus of an atom and released through fission, fusion, or radioactivity. In these processes a small amount of mass is converted to energy according to the relationship E = mc 2 , where E is energy, m
. Click the link for more information. .

### Properties of Stars

Stars differ widely in mass mass,
in physics, the quantity of matter in a body regardless of its volume or of any forces acting on it. The term should not be confused with weight, which is the measure of the force of gravity (see gravitation) acting on a body.
. Click the link for more information. , size, temperature temperature,
measure of the relative warmth or coolness of an object. Temperature is measured by means of a thermometer or other instrument having a scale calibrated in units called degrees. The size of a degree depends on the particular temperature scale being used.
. Click the link for more information. , and total energy output, or luminosity luminosity,
in astronomy, the rate at which energy of all types is radiated by an object in all directions. A star's luminosity depends on its size and its temperature, varying as the square of the radius and the fourth power of the absolute surface temperature.
. Click the link for more information. . The sun sun,
intensely hot, self-luminous body of gases at the center of the solar system. Its gravitational attraction maintains the planets, comets, and other bodies of the solar system in their orbits.
. Click the link for more information. has a mass of about 2 × 10 33 grams, a radius of about 7 × 10 10 cm, a surface temperature of about 6,000°C, and a luminosity of about 4 × 10 33 erg/sec. More than 90% of all stars have masses between one tenth and 50 times that of the sun the majority are relatively dim dwarf stars. Roughly three quarters of all the Milky Way's stars are believed to be red dwarfs. Other stellar quantities vary over a much larger range. The most luminous stars (excluding supernovas supernova,
a massive star in the latter stages of stellar evolution that suddenly contracts and then explodes, increasing its energy output as much as a billionfold. Supernovas are the principal distributors of heavy elements throughout the universe all elements heavier than
. Click the link for more information. ) are about ten million times more powerful than the sun, while the least luminous are only one hundredth as powerful. Red giants red giant,
star that is relatively cool but very luminous because of its great size. All normal stars are expected to pass eventually through a red-giant phase as a consequence of stellar evolution.
. Click the link for more information. , the largest stars, are fifteen-hundred times greater in size than the sun if one were placed at the sun's position, it would stretch to halfway between Jupiter and Saturn. At the opposite extreme, white dwarfs white dwarf,
in astronomy, a type of star that is abnormally faint for its white-hot temperature (see mass-luminosity relation). Typically, a white dwarf star has the mass of the sun and the radius of the earth but does not emit enough light or other radiation to be easily
. Click the link for more information. are no larger than the earth, and neutron stars neutron star,
extremely small, extremely dense star, with as much as double the sun's mass but only a few miles in radius, in the final stage of stellar evolution. Astronomers Baade and Zwicky predicted the existence of neutron stars in 1933.
. Click the link for more information. are only a few kilometers in radius.

The visible stars are divided into six classes according to apparent brightness the brightest are first magnitude magnitude,
in astronomy, measure of the brightness of a star or other celestial object. The stars cataloged by Ptolemy (2d cent. A.D.), all visible with the unaided eye, were ranked on a brightness scale such that the brightest stars were of 1st magnitude and the dimmest stars
. Click the link for more information. and the faintest are sixth magnitude. The stars differ in apparent brightness both because they lie at different distances from us and because they vary in actual or intrinsic brightness. Variable stars variable star,
star that varies, either periodically or irregularly, in the intensity of the light it emits. Other physical changes are usually correlated with the fluctuations in brightness, such as pulsations in size, ejection of matter, and changes in spectral type, color, or
. Click the link for more information. do not shine steadily but fluctuate in either a regular or irregular fashion. The supernova, or exploding star, is the most spectacular variable star the eclipsing binary, where the two stars alternately hide and then reinforce each other's light, is not a true variable.

Light received from a star consists of a spectrum spectrum,
arrangement or display of light or other form of radiation separated according to wavelength, frequency, energy, or some other property. Beams of charged particles can be separated into a spectrum according to mass in a mass spectrometer (see mass spectrograph).
. Click the link for more information. of wavelengths the hotter the star, the shorter the wavelength at which the light is most intense. The color of a star is closely related to its surface temperature. Red stars have surface temperatures around 3,000°C and blue-white stars have surface temperatures above 20,000°C (see spectral class spectral class,
in astronomy, a classification of the stars by their spectrum and luminosity. In 1885, E. C. Pickering began the first extensive attempt to classify the stars spectroscopically.
. Click the link for more information. ).

### Stellar Structure and Stellar Evolution

The theory of stellar structure stellar structure,
physical properties of a star and the processes taking place within it. Except for that of the sun, astronomers must draw their conclusions regarding stellar structure on the basis of light and other radiation from stars that are light-years away this light
. Click the link for more information. applies the laws of physics to calculation of the equilibrium configurations of stars. According to this theory, the mass and chemical composition of a star determine all its other characteristics. Because most stars are more than 90% hydrogen, variations in chemical composition are small and have a small effect. Variation in mass is the main factor a doubling in mass increases the luminosity more than 10 times. For a star to be stable, the compressive force of gravitation must be exactly balanced by the tendency of the gas to expand. Thus, the size and temperature of a star are important, interrelated factors.

Despite the tremendous pressure generated by the massive layers above it, the central region, or core, of a star remains gaseous. This is possible because the core has a temperature of millions of degrees. At this temperature, nuclear energy is released by the fusion of hydrogen to form helium the principle is the same as that of the hydrogen bomb. By the time nuclear energy reaches the surface of the star, it has been largely converted into visible light with a spectrum characteristic of a very hot body (see blackbody blackbody,
in physics, an ideal black substance that absorbs all and reflects none of the radiant energy falling on it. Lampblack, or powdered carbon, which reflects less than 2% of the radiation falling on it, crudely approximates an ideal blackbody a material consisting of a
. Click the link for more information. ). The theory of stellar evolution stellar evolution,
life history of a star, beginning with its condensation out of the interstellar gas (see interstellar matter) and ending, sometimes catastrophically, when the star has exhausted its nuclear fuel or can no longer adjust itself to a stable configuration.
. Click the link for more information. states that a star must change as it consumes its hydrogen in the nuclear reactions that power it. Ultimately each star must die, rarely in a supernova explosion, when its capability for nuclear reactions is exhausted. The heavy atoms created in supernovas (see nucleosynthesis nucleosynthesis
or nucleogenesis,
in astronomy, production of all the chemical elements from the simplest element, hydrogen, by thermonuclear reactions within stars, supernovas, and in the big bang at the beginning of the universe (see nucleus nuclear energy).
. Click the link for more information. ) are spewed out to become part of the interstellar matter from which new stars are continuously formed.

### Location and Motion of Stars

The universe contains billions of galaxies, and each galaxy galaxy,
large aggregation of stars, gas, dust, and usually dark matter, typically containing billions of stars. Recognition that galaxies are independent star systems outside the Milky Way came from a study of the Andromeda Galaxy (1926󈞉) by Edwin P.
. Click the link for more information. contains billions of stars. The stars visible to the unaided eye are all in our own galaxy, the Milky Way Milky Way,
the galaxy of which the sun and solar system are a part, seen as a broad band of light arching across the night sky from horizon to horizon if not blocked by the horizon, it would be seen as a circle around the entire sky.
. Click the link for more information. . Stars are not spread uniformly through a galaxy. They are frequently bunched together in star clusters star cluster,
a group of stars near each other in space and resembling each other in certain characteristics that suggest a common origin for the group. Stars in the same cluster move at the same rate and in the same direction.
. Click the link for more information. of as many as 100,000 stars. Many stars that appear as single points of light in even the most powerful telescopes are actually systems of two or more stars orbiting one another or a common center of gravity, bound together by their mutual gravitational attraction the binary stars binary star
or binary system,
pair of stars that are held together by their mutual gravitational attraction and revolve about their common center of mass. In 1650 Riccioli made the first binary system discovery, that of the middle star in the Big Dipper's handle, Zeta
. Click the link for more information. are most common among these multiple star systems.

In ancient times, the stars were believed to be motionless their fixed patterns in the sky were designated as the constellations constellation,
in common usage, group of stars that appear to form a configuration in the sky properly speaking, a constellation is a definite region of the sky in which the configuration of stars is contained.
. Click the link for more information. . It is now known that the stars move through space, although their motion is too small to be detected during a human lifetime without exacting measurements. From the observed proper motion proper motion,
in astronomy, apparent movement of a star on the celestial sphere, usually measured as seconds of arc per year it is due both to the actual relative motions of the sun and the star through space. Proper motion reflects only transverse motion, i.e.
. Click the link for more information. (change in apparent position on the celestial sphere celestial sphere,
imaginary sphere of infinite radius with the earth at its center. It is used for describing the positions and motions of stars and other objects. For these purposes, any astronomical object can be thought of as being located at the point where the line of sight
. Click the link for more information. ), distance of the star from the earth, and radial velocity radial velocity,
in astronomy, the speed with which a star moves toward or away from the sun. It is determined from the red or blue shift in the star's spectrum.
. Click the link for more information. (motion along the line of sight), the true velocity of a star through space can be determined. See also brown dwarf brown dwarf,
in astronomy, celestial body that is larger than a planet but does not have sufficient mass to convert hydrogen into helium via nuclear fusion as stars do. Also called "failed stars," brown dwarfs form in the same way as true stars (by the contraction of a swirling
. Click the link for more information. .

### Bibliography

See C. de Jager, The Brightest Stars (1980) G. O. Abell, Exploration of the Universe (5th ed. 1987) R. J. Taylor, The Stars: Their Structure and Evolution (1994) A. C. Phillips, The Physics of Stars (1994).

Although there is only a relatively narrow range in normal stellar masses, it is the mass of a star that determines its other properties – luminosity, temperature, size – and the way in which it evolves. These quantities are related to the mass by the equations of stellar structure. Other stellar parameters show a far greater range than stellar mass: for example, the luminosity of a star is proportional to roughly the fourth power of its mass for a solar-type star, and the cube power of its mass for a massive star (see mass-luminosity relation) stars therefore show a range in luminosity of some 10 10 . A star's lifetime also depends on its mass: low-mass stars live considerably longer than high-mass ones.

All stars are composed predominantly of hydrogen and helium this was first proposed in 1925 by Cecilia Payne-Gaposchkin and confirmed in 1929 by H.N. Russell. The proportions of the chemical elements in the Sun are not significantly different from those in most other stars. This general composition by mass is 70% hydrogen, 28% helium, with the remaining elements – known in astronomy as metals or heavy elements – making up just 2% by numbers of atoms it is 90.8% hydrogen, 9.1% helium, 0.1% metals.

The characteristics of a star can be determined only when its distance is known. The method of distance determination depends on the distance itself: the shortest distances are found directly by measuring a star's annual parallax greater distances require indirect methods. The nearest star, Proxima Centauri, is 1.3 parsecs away. The stars in our immediate locality are found in the main to be young stars occupying the outer parts of the disk of our Galaxy, rotating around the galactic center. Many still remain in open clusters, and over 50% of all the stars we observe are binary stars or multiple stars.

A star is a self-luminous celestial body. Although not usually thought of in these terms, the Sun is also a star. Self-luminosity distinguishes stars from planets, which shine by virtue of reflected light. The ancients did not make this distinction but instead referred to the planets as wandering (the etymological meaning of the word planet) stars, and to the stars proper as fixed stars.

a self-luminous celestial body that consists of incandescent gases and is similar in nature to the sun. The sun seems incomparably larger than the stars only because of its proximity to the earth: light travels from the sun to the earth in 8⅓ min, while from the nearest star, &alpha Centauri, in four years and three months. Owing to their great distances from the earth, stars are visible as points not as disks, even in telescopes (in contrast to planets). About 5,000 stars are visible to the naked eye in both celestial hemispheres on a moonless night. Billions of stars are visible in powerful telescopes.

General information. Short history of the study of stars. The study of the stars grew out of efforts to meet specific needs of society (necessity for orientation during voyages, establishment of calendars, determination of exact time). As far back as remote antiquity the stellar sky had been divided into constellations. For a long time the stars were considered as fixed points in relation to which the motions of planets and comets were observed. From the time of Aristotle (fourth century B.C.) it was believed for many centuries that the stellar sky was an eternal and immutable crystal sphere, beyond the boundaries of which was the abode of the gods. At the end of the 16th century the Italian astronomer Giordano Bruno taught that the stars were distant bodies similar to our sun. The first variable star was discovered in 1596 (by the German astronomer D. Fabricius) and the first double star, in 1650 (by the Italian scientist G. Riccioli). In 1718 the English astronomer E. Halley discovered the proper motions of three stars. In the second half of the 18th century the Russian scientist M. V. Lomonosov, the German scientist I. Kant, and the British astronomers T. Wright and W. Herschel, among others, expressed correct ideas concerning the stellar system to which the sun belongs. Between 1835 and 1839 the Russian astronomer V. la. Struve, the German astronomer F. Bessel, and the British astronomer T. Henderson determined for the first time the distances to three nearby stars. In the 1860&rsquos the spectroscope was used for the study of the stars, and photographs began to be used in the 1880&rsquos. In 1900 the Russian astronomer A. A. Belopol&rsquoskii experimentally demonstrated the validity of Doppler&rsquos principle for optical phenomena, on the basis of which it is possible to determine the velocity of a celestial object along the line of sight according to the shift in the lines of its spectrum. The accumulation of observations and the development of physics have broadened our knowledge of stars.

