# Can orbits change?

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I was reading about how the planet Mercury changes its orbit. I was wondering if farther away planets, particularly ones with elongated orbits, could do that as well? Planets and objects such Halley's comet, Pluto, Sedna, the dwarf planets, or even planet Nine (if there is one). Could the same happen to those objects, and if so how great are those changes? Can other things change as well like the speed of the orbit, or the size?

Yes, especially early in a system's life-cycle, when things are less sorted. Resonances between neighboring planets' orbits can arise, inducing eccentricities which can enhance their mutual interactions, resulting in altered orbits, sometimes catastrophically of course, as with Theia and the proto-earth.

There is a theory that the Late Heavy Bombardment of the earth (4.1 - 3.8Ga ago) was caused by disruptions in the orbits of Saturn and Jupiter, which further disrupted asteroids in the asteroid and/or Kuiper belts. This is called the giant-planet migration hypothesis.

# Precession

I assume you're talking about the precession of Mercury, one of the famous tests of general relativity. One reason Mercury is a good planet to test the relativistic predictions of precession is that its precession is more dramatic than the other planets. We can calculate the shift in the longitude of perihelion by $$frac{mathrm{d}varpi}{mathrm{d}t} propto n^3a^2$$ with some other (important!) factors multiplied in. $$n$$ is the mean motion (where $$npropto 1/T$$) and $$a$$ is the semi-major axis. Over one orbit, the net change is approximately $$Deltavarpi=frac{Deltavarpi}{Delta t}Delta tapproxfrac{mathrm{d}varpi}{mathrm{d}t}Tpropto n^3a^2T=frac{a^2}{T^2}propto a^{-1}$$ Orbits with larger semi-major axes should have smaller $$Deltavarpi$$, meaning that Mercury's shift is the largest in the Solar System; therefore, the other planets' orbits do precess, but by smaller amounts.

# Planetary migration

theRiley mentioned this in their answer. Planets' orbits can change over time through a process called planetary migration. This often occurs by one of two mechanisms:

• Disk-driven migration, where interactions with a protoplanetary disk change a planet's semi-major axis. This is the main theory for the formation of hot Jupiters.
• Scattering, where interactions with other planets or planetesimals causes drastic orbital changes. This is thought to have happened in the Solar System several billion years ago (see the Nice model, the Nice II model, and variations).

## GOP Rep. Gohmert Asks if USFS or BLM Can Change Orbits of the Earth or Moon to Fight Climate Change

In a virtual House Natural Resources Committee hearing, Gohmert asked Jennifer Eberlien, the associate deputy chief for the U.S. Forest Service, whether the Forest Service or Bureau of Land Management can "change the course of the moon's orbit or the Earth's orbit around the sun" because "obviously, that would have profound effects on our climate ."

This was not the first time Gohmert made comments like this. Last month, in an interview with Fox Business Network, he said, "We can't do anything substantive about the climate change right now, when the moon's orbit is apparently changing some, the Earth's orbit is changing some, according to NASA." It's unclear if the comments, which were widely mocked on social media, were made in earnest, or if they were Gohmert's way of insinuating that addressing climate change is impossible.

He may also have been referring to a debunked myth that solar flares are to blame for climate change, as he stated "there's been significant solar flare activity" before posing the question. Gohmert is a long-time climate change denier , having repeated other classic climate denier talking points over the years.

"The 'science-y sounding' reasons most politicians use to reject climate change are not primarily due to lack of education or knowledge. No: they are deliberately manufactured and offered as palatable excuses to hide the real problem: solution aversion. They don't want to fix it," climate scientist Katharine Hayhoe explained on Twitter.

## Rep. Gohmert asks if federal agencies can change the orbits of the Earth and the moon

During a hearing of the House Committee on Natural Resources on Tuesday, Rep. Louie Gohmert, R-Texas, asked Jennifer Eberlien, an official from the U.S. Forest Service, if the Forest Service or the Bureau of Land Management could alter the orbits of the Earth or the moon to help fight climate change.