In the early 20th century, particularly after 1920, revolutionary ideas emerged in science about the stars. Stars began to be viewed as physical bodies their structure, the equilibrium conditions of their constituents, and their sources of energy began to be studied. The emergence of these ideas was connected with the successes of atomic physics, which led to a quantitative theory of stellar spectra, and with the achievements of nuclear physics, which made possible analogous calculations of the energy sources and of the internal structures of stars (the most important results were obtained by the German scientists R. Emden, K. Schwarzschild, and H. Bethe the British scientists A. Eddington, E. A. Milne, and J. Jeans the American scientists H. Russell and R. F. Christy and the Soviet scientist S. A. Zhevakin). In the mid-20th century the study of stars acquired still greater depth with the expansion of observational resources and the use of computers (the American scientists M. Schwarzschild and A. Sandage, the British scientist F. Hoyle, the Japanese scientist C. Hayashi). Great success was also achieved in studies of the transport of energy in stellar photospheres (the Soviet scientists E. R. Mustel&rsquo and V. V. Sobolev and the American scientist S. Chandrasekhar) and in investigations of the structure and dynamics of stellar systems (the Dutch scientist J. Oort, the Soviet scientists P. P. Parenago and B. V. Kukarkin).

Stellar parameters. The fundamental characteristics of a star are its mass, radius (excluding the outer transparent layers), and luminosity (total amount of radiated energy). These quantities are often expressed as fractions of the sun&rsquos mass, radius, and luminosity. The following parameters derived from the fundamental parameters are also used: the effective temperature the spectral class, which characterizes the degree of ionization and excitation of the atoms in the stellar atmosphere the absolute stellar magnitude (that is, the magnitude that the star would have at the standard distance of 10 parsecs) and the color index (the difference in magnitudes determined in two different spectral regions).

The stellar population is extremely diverse. Certain stars are millions of times larger (in volume) and brighter than the sun (giant stars). At the same time there are many stars that are significantly surpassed by the sun in size and the amount of energy they radiate (dwarfs) (see Figure 1). The luminosities of stars are also diverse. Thus, the luminosity of the star S Doradus is 400,000 times greater than that of the sun. Stars can be diffuse or extremely dense. The average density of a number of giants is hundreds of thousands of times less than the density of water, while the average density of the so-called white dwarfs is, on the contrary, hundreds of thousands of times greater. Stars vary less in mass.

The brightness of certain types of stars changes periodically such stars are called variable stars. Immense changes, accompanied by sudden increases in brightness, occur in novas. In these, a small star, a dwarf, increases for several days. A gaseous shell separates out. This shell continues to expand and, as it expands, dissipates in space. The star then contracts again to a small size. Still greater variations occur during the outbursts of supernovas.

The study of the spectra of stars permits the determination of the chemical composition of their atmospheres. Stars, like the sun, consist of the same chemical elements found on the earth. Hydrogen (about 70 percent by weight) and helium (about 25 percent) predominate in stars the remaining elements, among which the most abundant are oxygen, nitrogen, iron, carbon, and neon, are found in almost exactly the same ratios as on the earth. As yet, only the outer layers of stars are accessible to observation. However, the correlation of the data from direct observations with conclusions resulting from the general laws of physics have made it possible to construct a theory of the internal structure of stars and the sources of stellar energy.

From all indications, the sun is a typical star. There is every reason to believe that many stars have a planetary system like that of the sun. Because of their remoteness, it is still impossible to directly observe such satellites of the stars even with the most powerful telescopes. Subtle methods of investigation, accurate observations over dozens of years, and complex calculations are necessary for their detection. In 1938 the Swedish astronomer E. Holmberg began to suspect and later the Soviet astronomer A. N. Deich and others established the existence of invisible satellites belonging to the star 61 Cygni and other stars near the sun. Our planetary system is thus not an exceptional phenomenon. Life probably also exists on many planets circling other stars, and the earth does not represent an exception in this respect.

Stars are often located in pairs revolving around a common center of mass such stars are called binary stars. Triple stars and multiple stellar systems are also encountered.

The arrangement of the stars with respect to each other changes slowly with time because of their motion in the galaxy. Stars form huge stellar systems in space&mdashgalaxies. The Milky Way Galaxy (to which the sun belongs) is composed of more than 100 billion stars. The study of its structure shows that many stars are grouped into star clusters, stellar associations, and other formations.

There are two complementary approaches in the study of stars. Stellar astronomy, which views stars as objects characterized by certain properties, studies the motion of stars, their distribution in our galaxy and in clusters, and their different statistical regularities. The physical processes occurring in stars and their radiation, structure, and evolution are studied in astrophysics.

Stellar masses. Masses can be directly determined only for binary stars on the basis of the study of their orbits. For spectroscopic binaries, measuring the Doppler shift of the spectral lines makes it possible to determine the period of revolution of the components and the projection of the maximum velocity of each component on the line of sight. Similar measurements may be carried out for certain visual binaries. The data are sufficient for the calculation of the ratios of the masses of the components. The absolute values of the masses can be determined if the system is at the same time an eclipsing binary, that is, if its orbit is seen edgewise and the components alternately eclipse each other. The study of the masses of binary stars reveals the existence of a statistical relation between the masses and luminosities of main-sequence stars. This relation, which is also valid for single stars, permits an indirect estimate of the masses of stars by determining their luminosities.

Stellar luminosities and distances. The primary method of determining the distances to stars consists of measuring their apparent displacement against the background of more distant stars as the earth revolves around the sun. The distance itself is computed according to the displacement (parallax), whose magnitude is inversely proportional to the distance. However, this method of measurement is applicable only to the nearest stars.

If the distance to a star and its apparent magnitude m are known, the absolute magnitude M can be found from the formula

M = m + 5 &minus 5 log r

where r is the distance to the star expressed in parsecs. Having determined the average absolute magnitudes for stars of different spectral classes and having compared them with the apparent magnitudes of specific stars of these same classes, one may also determine the distances to remote stars, for which the parallactic displacements are imperceptible (so-called spectroscopic parallaxes). Absolute magnitudes of certain types of variable stars (for example, cepheids) can be determined from the period of their luminosity, and this also permits the determination of their distances.

Distances are also estimated from the systematic components of the radial velocities and proper motions of the stars caused by peculiarities of the rotation of the galaxy and the motion of the sun (together with the earth) in space and thus depending on the distance of the star. In order to eliminate the effects of the proper velocities of individual stars, distances to large groups of stars are determined at the same time (statistical or group parallaxes).

The brightest stars are given in Table 1 and the nearest stars, in Table 2.

Stellar temperatures and spectral classes. The distribution of energy in the spectra of incandescent bodies is not uniform. The maximum in radiation intensity falls at different wavelengths at different temperatures, and the color of the overall radiation changes. Investigation of these effects in stars, the study of the energy distribution in stellar spectra, and measurements of the color indexes allow the temperatures of stars to be determined. Stellar temperatures are also determined according to the relative intensities of certain lines in their spectra, permitting the spectral class of the stars to be ascertained. Spectral classes of stars depend on temperature and are designated by the letters O, B, A, F, G, K, and M in order of decreasing temperature. In addition, a secondary sequence of carbon stars C (formerly designated R and N) branches out from class G and a secondary branch S, from class K. The hotter stars&mdashnuclei of planetary nebulas (class P) and Wolf-Rayet stars with broad emission lines in the spectrum (class W)&mdashare separated from class O. If the mechanism of formation of spectral lines is known, then the temperature can be computed according to the spectral class if the acceleration of gravity on the star&rsquos surface is known. This is related to the average density of its photosphere and, consequently, to the dimensions of the star (the density may be evaluated from

Table 1. The brightest stars
NameApparent magnitude (system V)Spectral class and luminosity classProper motionParallaxRadial velocity (km/sec)Tangential velocity (km/sec)Absolute magnitude (system V)Luminosity (in units of solar luminosity)
&alpha Canis MajorisA1 V
A5
1.32"0.375"&minus817&minus1.4
+11.4
22.4
0.002
&alpha Carinae&minus0.75FO Ib&ndashII0.02"0.018"+205&minus4.44700
&alpha Bootis&minus0.05K2 IIIp2.28"0.090"&minus5120&minus0.3107
&alpha Lyrae+0.03AO V0.34"0.123"&minus1413+0.551
&alpha CentauriG2 V
K5
3.68"0.751"&minus2223+4.5
+5.9
1.3
0.34
&alpha Aurigae0.08G8 III0.44"0.073"+3029&minus0.6141
&beta Orionis0.13B8 Ia0.00"0.003"+240&minus7.581,000
&alpha Canis MinorisF5 IV-V
white dwarf
1.25"0.288"&minus320+2.6
+13.1
7.4
0.0004
&alpha Orionis0.42 varM2 lab0.03"0.005"+2128&minus6.122,400
&alpha Eridani047B5 IV0.10"0.032"+1915&minus2.0510
&beta Centauri0.59B1 II0.04"0.016"&minus1211&minus3.41,860
&alpha Aquilae0.76A7 IV-V0.66"0.198"&minus2616+2.39.8
&alpha CrucisB1 IV
B1
0.04"0.008"&minus624&minus4.7
4.2
6,200
3700
&alpha TauriK5 III
M2 V
0.20"0.048"+5420&minus0.7
+11.8
155
0.0015
&alpha ScorpiiM1 la
B4
0.03"0.019"&minus37&minus2.7
3.2
980
4.1
&alpha Virginis0.97 var.B1 V0.05"0.021"+111&minus2.4740
&beta Geminorum1.14KO III0.62"0.093"+332+1.032
&alpha Piscis Austrini1.16A3 V0.37"0.144"+612+2.013
&alpha Cygni1.25 var.A2 la0.00"0.003"&minus30&minus6.224,600
&alpha LeonisB7 V
K2
0.24"0.039"+329&minus0.7
+5.6
&minus11
155
0.45
0.003
Table 2. The nearest stars
NameApparent magnitudeSpectral class and luminosity classProper motionParallaxDistance (parsecs)Absolute magnitude (system V)
Proxima Centauri . 10.68M5e3.85"0.762&Prime1.31+ 15.1
&alpha Centauri A . 0.32G2V3.79&Prime0.751&Prime1.33+ 4.76
&alpha Centauri B . 1.72K5 V + 6.16
Barnard&rsquos Star . 9.54M5 V10.30&Prime0.545&Prime1.83+ 13.22
Wolf 359 . 13.66dM6e4.84&Prime0.427&Prime2.34+ 16.62
BD+36°2147 . 7.47M2V4.78&Prime0.396&Prime2.52+ 10.46
Sirius A . -1.47A1 V1.32&Prime0.375&Prime2.66+ 1.42
Sirius B . 8.67A5 + 11.55
. Luyten 726&rsquo8 (UV Ceti)dM6e
dM6e
3.36&Prime0.371&Prime2.69+ 15.3
+15.8
Ross 154 . 10.6dM4e0.67&Prime0.340&Prime2.93+ 13.3
Ross 248 . 12.24dM6e1.58&Prime0.316&Prime3.16+ 14.74
∊ Eridani . 3.73K2 V0.97&Prime0.303&Prime3.30+ 6.14
Ross 128 . 11.13dM51.40&Prime0.298&Prime3.34+ 13.50
Luyten 789&ndash6 . 12.58dM6e3.27&Prime0.298&Prime3.34+ 14.9
BD Cygni A . 5.19K5 V5.22&Prime0.292&Prime3.42+ 7.52
BD Cygni B . 6.02K7 V + 8.35
Procyon A . 0.34F5 IV-V1.25&Prime0.288&Prime3.48+ 2.67
Procyon B . 10.7dF + 13.1
∊ lndi . 4.73K5 V4.67&Prime0.285&Prime3.50+ 7.0
BD+59°1915 A . 8.90dM42.29&Prime0.278&Prime3.58+ 11.12
BD+59°1915 B . 9.69dM5 + 11.91
BD+ 43°44 A . 8.07M1 V2.91&Prime0.278&Prime3.58+ 10.29
BD+43°44 B . 11.04M6 V + 13.26
&tau Ceti . 3.50G8 Vp1.92&Prime0.275&Prime3.62+ 5.70
CD-f36°15693 . 7.39M2V6.87&Prime0.273&Prime3.65+9.57
BD+5°1668 . 9.82dM43.73&Prime0.266&Prime3.75+ 11.95
CD-39°4192 . 6.72MO I3.46&Prime0.255&Prime3.90+ 8.75
Kapteyn&rsquos Star . 8.8sdMO8.79&Prime0.251&Prime3.99+ 10.8

the details of the spectra). The dependence of the spectral class or color index on the effective temperature is called the effective temperature scale. If the temperature is known, then theoretically it is possible to ascertain which portion of a star&rsquos radiation is in the invisible regions of the spectrum&mdash ultraviolet and infrared. The absolute stellar magnitude and the correction allowing for radiation in the ultraviolet and infrared regions of the spectrum (the bolometric correction) allow the determination of the total luminosity of a star.

Stellar radii. If the effective temperature Tef and the luminosity L are known, the radius R of a star can be computed from the formula

based on the Stefan-Boltzmann law of radiation (&sigma is Stefan&rsquos constant). The radii of stars with large angular dimensions may be measured directly with the aid of stellar interferometers. In eclipsing binaries it is possible to compute the values of the maximum diameters of the components expressed as fractions of the semimajor axis of their relative orbit.

Stellar rotation. The rotation of stars is studied by means of their spectra. During rotation, one edge of the star&rsquos disk is receding from us and the other is approaching us at the same velocity. As a result, the lines are broadened in the star&rsquos spectrum, which is simultaneously received from the whole disk, and, according to Dopplefs principle, acquire a characteristic shape from which it is possible to determine the speed of rotation. Stars of the early spectral classes O, B, and A rotate with velocities (on the equator) of at least 100&ndash200 km/sec. The rotational velocities of cooler stars are significantly less (several km/sec). The decrease in the rotational velocity of a star is evidently connected with the transition of part of its angular momentum into the gas and dust disk surrounding it under the action of magnetic forces. Because of rapid rotation, the star assumes the form of an oblate spheroid. Radiation from stellar interiors escapes to the poles sooner than to the equator, as a result of which the temperature at the poles is higher. Therefore, a meridional flow from the poles to the equator arises on the star&rsquos surface, and this flow circuit is completed in the deep layers of the star. This movement plays an e.ssential role in the mixing of material in layers where there is no convection.

Relations between stellar parameters. Stellar masses range from 0.04 to 100 solar masses, luminosities from 5 x 10 &minus4 to 105 solar luminosities, and radii from 2 x 10 &minus1 to 103 solar radii. These parameters have specific interrelations. The most important of these are visualized in spectrum-luminosity (Hertzsprung-Russell) or effective temperature-luminosity diagrams. Almost all stars are situated on such diagrams along several branches, schematically depicted in Figure 2 and corresponding to different sequences or luminosity classes. The majority of stars are located on the main sequence (luminosity class V). Class O stars with temperatures of 30,000°-50,000°K form its left end, and class M red dwarfs with temperatures of 3000°-4000°K form its right end. On the diagram the sequence of giants (class III) can be seen, to which stars of high luminosity belong (that is, those with large radii). Sequences of still brighter la, Ib, and II supergiants are situated higher. (The fact that a star is a dwarf, giant, or supergiant was formerly denoted by the letters d, g, and s before the spectral class.) At the bottom of the diagram are situated white dwarfs (VII) whose sizes are comparable to the size of the earth at a density on the order of 10(i g/cm3. In addition to these fundamental sequences, subgiants (IV) and subdwarfs (VI) are also plotted.

The Hertzsprung-Russell diagram has found its explanation in the theory of the internal structure of stars.

Internal structure of stars. Inasmuch as the interiors of stars cannot be observed directly, the internal structure of stars is studied by means of constructing theoretical stellar models, which are assigned values of masses, radii, and luminosities observable in real stars. The theory of the internal structure of ordinary stars is based on the model of a star as a gaseous sphere that is in mechanical and thermal equilibrium and neither expands nor contracts over a prolonged period. Mechanical equilibrium is maintained by the forces of gravity, directed toward the center of the star, and by gas pressure in the star&rsquos interior acting outward and balancing the force of gravity. The pressure increases with depth, and both the density and temperature increase with it. Thermal equilibrium consists in the fact that the temperature of the star&mdashin every elementary volume&mdashpractically does not change with time, that is, the energy leaving each such volume is compensated both by the energy entering it and by the energy generated there by nuclear or other sources.

The temperature of ordinary stars varies from several thousand degrees on the surface to more than 10 million degrees in the center. At these temperatures, matter consists of almost completely ionized atoms, owing to which it becomes possible to use the equations of state of an ideal gas in the calculations of stellar models. Of great significance in the investigations of the internal stellar structure are hypotheses on energy sources, chemical composition of the stars, and the mechanism of energy transport.

The basic mechanism of energy transport in a star is radiative heat transfer. In this case, the diffusion of heat from the hotter internal regions of the star outward occurs by means of quanta of ultraviolet radiation emitted by the hot gas. These quanta are absorbed in other parts of the star and reemitted in passing into the outer, cooler layers, the frequency of the radiation decreases. The diffusion rate is determined by the mean free path of a quantum and thus depends on the transparency of the stellar material, which in turn is characterized by its absorption coefficient. The fundamental absorption mechanisms in stars are photoelectric absorption and scattering by free electrons.

Radiative heat transfer is the basic form of energy transport for most stars. However, in certain regions of a star and over almost the entire volume of a star of small mass, an important role is played by convection, that is, the transport of heat by gas masses rising and descending under the influence of temperature differences. Convection, if it is active, is a much more effective mode of heat transport than radiative heat transfer, but convection arises only where hydrogen or helium are partially ionized: in this case, the energy of their recombination sustains the motion of the gas masses. The convection zone in the sun occupies a layer extending from the surface to a depth equal to about one-tenth of its radius below this layer, hydrogen and helium are already completely ionized. In cool stars complete ionization occurs at greater depths, so that the convection zone in them is thicker and encompasses the greater part of the volume. In contrast, the hydrogen and helium in hot stars are completely ionized beginning almost at the surface itself, and therefore these stars do not have outer convection zones. However, they have a convection core, where the movement is sustained by the heat generated by the nuclear reactions.

Giant and supergiant stars are structured differently from main-sequence stars. Their small dense core (1 percent of the radius) contains 20&ndash30 percent of the mass, and the remaining portion is a rarefied shell that extends out to distances of tens or hundreds of solar radii. Temperatures in the core reach 100 million degrees and more. White dwarfs are essentially just the cores of giants, but without a shell and cooled to 8,000°-10,000°K. The dense gas of cores and of white dwarfs has special properties that differ from the properties of an ideal gas. Energy in it is transported not by radiation but by electron heat conduction, as in metals. The pressure of such a gas does not depend on temperature but only on density. Therefore, equilibrium is preserved even during the cooling of a star having no energy sources.

The chemical composition of matter in the interiors of stars at early stages in their evolution is similar to the chemical composition of stellar atmospheres as determined from spectroscopic observations (diffusion separation can occur only over a period exceeding the lifetime of the star). In the course of time, nuclear reactions change the chemical composition of stellar interiors, and the internal structure of the star changes.

Stellar energy sources and the evolution of stars. The primary energy source of stars is thermonuclear reactions, in which heavier nuclei are formed from light nuclei most often this is the transformation of hydrogen into helium. In stars of less than two solar masses it occurs chiefly by means of the fusion of two protons into a deuterium nucleus (the excess charge is carried away by a resulting positron). This is followed by the transformation of the deuterium into the isotope He 3 by means of proton capture and, finally, the transformation of two He 3 nuclei into a He 4 and two protons. In more massive stars the carbon-nitrogen cycle predominates: carbon captures four protons in succession, emitting two positrons in the process, transforms at first into nitrogen, and then decays into helium and carbon. The final result of both reactions is the synthesis of a helium nucleus out of four hydrogen nuclei with the release of energy. The nitrogen and carbon nuclei in the carbon-nitrogen reaction act as a catalyst. In order for the nuclei to approach to a distance where capture can occur, it is necessary to overcome the electrostatic repulsion therefore, the reactions can occur only at temperatures exceeding 10 70 K. These temperatures exist in the very central portions of stars. In stars of small mass, where the temperatures at the center are insufficient for thermonuclear reactions, the gravitational contraction of the star serves as a source of energy.

If the process of heat transfer and emission is known, it is possible to solve the system of equations of mechanical and thermal equilibrium and calculate out the internal structure of a star of given mass. In addition, the radius and luminosity of the star, which are functions of the mass, are also computed. The theoretical relations thus obtained can be compared to mass-luminosity and mass-radius diagrams, which are compiled from observations of stars. For main-sequence stars, the results of observations agree with theory. Stars of other sequences do not satisfy the theoretical relations. The reason for the appearance of other sequences consists in the change in the chemical composition of the interiors of stars in the process of evolution. The transformation of hydrogen into helium increases the molecular weight of the gas, resulting in core contraction and temperature increase with the gas of normal composition next to the core expanding. The star becomes a giant, while on the Hertzsprung-Russell diagram it moves along one of the lines called evolutionary tracks. Sometimes the tracks have a complex shape moving along them, stars cross several times from one end of the diagram to the other and back. After the expansion and diffusion of the shell, the star becomes a white dwarf.

In massive stars the core at the end of evolution is unstable, and its radius decreases to approximately 10 km, where-upon the star turns into a neutron star, which consists of neutrons and not of nuclei and electrons like ordinary stars. Neutron stars have an intense magnetic field and rotate rapidly. This leads to observable bursts of radio emission, and sometimes to bursts of both optical radiation and X-radiation. Such objects are called pulsars. In still greater masses, collapse occurs&mdashthe unrestricted fall of matter toward the center with a velocity close to that of light, Part of the gravitational energy of contraction ejects a shell at a rate of up to 7,000 km/sec. During this process the star transforms into a supernova, its radiation increases to several billion times the luminosity of the sun, and then it dies gradually in the course of several months.

Binary stars. Many stars are part of binary or multiple stellar systems. If the components of binary stars are situated sufficiently far from each other, they are visible separately. These are the so-called visual binaries. Sometimes one component, the fainter one, is not visible, and the binary nature is revealed by the nonlinear motion of the brighter star. Binary stars, however, are most often recognized by the periodic splitting of their spectral lines (spectroscopic binaries) or by characteristic changes in brightness (eclipsing binaries). Many binary stars form close pairs. Mutual tidal attractions exert a substantial influence on the evolution of the components of such stars. If one of the components of a binary star expands in the process of evolution, then under certain conditions an outflow of gas begins from the point of its surface facing the other component. The gas forms streamers around the second component and partially falls into it. As a result, the first component can lose a large part of its mass and turn into a subgiant or even a white dwarf. But the second component gains part of the lost mass, and its luminosity increases correspondingly. Since this mass can include gas not only from the atmosphere but also from the deep layers near the core of the first component, anomalies in chemical composition can be observed in binary stars. However, these anomalies concern only light elements, since heavy elements do not form in giants. The heavy elements appear during the outbursts of supernovas, when many neutrons are emitted that are captured by the nuclei of atoms and increase their weight.

Peculiar and magnetic stars. Anomalies of chemical composition, which vary from place to place on the surface of a star, are often observed in so-called magnetic stars. These stars, whose spectral class is close to AO, have magnetic fields of very high intensity (up to 10,000 gauss and greater) on their surfaces. The intensity of the fields changes periodically with a mean period of from four to nine days, and the sign of the intensity also often changes. The character of the spectrum usually changes with the same period, as if the chemical composition of the star were changing. Such changes can be explained by the rotation of a star having two or more magnetic poles that do not coincide with the rotational poles. The changes in chemical composition in this case occur because more of certain elements are concentrated at the magnetic poles and more of others at the magnetic equator. In various peculiar (special) stars, characterized by the most significant peculiarities in chemical composition, the anomalies can be different a large excess of individual elements like Si, Mg, Cr, Eu, and Mn is observed and a deficiency of He. The appearance of these anomalies is evidently caused by the suppression of convection by an intense magnetic field. In the absence of mixing, a slow diffusion of the elements under the influence of gravity and radiation pressure occurs. Certain elements sink and other elements rise, as a result of which a deficiency of the former and an excess of the latter are observed on the surface. A magnetic star rotates more slowly than an ordinary star of the same class. This is the result of the magnetic field retarding the rotation of the contracting condensate of matter out of which the star subsequently was formed.

In addition to ordinary peculiar stars there are the so-called stars with metallic lines of late spectral subclasses of A. They have a weaker magnetic field, and the anomalies in chemical composition are not as great. The nature of such stars has not yet been studied.