### Video Transcript

LOUIE GOHMERT: And I understand from what's been testified to, the Forest Service and the BLM, you want very much to work on the issue of climate change. I was informed by the immediate past director of NASA that they have found that the moon's orbit is changing slightly. And so is the Earth's orbit around the sun. We know there's been significant solar flare activity.

And so, is there anything that the National Forest Service or BLM can do to change the course of the moon's orbit or the Earth's orbit around the sun? Obviously, that would have profound effects on our climate.

JENNIFER EBERLIEN: I would have to follow up with you on that one, Mr. Gohmert.

LOUIE GOHMERT: Yeah, well, if you figure out a way that you in the Forrest Service can make that change, I'd like to know.

## The Atomic Nucleus

Figure 2: Hydrogen Atom

The simplest possible atom (and the most common one in the Sun and stars) is hydrogen. The nucleus of ordinary hydrogen contains a single proton. Moving around this proton is a single electron. The mass of an electron is nearly 2000 times smaller than the mass of a proton the electron carries an amount of charge exactly equal to that of the proton but opposite in sign (Figure 2). Opposite charges attract each other, so it is an electromagnetic force that holds the proton and electron together, just as gravity is the force that keeps planets in orbit around the Sun.

Figure 2 is a schematic diagram of a hydrogen atom in its lowest energy state, also called the ground state. The proton and electron have equal but opposite charges, which exert an electromagnetic force that binds the hydrogen atom together. In the illustration, the size of the particles is exaggerated so that you can see them they are not to scale. They are also shown much closer than they would actually be as it would take more than an entire page to show their actual distance to scale.

There are many other types of atoms in nature. Helium, for example, is the second-most abundant element in the Sun. Helium has two protons in its nucleus instead of the single proton that characterizes hydrogen. In addition, the helium nucleus contains two neutrons, particles with a mass comparable to that of the proton but with no electric charge. Moving around this nucleus are two electrons, so the total net charge of the helium atom is also zero (Figure 3).

Figure 3: Helium Atom

Figure three is a schematic diagram of a helium atom in its lowest energy state. Two protons are present in the nucleus of all helium atoms. In the most common variety of helium, the nucleus also contains two neutrons, which have nearly the same mass as the proton but carry no charge. Two electrons orbit the nucleus.

From this description of hydrogen and helium, perhaps you have guessed the pattern for building up all the elements (different types of atoms) that we find in the universe. The type of element is determined by the number of protons in the nucleus of the atom. For example, any atom with six protons is the element carbon, with eight protons is oxygen, with 26 is iron, and with 92 is uranium. On Earth, a typical atom has the same number of electrons as protons, and these electrons follow complex orbital patterns around the nucleus. Deep inside stars, however, it is so hot that the electrons get loose from the nucleus and (as we shall see) lead separate yet productive lives.

The ratio of neutrons to protons increases as the number of protons increases, but each element is unique. The number of neutrons is not necessarily the same for all atoms of a given element. For example, most hydrogen atoms contain no neutrons at all. There are, however, hydrogen atoms that contain one proton and one neutron, and others that contain one proton and two neutrons. The various types of hydrogen nuclei with different numbers of neutrons are called isotopes of hydrogen (Figure 4) and all other elements have isotopes as well. You can think of isotopes as siblings in the same element “family”—closely related but with different characteristics and behaviors.

Figure 4: Isotopes of Hydrogen. A single proton in the nucleus defines the atom to be hydrogen, but there may be zero, one, or two neutrons. The most common isotope of hydrogen is the one with only a single proton and no neutrons.

In this interactive, you can explore the structure of atoms as you add protons, neutrons, or electrons to a model and the name of the element you have created will appear. You can also see the net charge, the mass number, whether it is stable or unstable, and whether it is an ion or a neutral atom.