Certain types of anomalies, for example, an abundance of Li, are connected with the breakup of heavier nuclei by cosmic rays that are formed in the same star as a result of electromagnetic phenomena similar to chromospheric flares. These anomalies are observed, for example, in still-contracting T Tauri stars with strong convection.

Anomalies of another kind, which are observable, for example, in giants of spectral class S, are caused by the linking of a deep surface convection zone with the central convection zone, which is brought about by the intensification of nuclear reactions at a specific stage in the star&rsquos evolution. As a result, the material of the entire star is mixed, and elements synthesized in its central regions are carried outward.

Variable stars. The brightness of many stars is not constant and varies in accordance with one law or another these stars are called variable stars. Stars in which the changes in brightness are connected with physical processes occurring in them are physical variables (as distinguished from optical variables, which include eclipsing binaries). Periodic and semiperiodic variability is usually associated with the pulsations of stars, and sometimes with large-scale convection. Generally speaking, stars, as systems in stable equilibrium, are characterized by pulsations with their distinctive periods. Oscillations can arise in the process of rearrangement in a star&rsquos structure, which is connected with evolutionary changes. However, to prevent damping, mechanisms must exist that sustain or intensify them: during the period of maximum contraction of the star, it needs to receive the thermal energy that would escape outward during the period of expansion. In agreement with modern theories, the pulsations of many types of variables (cepheids, RR Lyrae type variables) are explained by an increase in the absorption coefficient during the star&rsquos contraction this inhibits the total flux of radiation, and the gas receives additional energy. During expansion, the absorption decreases and the energy escapes outward. The inhomogeneous structure of a star&mdashthe presence of several layers with different properties&mdashdistorts the normal pattern and produces deviations from a truly sinusoidal behavior of the star&rsquos parameters. A fundamental standing wave is often located in the depths of the star, and it generates traveling waves that emerge at the surface and affect the phases of the variations in brightness, velocity, and other parameters.

Certain types of variable stars undergo outbursts during which the brightness increases by 10&ndash15 magnitudes (so-called novas), by 7&ndash8 magnitudes (recurrent novas), or by 3&ndash4 magnitudes (novalike stars). Such outbursts are associated with a sudden expansion of the photosphere with great velocities (up to 1,000&ndash2,000 km/sec in novas) that leads to ejection of the shell with a mass of about 10

4 solar masses. After the outburst the brightness begins to decrease with a characteristic time of 50&ndash100 days. During this time the escape of gases from the surface continues with a velocity of several thousand km/sec. All these stars prove to be close binaries, and their outbursts are undoubtedly related to the interaction of the components of the system, one or both of which are usually hot dwarfs. The intense magnetic field of the stars apparently influences the structure of the shells ejected by novas. The rapid irregular variability of T Tauri, UV Ceti, and other types of young contracting stars is linked to powerful convection movements in these stars, which carry hot gas to the surface. The previously mentioned supernovas may also belong to the class of variable stars. The Milky Way Galaxy numbers more than 30,000 variable stars.

Work on the study of stars is being conducted in the USSR at the Crimean Astrophysical Observatory of the Academy of Sciences of the USSR, at the Central Astronomical Observatory of the Academy of Sciences of the USSR, at the P. K. Shternberg State Astronomical Institute, at the Astronomical Council of the Academy of Sciences of the USSR, and at other astronomical institutions. Reports on these studies are published in the journals Astronomicheskii Zhurnal and Astrofizika and in publication of the observatories. Abroad, investigations of stars are conducted in the USA, Great Britain, Australia, and many other countries. The principal journal in the foreign literature is Astrophysical Journal (USA), and there are a number of other important publications in the USA, Great Britain, and other countries.

"Over the past few hundred years, there has been a steady increase in the numbers of sunspots, at the time when the Earth has been getting warmer. The data suggests solar activity is influencing the global climate causing the world to get warmer." (BBC)

Over the last 35 years the sun has shown a cooling trend. However global temperatures continue to increase. If the sun's energy is decreasing while the Earth is warming, then the sun can't be the main control of the temperature.

Figure 1 shows the trend in global temperature compared to changes in the amount of solar energy that hits the Earth. The sun's energy fluctuates on a cycle that's about 11 years long. The energy changes by about 0.1% on each cycle. If the Earth's temperature was controlled mainly by the sun, then it should have cooled between 2000 and 2008.

Figure 1: Annual global temperature change (thin light red) with 11 year moving average of temperature (thick dark red). Temperature from NASA GISS . Annual Total Solar Irradiance (thin light blue) with 11 year moving average of TSI (thick dark blue). TSI from 1880 to 1978 from Krivova et al 2007. TSI from 1979 to 2015 from the World Radiation Center (see their PMOD index page for data updates). Plots of the most recent solar irradiance can be found at the Laboratory for Atmospheric and Space Physics LISIRD site.

The solar fluctuations since 1870 have contributed a maximum of 0.1 °C to temperature changes. In recent times the biggest solar fluctuation happened around 1960. But the fastest global warming started in 1980.

Figure 2 shows how much different factors have contributed recent warming. It compares the contributions from the sun, volcanoes, El Niño and greenhouse gases. The sun adds 0.02 to 0.1 °C. Volcanoes cool the Earth by 0.1-0.2 °C. Natural variability (like El Niño) heats or cools by about 0.1-0.2 °C. Greenhouse gases have heated the climate by over 0.8 °C.

Figure 2 Global surface temperature anomalies from 1870 to 2010, and the natural (solar, volcanic, and internal) and anthropogenic factors that influence them. (a) Global surface temperature record (1870&ndash2010) relative to the average global surface temperature for 1961&ndash1990 (black line). A model of global surface temperature change (a: red line) produced using the sum of the impacts on temperature of natural (b, c, d) and anthropogenic factors (e). (b) Estimated temperature response to solar forcing. (c) Estimated temperature response to volcanic eruptions. (d) Estimated temperature variability due to internal variability, here related to the El Niño-Southern Oscillation. (e) Estimated temperature response to anthropogenic forcing, consisting of a warming component from greenhouse gases, and a cooling component from most aerosols. (IPCC AR5, Chap 5)

Some people try to blame the sun for the current rise in temperatures by cherry picking the data. They only show data from periods when sun and climate data track together. They draw a false conclusion by ignoring the last few decades when the data shows the opposite result.

## If the Sun got larger, but maintained its luminosity, would the Earth get hotter or colder? - Astronomy

Write your name at the top of this quiz as well as on your answer sheet. WRITE YOUR VERSION ON YOUR ANSWER SHEET. Feel free to write or draw on the quiz.

Please put away all electronic devices. You will not need a calculator for this quiz.

SELECT THE BEST ANSWER TO EACH PROBLEM.

1. Which layer of the Sun is the thinnest, in kilometers?
a) The radiative zone.
b) The convective zone.
c) The corona.
d) The chromosphere.
e) The photosphere.

e) The photosphere.

2. By accurately measuring the positions of stars in the sky over and over again, Astronomers can sometimes determine which property of some stars?
a) distance.
b) velocity through space in the plane of the sky.
c) whether the star is part of a binary star.
d) all of the above.
e) none of the above.

d) all of the above.

3. Which of the following is a white dwarf?
a) Proxima Cen.
b) alpha Cen B.
c) the Sun.
d) Sirius B.
e) All of the above.

d) Sirius B.

4. Which of the following stars has the coldest photosphere?
a) Pollux (type K0III)
b) Arctaurus (type K2III)
c) 42 Draco (between type K1III and type K2III)
d) Formalhaut (type A3V).
e) Aldebaran (type K5III)

e) Aldebaran (type K5III)

5. What is Ejnar Hertzsprung known for?
a) Pioneering the use of plots of luminosity vs. temperature for stars.
b) Re-organizing the spectral sequence ABCDEF. to the sequence used today.
c) Determining that the acceleration of an object is inversely proportional to its mass.
d) Determining that the gravitational force between two objects is inversely proportional to the square of the distance apart.
e) Determining that stars are made up of mostly hydrogen and helium.

a) Pioneering the use of plots of luminosity vs. temperature for stars.

6. Why does it take so long for the energy produced in the core of the Sun to make its way out of the Sun?
a) The convective cells in the convective layer move very slowly, transporting the energy very slowly.
b) The speed of light is very low in the interior of the Sun because of the strong gravity.
c) Photons do not travel very far without being absorbed, and when they are re-emitted, it is in a random direction.
d) Millions of small black holes throughout the Sun trap the energy.
e) The nuclear reactions in the core produce mostly radio waves, which travel very slowly.

c) Photons do not travel very far without being absorbed, and when they are re-emitted, it is in a random direction.

7. What is the equation lambda(max) = 0.0029/T called?
a) Stefan's Law.
b) Wien's Law.
c) The parallax law.
d) Newton's Second Law.
e) The inverse Square Law of Light.

b) Wien's Law.

8. A period of 5 - 10 minutes is:
a) Approximately the lifetime of a sunspot.
b) Approximately the lifetime of a granule on the Sun's surface.
c) Approximately the time it takes the Sun to spin once on its axis.
d) Approximately how often the overall magnetic polarity of the Sun reverses.
e) Approximately how often the overall magnetic polarity of the Earth reverses.

b) Approximately the lifetime of a granule on the Sun's surface.

9. Giant stars like Capella (a yellow star about ten times the radius of the Sun) are classified as Luminosity Class:
a) III.
b) I.
c) V.
d) X.
e) XXX.

a) III.

10. Neutral helium lines are strongest in the spectra of:
a) F stars.
b) G stars.
c) M stars.
d) K stars.
e) B stars.

e) B stars.

11. The ancient Greek Astronomer Hipparchus:
a) Came up with the formula F = GM(1)M(2)/R 2 to describe the gravitational force.
b) Invented the magnitude system we use today.
c) Was the first person to plot the luminosity of stars vs. their temperatures.
d) Invented the sequence of stellar spectral types that we use today in modern Astronomy.
e) Was the first person to realize that the acceleration of an object is equal to the force applied to it, divided by its mass.

b) Invented the magnitude system we use today.

12. Stefan's Law (the Stefan-Boltzmann Law) describes:
a) The back-and-forth shift of a star on the sky, due to the Earth's orbit around the Sun.
b) The shift in the position of a star on the sky relative to background stars, due to a true motion of the star through space.
c) For a hot solid or hot dense gas, the increase in the wavelength of the peak of the spectrum with decreasing temperature.
d) An increase in the luminosity of an star due to an increase in its temperature and/or radius.
e) The shifting of the wavelength of the light seen by an observer, due to the relative motion of the observer and the source of light.

d) An increase in the luminosity of an star due to an increase in its temperature and/or radius.

13. In Astronomy, the term spicule' refers to:
a) The strong red emission line of hydrogen.
b) A very low mass neutral particle created by nuclear reactions in the core of the Sun.
c) Short-lived jets of gas above the photosphere of the Sun.
d) The force that holds the nuclei of atoms together.
e) The shift in the wavelength of light due to the relative motion of the source of light and the observer.

c) Short-lived jets of gas above the photosphere of the Sun.

14. Star A has a magnitude of 1. If Star B has a brightness 100 times less than Star A (i.e., the brightness of Star B is 1/100 times that of Star A), what is the magnitude of Star B?
a) 2.
b) 3.
c) 6.
d) -4.
e) 0.

c) 6.

15. If a hydrogen atom has an electron in its ground energy level, what kind of photon is needed to ionize it?
a) ultraviolet.
b) red.
c) blue.
d) infrared.
e) radio.

a) ultraviolet.

16. What's the difference between acceleration and velocity?
a) Acceleration is a change in velocity with time.
b) Acceleration has a direction associated with it, velocity does not.
c) Velocity has a direction associated with it, acceleration does not.
d) Acceleration has units of distance per time, while velocity has units of distance per time 2 .
e) Acceleration and velocity are the same thing.

a) Acceleration is a change in velocity with time.

17. Which of the following types of stars have spectra that peak in the UV, according to Wien's Law?
a) M.
b) G.
c) K.
d) O.
e) both K and M.

d) O.

18. An M2I star is:
a) hotter and larger than the Sun.
b) hotter but smaller than the Sun.
c) colder and larger than the Sun.
d) colder and smaller than the Sun.
e) the same temperature as the Sun, but larger.

c) colder and larger than the Sun.

19. Which of the following spectral types of stars are colder than type G stars?
a) K,M.
b) O,B.
c) B,F.
d) A,B,O.
e) A,B.

a) K,M.

20. The Super Kamiokande experiment beneath a mountain in Japan was designed to detect what kind of particle produced in the Sun?
a) Neutrons.
b) Neutrinos.
c) Protons.
d) Positrons.
e) Gamma ray photons.

b) Neutrinos.

## If the Sun got larger, but maintained its luminosity, would the Earth get hotter or colder? - Astronomy

Section 3 - Habitable Zones and Extra-Solar Planets

As we move to stars other than the Sun we may ask if they have planets, and if so, if these planets could harbor life.

What determines the "suitable zones" or "habitable zones" where life might exist on planets, in terms of the properties of the central star and the conditions on the planet.

What do we mean with suitable conditions? The main criterion to define the "habitable zone" is: Temperature on the planet such that water may exist in liquid form.

Other factors, besides the requirement for liquid water, that might affect chances of forming life on a planet:
a. radiation spectrum or color of the star: too much UV light may be bad, depending on the planet's capability to shield the surface from UV light. So the atmosphere of the planet will matter for this too, but also the temperature of the star : hot stars emit much more UV light than cooler stars. Star cluster M39 showing hotter (blue) stars are more luminous than cooler red stars.

b. For how long will the conditions be suitable ? If Earth is typical, it has taken a long time to develop advanced life forms. A long time time implies that we must have stars that can shine for a long time. We therefore need to find out how long different stars can shine. This is a matter of their mass and their energy output per unit time, which we measure as the star's LUMINOSITY or light power. We come back to this below, in the notes on Chapter 11.

Clicker question. The luminosity, or power, of a star measures (compare power of a light bulb):

a. How much light the star emits over its life time.

b. How much light the star has emitted in the past.

c. How much light the star emits per second over all wavelength.

d. How much light we receive from the star per second.

Stars become hotter and more luminous the more massive they are . This is because a higher mass star needs more pressure to balance the gravity causes by its mass and higher temperature produces higher pressure. The higher temperature and larger size makes the star much more luminous than the Sun. The light emitted by a hotter and more luminous star has more energy to heat planets further away from the star than for a less luminous star. As we already discussed, the amount of light intercepted per unit surface area by a planet decreases as the inverse of the distance squared to the star. This is simply a consequence of energy conservation: the light from the star is spread out over a larger area and volume as it moves away from the star.

The temperature on the planet or moon thus depends on several factors that we already discussed before:

amount of energy received as light from the central star, this is the principal factor in many cases.

how reflective is the planet? If it is very reflective, more of the star light will be bounced back into space and the planet will be colder. We call the reflectivity the "albedo".

properties of the atmosphere (composition, density, greenhouse gasses)

other heat sources: internal or external (e.g. tidal forces on moons). Even if it is too cold in terms of solar radiation near Jupiter and Saturn, there can still be moons with liquid water, providing a possible local habitable zone.

How large is the habitable zone in the Solar System? We call the distance between Earth and Sun 1 Astronomical Unit. Is the habitable zone 0.5-1.5 Astronomical Units? Or 0.95-1.05 A.U? Venus is too hot, Mars perhaps too cold but probably still inside the habitable zone. There may also be habitable zones around some of the giant planets, as we saw. We don't actually know the answer to this question all that well.

Changes in solar system's habitable zone over time:

The Sun's energy output is gradually climbing from its early days of hydrogen fusion to the present. This general increase in brightness since the Sun's formation is about 30% it is very important but happens very slowly so it is not something we need to worry about now. It implies the habitable zone was closer to the Sun in the past and is slowly moving outward.

A more dramatic change comes about when the Sun has exhausted the hydrogen in its core available for nuclear fusion . The center will shrink and heat up a lot, while the other layers will swell to enormous size. Eventually, in the center, helium will fuse into carbon. The Sun's luminosity will increase by factor of a 100-1000, its diameter by a factor of a 100. The color of the Sun will turn redder, as it is cooler in the outer atmosphere. However, the higher luminosity will greatly increase temperatures throughout the solar system, with Earth getting warmer than 700 C. This very luminous phase of the sun will last a billion years, and then it will expell its outer layers and slowly cool as a white dwarf (see further below in Chapter 11 section)

Discussion question: What will happen to the planets in the solar system as the Sun goes through the red giant and white dwarf phases?

Thus the long time fate of the solar system is darkness and cold temperatures. A similar fate awaits the universe as a whole, as it keeps expanding and gradually converts any remaining gas clouds in stars with cold stellar remnants left at the end. This is many, many billions of years in the future.

Properties of stars relevant to how large their habitable zones may be and how long the stars can shine.

What are stars other than Sun like? Are they all the same size and temperature? Do they emit the same amount of light per second (we call this "luminosity")? The answer is no to all questions.

The principal factor that determines the main properties, including its life time, of a star is its MASS. Secondary to that is the CHEMICAL COMPOSITION of the star.

Mass affects: Temperature (due to equilibrium between gravity and pressure in the star) Rate of energy production so the stars "Luminosity" and hence Life Time and the End Phase of the star.

Possible end phases of stars:

Low to medium mass stars (0.1 - 8 times mass of Sun): Planetary Nebula stage, white dwarf remnant.

High mass stars (above 8 times mass of Sun): Supernova explosion, neutron star or black hole remnant.

Question : How do we tell the temperatures of stars?

Question : How do we determine the luminosity of a star? What do we need to measure?

Question : How do we determine the mass of a star? This is relevant to find out how long it can shine.

What the important parameters we need to know about stars to understand how they compare to the Sun?

a. Color or detailed spectrum gives us the temperature of the star.

b. We need to know the distance to the star or else we cannot determine its total luminosity, nor its mass.

c. The apparent brightness (or flux) is the energy that we measure we get from the star at Earth. Combining that with the distance to the star, we can determine the "luminosity" of the star . This is the total energy emitted per second by the star.

d. Once we have the temperature and the luminosity, we can calculate the star's size . If you have two objects with the same temperature but one is more luminous than the other, it has to be bigger. That lets us calculate the star's diameter relative to the Sun's size.

e. The mass of the star can only be determined directly if we find something orbiting the star, just as the mass of the sun can be determined from the planets orbiting it, using Kepler's laws. Hence binary stars are important for measuring masses of stars.

f. The last important property is the chemical composition of the star. This also can be derived from the star's light, by splitting it over all its wavelengths into a detailed spectrum.

The results of our studies are that not all stars are same : we see stars of different luminosities, masses, temperatures, and sizes. What causes these differences? Why do we need to know?

What kind of stars exist in galaxies? Can all stars shine as long as the Sun? The answer is definitely NO . However, there are also very many stars like the Sun in the MW.

If stars are different from the Sun, how does that affect their habitable zone? There are several important effects to consider:

- Stars that are hotter and more massive than the Sun emit more UV light which may affect development of life on planets. The temperature of a normal star depends on its mass in general, high mass stars are hot and also much more luminous than the Sun.

- Stars that are more luminous than the Sun will have their habitable zone away further away from the star that is the case in in our solar system.

- Many stars are much cooler than the Sun which would imply the habitable zone will be much closer to the star. This implies that planets in such a habitable zone would have much shorter orbital periods than the Earth has.

- H ot, luminous stars, as we will see, can not shine very long . Therefore, their habitable zone is also limited in the time available to develop life.

- Low luminosity small stars can shine much longer than the Sun and could still support life possibly since there is much time available.

MASS-LUMINOSITY RELATIONSHIP FOR STARS

How long can a star shine ? That is given by:

available energy supply divided by how much energy the star loses each second this is thus proportional to the mass of the star divided by the stellar luminosity. The unit you get when you do this calculation is a unit of time, as it should be.

Here comes the interesting part : massive stars produce far more luminosity than low-mass stars. The relationship is not linear (in which case all stars would be able to shine equally long) but cubic, that is, the luminosity of a star scales as the mass to the power 3 . The net result is that a star that is, say, 10 times more massive than the Sun will use up its total energy 100 times faster than the Sun, so it will only shine 1/100th of the time the Sun can shine, and a star that is 100 times more massive will only be able to shine for 10,000 less long than the Sun before it runs out of energy.

Conclusion: if life takes billions of years to develop to fairly advanced stages around stars like the Sun, very massive stars are unlikely to be good places to look for planets with life. A massive star's life is measured in millions of years, rather than billions of years

Summary of what we have learned about the properties of stars that are in the main, stable phase of their life, like the Sun is:

Stars less massive than the Sun are cooler, redder in color, smaller in size, emit much less total light per second, but can shine for a very long time, much longer than the Sun.

Stars more massive than the Sun are hotter, bluer in color, bigger in size, emit much more total light per second, but can shine for only a short time compared to the Sun.

Galaxies like our Milky Way contain many stars like the Sun, fewer massive stars, and many more low-mass stars . The low-mass stars will be cooler than our Sun but can shine much longer and they may be good places to look for planets and life.

Another interesting bit of information: as much as 50% of all stars may be occurring in binary systems , that is, two stars orbiting around each other. We also call them double stars. Some systems have 3 or even more stars orbiting each other. Finding planets is a bit like finding binary star systems, except much harder.

As we saw above, stars like the Sun leave "white dwarfs" as remnants when their life is over. Almost half of the star's mass is expelled back into the interstellar medium, the core is left as very dense, initally very hot, carbon-rich star, which we call a white dwarf. White dwarfs are peculiar they are very dense, about a million times denser than ordinary matter . Even though the white dwarf that the Sun will leave behind has still about 60% of the Sun's mass, it will only be about the size of the Earth. Some planets may become unbound from the star as this happens and become lonely planets orbiting alone in the Milky Way.

More massive stars leave even more peculiar remnants . They don't end their lives as planetary nebula with a white dwarf remnant, but in violent explosions as a supernova . The supernova too expels a large amount of material from the star back into the interstellar medium. This gas is enriched with the heavy elements created by nuclear fusion in the star during its life and created during the supernova blast. There are two options for the remnant:

a. If the star is massive but not extremely massive, a neutron star will be left. This star literally consists mostly of neutrons packed densely together. The neutron star will spin rapidly (periods of milli-seconds to seconds), emitting beams of light that we can detect. A neutron star is another factor of one to hundred million times denser than a white dwarf. If we shrink the Sun to the size of a neutron star, it would be about 10 miles across. Neutron stars can only exist up to a certain mass limit, somewhere between 2 and 3 times the mass of the Sun.

b. If the star is extremely massive, it will not leave a neutron star but a black hole : the core is too massive to be supported as a neutron star, and will continue to collapse after the supernova explosion to a region of infinite density in an infinitely small volume. We have found such black holes in binary stars where a star orbits around a mysterious object which consists of a bright disk of emission surrounding the black hole.

Examples of massive star remnants:

DETECTING PLANETS AROUND OTHER STARS

The last planet in our solar system was discovered in 1930 (ignoring the debate of whether it is a planet!). It has taken about another 65 years since then to find the first solid evidence for planets around other normal stars. Why is it so hard to find planets around other stars?

There are several ways we might detect planets:

1. Direct imaging to look for planets around nearby stars.

Let's consider this: The major problem is that the stars are bright, the planets are faint! Here is how hard this is:

The closest star to us other than the Sun is 4 light years away. This star's brightness as seen by us is about the same as that of a 150 Watts light bulb at a distance of 15 miles away from us. On this scale of 15 miles distance, the Earth would be a dust speck much smaller than a mm. It would be about 10 cm away from the light bulb. Imagine trying to detect a dust speck that is next to a 150 Watts light bulb from a distance of 15 miles away. That is how hard it is to detect Earth sized planets around stars. How about Jupiter? Jupiter would be about 50 cm away from the light bulb, and still be at least a billion times fainter than the light bulb.

The situation may seem rather hopeless for planet detection through imaging, yet imaging techniques already have allowed detection of these planets in a few cases. Here is an example. But most of the planets now known to exist around other stars have been discovered in other ways, that are essentially methods similar to those how most close binary star systems have been discovered. The situation is slightly better for large planets orbiting cool stars and images of several star-planet systems have now been obtained, especially with the Gemini telescopes.

2 . Through "occultations", or "transits" . The planet moves in front of the star, and temporarily dims the light. What is required for this? How much would star light be dimmed?

Clicker question. The diameter of Jupiter is about one tenth of that of the Sun. Suppose that we are far away from the Solar System and could observe Jupiter transiting across the Sun. How much would the light from the Sun be dimmed during the transit, that is how much weaker would the Sun appear during the transit?

Would it matter how far away Jupiter is from the Sun? In other words, if Jupiter were at the place of the Earth's orbit, would the dimming be the same or not?

The answer is quite simple. From our perspective, the distant star and its planet are about equally far away. Thus, the planet will cover a fraction of the area of the star that is equal to the ratio of the area of the planet to the area of the star:
(planet diameter) 2 /(star diameter) 2 . In the case of a planet like Jupiter, it would block about 1% of the star's light in the transit, while a planet like Earth would only block 0.01% of the star's light with modern instruments we can detect the 1% dip easily, while the 0.01% dip is very difficult to measure.

Moreover, from multiple transits we can deduce the orbital period for the planet. This, together with knowledge of the size and mass of the star, will allow us to determine the distance of the planet to the star we can tell if it is in the habitable zone or not!

3 . Through motion of star. If you can't see the planet, look for the effect of the planet's motion on the star: the star wobbles due to force of gravity exerted on it by the planet. The wobble can be detected in star's velocity or through its changes of position on the sky. What would the size of the wobble depend on? How fast would it wobble?

The star wobbles at the same rate as the planet completes an orbit. It is easiest to imagine this first for the case of having two stars of equal mass orbiting each other. In that case, intuition tells us the stars would be moving at the same rate and would always be opposite each other in their orbit. Newton's laws can be used to show that this intuition is right. In the case of objects of very different mass, the speeds of the two objects vary inverse to their mass, but the two objects still each complete their orbit in the same time. The orbit of the more massive object is just much smaller than the orbit of the less massive object (which is why Kepler concluded that the Sun was at rest it isn't, but it's motion is very small).

If the star is 1000 times more massive than the planet, the star's velocity in its orbit will be 1000 less than the planet's velocity. A planet like Jupiter is about 1000 times less massive than the Sun. Jupiter orbits at 750,000,000 km from the Sun, and completes one orbit in 11 years. As a result of Jupiter's motion around the Sun, the Sun completes its own little orbit in 11 years, and the radius of the orbit is 1000 times less than that of Jupiter, so 750,000 km, which is about equal to the radius of the Sun.

Kepler was wrong: stars are not at rest in the ellipse.

Doppler effect shifts light to bluer colors when star approaches us, and to redder colors when star is moving away from us. We can detect this!
Question: why not observe the Doppler effect for the planet which moves faster?

Here is a simulation that shows how the star moves as the planet orbits it. It is not too scale, in reality the star's motion is tiny: Doppler spectroscopy.

The stars spectrum has dark absorption lines that we can measure the blue and red shift and thus measure the motion of the star as the planet orbits it.

astrometry: in principle, we can also detect the motion of the star as a wobble on the sky compared to other distant stars. This has been tried in the past, but the motion is so small it is difficult to detect. Still, this will be an important technique in the future as our accuracy in imaging improves. Many double stars have been found this way.

Clicker question: What planet would cause the largest "wobble" motion in its star, hence would be easiest to detect, be it through the Doppler method or the astrometry method?

a. Big planet far from star.

b. Big planet close to star.

c. Small planet far from star.

d. Small planet close to star.

For the same 4 choices above, which planet would be easiest to detect with the transit method?

And lastly, what about in the direct imaging method?

4. Yet another technique: through gravitational lensing . The light from background stars can be amplified by a foreground system, causing a star to vary systematically in brightness. If the foreground system has planets, the light variations may be different. Here is an example:micro lensing by a star with a planet.
The big curve shows the overall brightening of the background star by the amplification of the light by the foreground star, which acts like a lens and bends the light of the background star by its gravity. The little dip on the curve is due to a planet that orbits the foreground star and that causes additional amplification of the light as the gravity of the planet acts like an additional lens.

Here is an interesting link that Stephanie found on a massive planet detected by microlensing: New result on an extra-solar planet!

Can we take pictures of the planets that have been discovered? Only of a few so far, and more in the future, although they will be tiny pictures with not any detail. Coronographic techniques are used to block the star light as best as possible. Scattered light is a problem, so we need to go outside the Earth's atmosphere and use clever imaging techniques in space to block the light of the star. We also need larger telescopes to improve the angular resolution. This can be done through interferometry or a large ground-based telescope that is being planned.

What is the problem with finding Earth sized planets?

Both principle detection techniques (Doppler shift and occultations) produce weakest signal for low mass planets or for planets far away from the star. So, the planets that have been found are typically close to the star and massive. This was surprising (since people thought you could not form Jupiter size planets close to a star) but we have to keep in mind that there is a strong bias here, since those are the ones that can be most easily found.

What has been discovered about the extra-solar planets thus far:

- Most stars have planets. Estimates of the number of stars that has Earth-mass planets are not that accurate yet, but there are likely very many of them.

- In many stars multiple planets have been detected. The ability to detect multiple planets relies on very well measured Doppler shifts for the stars (and/or patience to detect eclipses of the star by the planets!)

Challenge in measuring the masses of planets: inclination of the orbit not known unless the planet transits across the star (then we know we see the system "edge-on" and not from above. So many masses derived for planets are "LOWER LIMITS", except for the cases where we know the system is seen from "edge-on", which we know for sure when we see the planets transiting across their star.

- Some knowledge of planetary atmospheres has been found too, with Hubble Space Telescope, where sodium was detected in planet's atmosphere. This technique shows great promise for future. It relies on detecting the change in the star's spectrum during a transit by the planet.

- Planets have also been found in binary star systems!

Doppler shift in velocities detected in light from star, could be in normal stars or in neutron star (= pulsar) where we detect Doppler shift in the frequency of the pulses of radio emission

- Gravitational lensing ("micro lensing") of normal stars, where we look for light variations in star due to lensing of background object. Presence of planet may give different light variation. Drawback: one time even for each star!

- Direct imaging to see the planet and its motion around the star. This will become more feasible in the future.

Results:
- Planets with mass of about Earth only found so far around neutron star, but planets with just a few times the mass of Earth found around normal stars with Doppler technique, only possible if they are very close to the star and the star has low mass so it wobbles more.
- Many planets found, sometimes multiple per star, up to as many as 5 per star.
- Results biased towards detecting massive planets close to stars a large part of the search space cannot yet be explored (e.g. Earth size planets or large planets very far from star)
comparison of extra-solar planets with solar system planets

- Stars with higher abundance of "heavy elements" (meaning anything above Helium) have higher probability of having planets detected around them.

Is the Earth unusual? The "rare Earth hypothesis"

Are conditions on Earth so special that it is likely few planets will exist that are like Earth? This is a tricky question that can easily lead to incorrect reasoning . It is very easy to point at any situation as being miraculous in some ways, and hence extremely unlikely. E.g. a couple may find that one split decision in their lives led their future together. But this doesn't mean they would not have had a future without that decision. It might have been a different future, but.

Likewise, we can point at many unique features of Earth and think that a miracle or at least a very non-scientifically explainable set of events must have happened for us to be here. But this ignores one important fact: if the events had not happened, we would not be here to ask the question! So, the very fact we can ask the question implies that things worked out OK so far.

Nevertheless, let us wade into this treacherous terrain.

What is special about Earth?

a. Requirement for high abundance of heavy elements to form rocky planets. Likely not an issue, since most of the Galactic disk has abundance of heavy elements like Sun or higher.

b. Requirement for avoiding major impacts from occurring too frequently? Jupiter plays a critical role in keeping the asteroid belt where it is (between Mars and Jupiter and not crossing Earth's orbit). Also, most of comets are far from Sun in comet cloud, but they may have been formed much closer in, in region where major gas giants formed. Again, the massive planets are responsible for sweeping them to the outer orbits. The Moon may also play some role in the impact rate of asteroids and comets on earth.

Does every Earth need a Jupiter in the right place so that life has enough time to form and evolve?

We don't know enough to be sure of this. But it surely is no problem to form Jupiter size planets as the extra-solar planet results thus far show.

c. Is a stable climate rare?

The stability of the Earth's climate may be related to the Earth's ability to regulate the amount of natural greenhouse gases (notably CO2) in the atmosphere. Plate tectonics plays an important role in this cycle.

A second important factor is the presence of the Moon . The Moon is responsible for keeping the Earth's tilt at a pretty constant angle. There is some evidence that Mars's axis shows much larger variations in the tilt over long periods. The likely formation mechanism for the Moon is a giant impact of a mars-sized object with Earth early in the formation of the solar system. The Earth is not massive enough on its own to attract enough matter to form large moons like the gas giants did. Thus, the presence of the Moon could be quite rare.

However, we don't know though, if a variation in tilt axis would preclude development of (advanced) life. It may depend on the time scales of the change.

On a larger scale, we can ask the same questions about our universe. With only a small change in some of the basic physical constants, for example, matter might not have been stable. Could we imagine a universe with no stable matter, just light and a myriad of elementary particles that never formed atoms? Again, we can invoke miracles, but with only the example of one universe we can learn about so far, it can lead to a lot of philosophical speculation but no hard conclusion.

In balance, "reasoning after the fact ("a posteriori") always can seem to point at magical coincidences for certain events to happen. But that is a dangerous thing to do from a scientific perspective. It is much better to get real data on the variation of planetary systems and from there draw the conclusions what is required for life and what is rare or common.

As a wrap up, here is a recent video about the search for earth-like planets:

## Energy from the Sun

Although much hotter on the inside, we can closely approximate the surface of the sun, from which its emission occurs, as a black body at a temperature of about 5800 K. The Stefan-Boltzmann equation then gives the energy flux emitted at the sun’s surface.

SS = (5.67 × 10 –8 W·m –2 ·K –4 )(5800 K) 4 = 63 × 10 6 W·m –2

The surface area of a sphere with a radius r is 4πr 2 . If rS is the radius of the Sun, the total energy it emits is SS4πrs 2 . As the radiation is emitted from this spherical surface, it is spread over larger and larger spherical surfaces, so the energy per square meter decreases, as illustrated schematically in the diagram below.

The figure at the right compares the experimental solar emission curve observed outside the Earth’s atmosphere to the emission curve for a 5800 K black body located at the sun’s distance from the Earth. The structure in the experimental curve is a result of absorption of some wavelengths by atoms and ions in the cooler layers outside the sun’s emitting surface.

When the energy emitted by the sun reaches the orbit of a planet, the large spherical surface over which the energy is spread has a radius, dP, equal to the distance from the sun to the planet. The energy flux at any place on this surface, SP, is less than what it was at the Sun’s surface. But the total energy spread over this large surface is the same as the total energy that left the sun, so we can equate them:

Values for the average planetary distances, dP, and the corresponding SP, calculated using rs = 700,000 km, are given in the table below.

When radiation from the sun reaches a planet, it does not strike all areas of the planet at the same angle. It strikes directly near the equator, but more obliquely near the poles. To find the amount of energy entering the planetary atmosphere (if any) averaged over the entire planet, consider the diagram. The total amount of radiation incident on the planet (and atmosphere) is equal to the amount the planet intercepts to cast the imaginary shadow shown in the diagram. That is, SPπrP 2 . If the average energy flux over the area of the planet is Save, the total energy for the planet is Save4πrP 2 . These two total energies must be equal, so: Save = SP/4. These average fluxes are also included in the table. To find out how this incoming energy is connected to the temperature of the planets see Predicted Planetary Temperatures.

## I read that the sun's surface temperature is about 6,000 degrees Celsius but that the corona--the sun's atmosphere--is much hotter, millions of degrees. How does all that energy get into the corona without heating up the surface?

David Van Blerkom, a professor of astronomy at the University of Massachusetts at Amherst, provides a nice overview, focusing on the second part of the query:

"The fact that the outermost region of the sun's atmosphere is at millions of degrees while the temperature of the underlying photosphere is only 6,000 kelvins (degrees C. above absolute zero) is quite nonintuitive. One would have expected a gradual cooling as one moves away from the central heat source. A related question is why, if the corona is so hot, it does not heat up the photosphere until it has an equally high temperature.

"I will address these questions in reverse order. Let us first ask what it means for a gas to have a high temperature. The answer is that temperature is a measure of the average kinetic energy of the gas atoms, that is, a measure of how fast they are moving. A high temperature gas has atoms with a larger average velocity than a low temperature gas of the same composition. We thus infer that the atoms in the corona are moving much more rapidly than those in the photosphere.

"In order for the corona to make the photospheric temperature rise, the coronal gas must cause the photospheric atoms to move faster. It could do so by colliding and mixing with the cooler gas and thus transfering some of its kinetic energy. Another way is also possible: At a temperature of millions of degrees, the gas in the corona is highly ionized, that is, electrons are stripped off neutral atoms and move freely. Because electrons are thousands of times less massive than atoms, the hot electrons have very high speeds. These electrons could travel into the photospheric gas and collide with the atoms there, again increasing their velocities. These two heating mechanisms are called convection and conduction, respectively.

"A gas at millions of degrees also radiates energy much of it is emitted in the form of very high-energy x-ray photons. X-ray photons impinging on the photosphere could also transfer energy to the gas atoms there. This heating mechanism is radiation.

"Yet the three traditional methods of heating do not raise the photospheric temperature for a simple reason. Suppose, as a thought experiment, one had a thermometer that could measure temperatures of millions of degrees and placed it in the corona. In order to make a temperature measurement, the coronal atoms or electrons must strike the thermometer, or x-ray photons must impinge upon it. The corona, however, has such a low density that the thermometer will almost never be hit. So while the thermometer is technically sitting in a gas that is at 2,000,000 kelvins, it doesn't know it. The gas has a high temperature but a low heat content. There are just not enough atoms around to heat our hypothetical thermometer or the underlying photosphere.

"The question of why the corona has such a high temperature is harder to explain, and probably the last word on the physical mechanism has not yet been given. Most astronomers assume that the gas is heated by the magnetic field that pervades the corona. The solar magnetic field has long been known to cause the sunspot cycle, and the physical shape and activity in the corona also varies with the sunspot cycle. Magnetic fields are known to be able to transfer large amounts of energy to the solar atmosphere, sometimes explosively as in flares. Huge magnetic loops can be seen to rise far into the corona, and it is quite plausible that the solar magnetic field is the ultimate source of physical heating of the corona."

Vic Pizzo of the Space Environment Center in Boulder, Colo., reiterates how mysterious this process is:

"The precise mechanism by which the corona overlying the solar surface is heated to temperatures of one to two million kelvins remains one of the outstanding problems of solar physics. It has long been suspected that turbulent motions in the lower solar atmosphere are propagated outward as waves in some form, which ultimately shock the thin atmosphere above the surface (the photosphere). The shocks thereby dissipate mechanical energy in the waves as heat. When magnetic field lines reconnect, they release energy some researchers suspect that fine-scale magnetic reconnections above the sun's surface provide the energy to heat the corona.

"Whatever the cause, some heat does indeed leak back toward the solar surface, but the total amount of energy so transported is really quite small, and cannot raise the photospheric temperature very much. The reason for this is the extremely rapid fall-off of mass density with height above the solar surface. That is, although the material in the corona is very hot, it is also very tenuous. Thus, the energy transported back toward the surface is dissipated into an ever increasing mass of material as it works its way down, whereas the heat transported outward is readily dissipated into the vacuum of space. "

Leo Connolly, the chair of the department of physics at California State University, San Bernardino, adds the following information:

"You are quite right about the corona being much hotter than the photosphere of the sun. The photosphere is the outer layer of the sun that produces the visible light we receive. The corona is a large, tenuous layer of gas whose structure is governed by the Sun's magnetic field. The gas in the corona is actually escaping from the Sun, forming the solar wind.

"What accelerates the atoms of gas to high velocity and temperature in the corona? It is likely that the solar magnetic field provides the necessary energy, but the mechanism is poorly understood. At the photosphere, the temperature is about 6,000 kelvins. The region of interest is above the top of the photosphere, where the temperature actually drops (to about 4,500 kelvins at a level of 500 kilometers above the photosphere). At 1,500 kilometers, the temperature starts to rise and by 10,000 kilometers above the photosphere the temperature reaches one million kelvins. Between 1,500 kilometers from the top of the photosphere and 10,000 kilometers is a region called the 'transition zone,' which is where the atoms are accelerated. The corona starts at 10,000 kilometers and extends out to about 10 million kilometers, where the gas finally escapes the sun's gravity and becomes part of the solar wind.

"We know that atoms, stripped of one or more electrons, are trapped by magnetic fields and move along the field lines. But what causes these atoms to be accelerated, producing the high temperatures of the corona, is not understood. All we know is that it definitely occurs in the transition zone."

Last but not least, Jay M. Pasachoff, Chair of the Department of Astronomy at Williams College in Williamstown, Mass., offers a perspective on some of the current attempts (including his own) to solve the riddle of the solar corona:

"One of the nice things about astronomy is that questions that are simply phrased often turn out to be profound. The manner in which the solar corona is heated to millions of degrees Celsius is one of the important unsolved problems of astrophysics. I have conducted experiments during a series of total solar eclipses to address the question, and there has been much theoretical work in this area recently. The problem was much addressed at a NATO Advanced Research Workshop on Observational and Theoretical Problems Related to Solar Eclipses, held in Bucharest, Romania in the first week of June 1996 the proceedings of that workshop will be available in a year or two.

"Basically, one cannot account for the heating of the corona by a radiative flow, so we think the corona is heated by some sort of magnetohydrodynamic (MHD) wave flowing out of lower levels of the sun. Images of the sun in the far ultraviolet and in X-rays (acquired most recently by the Solar and Heliospheric Observatory spacecraft, the Yohkoh satellite, and the NIXT rockets) show that the heating of the corona is localized in solar active regions, which indicates the important role played by the magnetic field. There are perhaps a dozen specific models that have been proposed to account for the high temperature of the corona. These models involve fast-mode MHD waves, slow-mode MHD waves, Alfren waves, et cetera. The older idea that acoustic waves flowing out of lower levels heats the corona was abandoned in the 1970s, when the Orbiting Solar Observatory 8 spacecraft did not see such waves in the chromosphere, the layer just above the photosphere (the apparent 'surface' of the sun in visible light). It remains possible, however, that some acoustic waves can be formed at higher levels.

"My work on the coronal heating problem is summarized in my chapter 'Measurements of 1-Hz coronal oscillations at total eclipses and their implications for coronal heating,' in Mechanisms of Chromospheric and Coronal Heating (Proceedings of the Heidelberg Conference), edited by P. Ulmschneider, E. R. Priest and R. Rosner (Springer-Verlag, 1991). The book also contains many other theoretical and observational papers.

## If the Sun got larger, but maintained its luminosity, would the Earth get hotter or colder? - Astronomy

Q: What planets might you expect to exhibit differential rotation?

A1: Those made of a crust of ice. The melting and refreezing with the dirt/dust on the planet would change any evident spots.

A2: . planets with a highly elliptical orbit probably exhibit differential rotation.

Q: Now that you are an apprentice astrophysicist, discuss the two components of the binary star. Which one is the hotter one? Which one is probably the larger one?

A: The star that isn't blinking is the larger one, since the other one orbits around it.

Solar Rotation Lab Report:

Purpose: To completely baffle ourselves with unintelligible data and archaic graphing techniques with the help of a solar telescope and some differential rotation of the sun.

• Collect data from some marks on pieces of paper.
• Bang head against wall trying to keep track of latitudes while plotting longitude
• Flush data down the toilet when latitudes don't match up.
• Hand in unintentionally disrespectful report despite being a day late.
• Apologize, and invite TA to party.

A: A "blue moon" is an expression which says that when things happen, it is very rare. It is very rare that you will get a "blue moon". You might get a "red moon", but you hardly see a blue one. Eclipses are rare to [sic] because they don't happen every day. During the January-March period, Earth will see 2 eclipses. Since eclipses are rare, astronomers can study them when they are occuring.

Q: Why are most stars in an HR diagram located on the main sequence?

A: Most stars are found in the main sequence because they only spend a small fraction of their lives in the transitional regions outside the main sequence, like cars in garages.

Q: One reason why radio and infrared radiation is more useful than visible light in studying molecular clouds is that the clouds are more transparent at those wavelengths. What is another reason why the longer wavelengths are more useful?

A: They are not as dangerous.

"Kepler's laws were more like rules in his time because they could not be fully explained but they proved many unexplainable theories at the time."

Q: Consider two regions of the ISM that are in pressure equilibrium with one another. One of the regions has a temperature of 10K and the other is at 1000K. What is the ratio of their densities?

A: The density of the cooler region is greater then [sic] the hotter region. It's like if you put a rock in a pot of boiling water, but not really, because it would be hard to achieve pressure equilibrium in this way, but kind of. The only was [sic] rock can withstand the pressure is if it were dense, according to pv=nRT.

Q: What is the most common molecule in interstellar space? What is the most heavily observed molecule?

A: The most common molecule is H2, but it is difficult to observe, so the most heavily observed molecule is Titanium oxyllar [sic] because the emission lines are easier to observe.

Q: The surface of a lake is an equipotential while the surface of a river is not. Why is that difference important?

A: A lake that is in equipotential has come to a constant elevation whereas a river flows either from high elevation to low elevation or vice versa. [!!]

[Student is to write a report on Pleiades. It begins with normal information about star names and descriptions. Then the following is written.] ". Alcyone [sic] is the central sun of the Pleiades. An interesting theory known as the Photon Belt story concerns this particular star. Our solar system makes one complete orbit around Alcyone everyone [sic] 25,000 to 26,000 years. In 1961, a group of scientists discovered a belt a [sic] photon light particles encircling the star cluster. Every 12,500 years, our sun reaches the midpoint of this belt. It takes 2000 years to travel through the midpoint and another 10,500 before the solar system enters it again. A null zone is located at the edge of the belt in which the earth will experience three days of absolute darkness. During these three days, no electrical device will be able to operate. The main part of the belt is where earth will experience 24 hours of daylight. Because of this entrance into the belt, some believe that people will develop psychic abilities like telepathy and telekinesis. Before entering the belt, however, a Supreme Creator Force will rescue the solar system by thrusting the [sic] it through the fifth dimension in an interdimensional rescue bubble. Supposedly, the solar system will find a new location only three light years from the Sirius star system. The solar system will reach the bubble around 2013. The period from 1996-2013 marks the end of 24 hours of daylight and brings back days consisting of 12 hours of sunlight and 12 hours of darkness."

Q: Describe the evidence that quasars are only a few parsecs or smaller in size.

A: Quasars are only a few parsecs or smaller in size because of their extreme distance.

[Quote from a Changing Seasons lab report, which was unpopular because its conclusions were so obvious.] ". In conclusion, it is now apparent that the change in position of the sun causes the temperature changes associated with the seasons. This came as quite a shocker to me I had always figured the earth became more massive (and thus gravity became stronger) in the wintertime, which caused two things to happen. First, the cold air from the upper atmosphere would get pulled in closer to the surface, making it colder second, the increase in gravity pulled all the leaves off the trees. But after careful consideration of the data that was collection [sic], I now know that the seasons change because the sun appears to change elevation in the sky, which occurs because the earth is tilted. Go figure."

[Actual situation that occurred in Prof. Spence's AS101 final exam, 9-11am]

Student, approaching Professor at 9:30am: "Here's my test. I'll be back at 11:15 to finish it." Walks out. Professor was speechless. At 11:15am in Professor's office, student returns. Student: "I'm back to finish my test." Professor: "Why did you leave?" Student: "I had to go see my English professor." Professor: "Right now? You couldn't schedule it for after the exam?" Student: "Well, um, he'll be gone, and I really had to pick up my term paper." Professor: "You left to pick up a term paper?" Student: "Well, no. Actually I had to go study for another exam." Professor: "Do you really think I'm going to let you finish the exam now?" Student: "No, I guess not!" Leaves. Q: In the space below. present one of the major theories or ideas which aims to account for the spiral structure of galaxies.

A: Galaxy collision is one theory, huge pieces of mass collided (supposedly in the "big bang"), creating many planets which all were gravitationally attracted to one another thus forming this spherical orbitting [sic] system which we now know to be our galaxy.

Q: List two observations which support the Big Bang model of the universe. Indicate what aspect of the model each supports.

A: different galaxies -- supports collision theory and gravitational manner craterings of Earth -- suggests earth was ripped off or smashed with other huge masses

Q: Which planets(s) could never be seen from Earth at midnight?

A: The temperature will probably be cold, because it is far in space. Maybe use big termomiter [sic].

Q: The Sun's corona shows weak emission lines. Why?

A: According to fraunhofer [sic] lines the Sun has the most extensive set of observed absorption lines. Also, the sun has low density but the emission spectrum does not have any density.

Q: Why do we see the sky? At night we see through the sky to view the stars. Why don't we see through the sky during the daytime?

A: Due to all the life that takes place on earth it makes its way up to the sky and thereby creating a visible atmosphere. It is too bright out during the daytime to view stars.

Q: Why does the sky appear blue during the day? Especially, why is it bluer than the Sun?

A: The sky appears blue during the day b/c there is a lot of Hydrogen in the air. The sky has more emmission [sic] spectrum and the Sun is full of absorption spectrum. The Sun wants to gain energy but the sky wants to get rid of the energy by ejecting a photon.

Q: Towards which direction would you launch [the space shuttle]? Explain.

A1: You would want to launch East so as to go with the flow of gravity which moves counter-clockwise.

A2: You would launch it going south because it takes less energy to move something down than it does to move that same object up/to the side. Then, once the object is in motion, it will stay in motion until another force stops/slows it.

Q: Suppose you want to set up a spaceport to launch space shuttle [sic]. Based only on energy requirement [sic], what would be the best place for the launch complex?

A: The best place for the launch complex would be wherever it would be closest to the horizon so it could escape into the horizon as quickly as possible. Also a flat plane so that the rocket aims straight into the horizon.

"If the distance b/w two objects were tripled, then the gravitational force between them would drop by a factor of 16. This is b/c gravity is an inverse square law. Double the distance, four times weaker triple distance, sixteen times weeker, etc. "

Q: [Student Survey for AS202] Comment on the night labs. Are they interesting and relevant? What could be done to improve them?

A: Too cold. Ask God to turn on the heater.

Q: Metabolizing a candy bar releases about 10^6 J. How fast must the candy bar travel to have the same 10^6 J in the form of kinetic energy? (Assume the candy bar's mass is 0.2 kg.) Is your answer faster or slower than you expected?

A: [math calculations] v=3162m/s. This is a much faster speed than I would have expected for a candy bar, especially considering that candy bars have no self propelled movement. The only time a candy bar should be moving is when I'm bringing it toward my mouth.

Q: The diffraction-limited resolution of a 5-meter telescope is about 0.01 arcsecond for visible light. Would you expect the angular resolution of a 5-meter radio telescope to be better than, equal to, or worse than 0.01 arcsecond?

A: I would expect the angular resolution of a 5-meter radio telescope to be better than 0.01 arcsecond because a radio telescope has to deal with light and spectrums. [sic]

Q: Suppose that two atmosphere-less planets with identical densities have the same surface temperature. If the larger planet is 8 times more massive than the smaller one, which one will cool faster? How much faster?

A1: The larger one will cool faster because it will cool slower because the inner temp will escape in less time as it works its way through the surface.

A2: Since larger is 8 times more massive and density is equal, the larger is 8 times as voluptuous. Since the cooling varies directly with surface area/volume ratio, which is 3/r, the smaller one will cool 8 times faster.

A3: The planet with more density would cool faster.

Q: Explain how we could observe from far away if a planet has a magnetic field.

A: Magnetic field would create gravity thus, planet would influence motion of other planets or capture asteroids or get moons.

Q: When would Venus be best observed? When would Jupiter be best observed?

A: Venus would be best observed when it in [sic] opposition with the sun. Meanwhile Jupiter would be best observed while in conjunction.

Q: If the Earth had no atmosphere, name one thing of astronomical significance that would be different and explain why.

A: If the Earth didn't have an atmosphere then it probably wouldn't have much gravity. This is astronomically significant because we would probably not have a moon.

Q: What are the main internal energy sources of the following objects and how do they work? (The Sun, Jupiter)

A1: Radioactive decay causes the release of energy in the sun's core which then travels outward towards the surface.

A2: [For the Sun] The energy source for the sun is its mantle. [For Jupiter] The energy source of Jupiter may be its methane. This burns up in the mantle and thus gives off pressure that forms volcanoes.

Q: Explain what convection is. Then name two places it can be found in the solar system: what object and where in the object convection is found.

A: When 2 planets or objects align with the Sun on the same side of the Solar System and form a right angle. a) When the earth, aligns with Mars and the Sun to form a right angle. b) When the Venus [sic] and Mercury align in such a way as to form a right angle.

Q: Before the invention of telescopes, how did we know there were planets, different from stars?

A: Because some of them were more visible, but more importantly because they moved horizontally, from W to E, and not vertically like the stars.

Q: Choose one planet or large moon other than the Earth and describe what we know about its interior.

A: We know that Jupiter has many different layers of compressed gasses like metalic [sic] hydrogen, some silicates, and a metal core that is a little larger than earth because the Russians sent a wearther [sic] balloon through its atmosphere.

Q: What phase must the Moon be in for a solar eclipse to occur? At approximately what time of day would the Moon rise when it is in this phase?

A: The phase must be full moon. The moon will rise at sunset, probably around 6AM.

Q: If you could take a sample of the material of any object in the solar system in order to find the age of the solar system, what object would you choose and why?

A: If it were possible, I would choose air bubbles because no matter how many times they have been recycled through different stages, they would be the best indicator. On earth, air bubbles give evidence of a longer history than rocks do because rocks get sucked into the earth sometimes through plate tect.

Q: Explain the conditions necessary for the Earth to generate a magnetic field. What is different about how Jupiter's magnetic field is created?

A: For the Earth to have a magnetic field, it is essential for it to have its core emitting waves and to receive the Electro Magnetic [sic] waves from the Sun to interact with its own atmosphere. Of course, it also needs the gravity to maintain this atmosphere. Jupiter generates its atmosphere and m. field through its rapid rotation which heats up the core.

Q: Are there any abberations similar to those seen through the refracting telescope?

A: No, the image is very lucid.

Q: You and the Earth attract each other gravitationally, so you should also be subject to a tidal force resulting from the difference between the gravitational attraction felt by your feet and that felt by your head. Explain why you can't feel this tidal force.

A: Because the air and atmosphere interfere.

Q: [Explain why statement is sensible or not sensible.] If you put an ice cube outside the Space Station, it would take a very long time to melt, even though the temperature in Earth orbit is several thousand degrees (Celsius).

A: It would still be held together because there is no gravity and the atoms wouldn't separate.

Q: Why does a 100-kg satellite orbiting Jupiter have more gravitational potential energy than a 100-kg satellite orbiting the Earth, assuming both satellites orbit at the same distance from the planet centers?

A: A 100-kg satellite orbiting Jupiter has more gravitational potential energy than a 100-kg satellite orbiting the Earth, assuming both satellites orbit at the same distance from the planet centers, because there is more gravity on Earth, and Earth is more solid -- it could keep falling through Jupiter.

Q: The Sun's corona shows emission lines. Why?

A: [Student has English as a second language. This is a partial answer.] The corona is at a very high temperature location, so hydrogen and helium do not have their erections.

Q: The nearest star has a parallax of 0.75 arc-seconds. What is its distance?

A: 0.8660254 meters [no work shown]

Q: What is the total mass (in solar masses) of a visual binary system in which the average separation of its components is 10AU and the period is 10 years?

A: [Student uses Kepler's law correctly, but puts units on at end] 10 grams = total mass

[The following is a student essay. Spelling and typos reproduced.]

### The Two Faces of the Moon

The center of the moon's mass is not at the center of the moon because the gravity is stronger on the far side of the moon. This causes the light face of the moon to face us. The dark side of the moon has heavier magma made of "basalt rock". This is how the dark side of the moon is so dark.

The dark side of the moon does not face use ever because the gravity is heavier and the moon is asymmetrical. Its development is different from the light side of the moon. The lava of the moon could not make through the dense material that was on the dark side of the moon. The lava was trapped to form hard magma.

On the light side of the moon the lava was able to burst through. On the light side of the moon lava is hotter and thats why its lighter. On the Dark side lava is cooler. Thats why dark side is heavier than the light side. We can only see the light side. Also the moons gravity tilts the dark side so we can't see it.

[Student has a picture of the near side of the Moon labeled "The Dark side of the Moon" and a picture of the far side labeled "The light side of the moon".]

Q: If two white dwarf stars have different masses but the same surface temperature, which star will be more luminous?

A: The one with the smaller mass will be less luminous than the one with the larger mass because the one with larger mass will secrete more energy per second than the one with the smaller mass.

Q: When the Sun becomes a red giant, it will swell to perhaps 100 times its present size. How will its average density then compare with the density of water (which is 1000 kg/m^3)?

A: It's [sic] average density will be much less than the density of water due to the fact that all of the central energy and emission would red-shift with the growth, thus leaving it not as dense as it was earlier and definitely less than water.

Q: A spectral type B main-sequence star has a luminosity 10,000 times that of the Sun, and a mass of 10 solar masses. Compare the lifetime of this star with that of the Sun.

A: The Sun will have a shorter lifetime then [sic] that star because the Sun does not have as much matter to ignite in its core to maintain the stars [sic] shells from not collapsing in. The material in the star will be consumed more quickly then [sic] that of the Suns [sic], but the Sun will most likely seize to exist before the other star.

Q: What do you call an atom missing an electron?

Q: Detroit, MI, has coordinates of about 84 deg W and 42 deg N, so it must be 84 deg west of Greenwich, England, and 42 deg north of _____.

Some answers: Miami, FL Texas Boston Detroit Greenwich Mexico Ecuador South America Australia.

Q: State Newton's Third Law.

A: In a vaccuum[sic], objects accelerate at 8 m/s/s.

Q: A planets orbits in an ellipse around the Sun, with the Sun at one focus. What is at the other focus?

A2: The peripheal [I don't know what this is].

Q: Why do we send satellites into orbit around the Earth to observe ultraviolet and x-ray light?

A: Because there needs some power to accelerate against gravity.

Q: State Kepler's Three Laws of Planetary Motion.

A: [1st and 3rd laws correct] 2. The orbit of a planet will scoop out an equilarium.

Q: Which color of star corresponds to cooler stars, and which to hotter ones? Explain your reasoning.

A1: Blue would be cooler and red hotter because red is fire and blue is water.

A2: Blue corresponds to cooler stars and red corresponds to hotter ones. According to humans, red is the universal symbol for hot and blue is the universal symbol for cold.

Q: In what way did, or would, the presence of the Moon affect your observations?

A: The Moon increases the amount of light that reaches Earth, therefore, decreasing the disparity between the void of space and the light of the stars.

Q: Explain how the greehouse effect works to cause the surface of Venus to be so hot.

A: The Venus's atmosphere, mostly covers with surfuric [sic] acid. When Sun's radioactive ray heats the Venus's cruster [sic], it converted to CO2 and worth the surface.

Q: Why are impact craters circular?

A: Impact craters are circular because when they travel near the sun, the sun creates tails or gas and dust on the craters. The sun smooths out the shape and the craters remain circular.

Q: We are confident that the present meteor rate has been fairly constant for the last 3.8 billion years. Parts of the Moon's highlands appear to be older than the universe based on the number of craters. How do we resolve this?

A1: The moon may have been hit by craters perhaps not of this universe, or the universe may be older than we actually believe it to be.

A2: The highlands have more craters b/c They're [sic] higher up in elevation so more bolides can hit That [sic] area because They're [sic] closer.

A3: That part had craters on it when it was still part of the Earth.

Q: [difficult math problem]

A: No idea. Honestly, if I tried it would just look like a monkey had attempted it. About the same math skills, anyway.

Q: What is a lunar rille?

A: Canyons in moons [sic] surface where lava may have once flown.

Q: What caused the solar nebula disk to develop two zones? [terrestrial and jovian]

A: The asteroids got in between them.

Q: Which planets might you expect to exhibit differential rotation? Explain your line of reasoning.

A: Mercury, Venus. Because they are the only planets that come between us and the sun and therefore exhibit differential rotation.

Q: Describe the electromagnetic spectrum in terms of frequency, wavelength, and energy. Distinguish among radio, infrared, visible light, ultraviolet, x-rays and gamma rays.

A: The electro magnetic [sic] spectrum is an electrical magnetic field that covers the earth[sic]. These electric and magnetic fields vibrate. This electro magnetic [sic] field (light) is made up of small particles called "photons". [Student writes correctly about visible light and infrared.] Radio waves are even more further right then infrared waves. Radio waves are the longest and detected as vibrations in the human ear (which allows us to hear).

Q: List three observations Galileo made and indicate how they supported the Copernican view of the solar system.

A1: [partial answer] Rings of Saturn -- showed that the Earth moved due to the existance[sic] of these + gravity.

A2: Objects in the sky, such as birds and clouds, move with the earth[sic]. This supported the Copernican view that the planets orbit the Sun.

Q: How does Pluto fit into the terrestrial and jovian planets?

A: Pluto is a bit different than the rest. It is small like a terrestrial planet but is comprised of low densit ice and is rather cold considering its distance from the Sun. It is possible that Pluto is an object roaming the outer portions of our solar system.

"Even though the moon isn't a planet, it fits all the symptoms of the terrestrial planets."

Q: In what way did the presence or absence of the Moon affect your observations?

A: The moon[sic] acted as to light up the sky. This helped us see more stars than we would be able to without that light.

Q: Which planets might you expect to exhibit differential rotation? Explain your line of reasoning.

A1: All except Uranus. On all the planets except Uranuse [sic], regions near the equator have to rotate faster in order to make the same rotation as regions on the poles. Because Uranus is tilted on its side and rotates vertically, spots on its 90 degree longitude will rotate faster than on 0 degree or 180 degree, but the principle is the same for all planets.

A2: Ones affected by other planets/moons/objects. Magnetism & gravity slightly speeding up or slowing down the rotation period.

Q: How do we think Jupiter generates its internal heat? How do the other Jovian planets generate internal heat?

A: Even though the Jovian planets are far away from the Sun, they still have a lot of greenhouse gasses which trap the heat from the Sun. The planets also create their own internal heat which the gas then traps inside. As a result, all the planets are very hot.

"Uranus doesn't admit much excess internal heat."

Q: Why do objects observed at the zenith appear sharper than objects located at lower altitudes?

A1: The objects at lower altitudes may have a direction further away. The zenith is 90 degrees altitude but has no direction since it is straight overhead.

A2: Below the zenith, the light, coming from the object of observation, has to travel the least distance and has the best angular resolution.

A3: They are closer therefore sharper + the Earth's shape is more oblong than spherical.