## Gohmert asks if federal agencies can change Earth's or moon's orbits to fight climate change

Rep. Louie Gohmert Louis (Louie) Buller GohmertGOP increasingly balks at calling Jan. 6 an insurrection 21 Republicans vote against awarding medals to police who defended Capitol GOP's Gohmert, Clyde file lawsuit over metal detector fines MORE (R-Texas) on Tuesday asked a representative from the U.S. Forest Service if it was possible to alter the orbit of the moon or the Earth as a way of combating climate change, though it was unclear if he was being serious.

Gohmert was speaking with Jennifer Eberlien, associate deputy chief of the National Forest System, during a House Natural Resources Committee hearing.

"I understand from what's been testified to the Forest Service and the BLM [Bureau of Land Management], you want very much to work on the issue of climate change," Gohmert said to Eberlien, adding that a past director of NASA had once told him that orbits of the moon and the Earth were changing.

"Is there anything that the National Forest Service, or BLM can do to change the course of the moon's orbit or the Earth's orbit around the sun?" Gohmert asked Eberlien. "Obviously they would have profound effects on our climate."

"I would have to follow up with you on that one, Mr. Gohmert," Eberlien responded.

"Well, if you figure out a way that you in the Forest Service can make that change, I'd like to know," Gohmert added.

ORBITS: Rep. Louie Gohmert (R-TX) asks whether the Forest Service or the BLM can alter the orbit of the moon or the Earth in order to fight climate change during a House Natural Resources hearing pic.twitter.com/yYiOyi2cMZ

— Forbes (@Forbes) June 8, 2021

Gohmert later responded to tweets about his question by noting BLM stands for the Bureau of Land Management.

Exceedingly devious how you hid the context with an ellipses in your tweet. The hearing was about the BUREAU OF LAND MANAGEMENT & climate change.

BLM stands for the BUREAU OF LAND MANAGEMENT. #FakeNews https://t.co/WyIio5BQJM

— Louie Gohmert (@replouiegohmert) June 9, 2021

As NASA explains in a blog post, Earth's orbit changes from being close to perfectly circular to being slightly more elliptical in a cycle that takes about 100,000 years. The orbit is currently around as close to being circular as it can be.

The angle at which the Earth tilts also shifts slightly or "wobbles" on its axis over the course of tens of thousands of years.

These changes are called Milanković cycles after Milutin Milanković, the Serbian astronomer who first hypothesized them.

These shifts affect Earth's climate in both the short-term and long-term, though they have a relatively minor impact on the planet's seasons and are not behind global warming, according to NASA.

Astronomers have long observed that the Earth's moon is slowly drifting away, moving about an inch away every year.

## Does the moon rotate?

Observers on Earth might notice that the moon essentially keeps the same side facing our planet as it passes through its orbit. This may lead to the question, does the moon rotate? The answer is yes, though it may seem contrary to what our eyes observe.

### Near and far sides of the moon

The moon orbits the Earth once every 27.322 days. It also takes approximately 27 days for the moon to rotate once on its axis. As a result, the moon does not seem to be spinning but appears to observers from Earth to be keeping almost perfectly still. Scientists call this synchronous rotation.

The side of the moon that perpetually faces Earth is known as the near side. The opposite or "back" side is the far side. Sometimes the far side is called the dark side of the moon, but this is inaccurate. When the moon is between the Earth and the sun, during one of the moon phases called the new moon, the back side of the moon is bathed in daylight.

The orbit and the rotation aren't perfectly matched, however. The moon travels around the Earth in an elliptical orbit, a slightly stretched-out circle. When the moon is closest to Earth, its rotation is slower than its journey through space, allowing observers to see an additional 8 degrees on the eastern side. When the moon is farthest, the rotation is faster, so an additional 8 degrees are visible on the western side.

If you could journey around to the far side of the moon as the Apollo 8 astronauts once did, you would see a very different surface from the one you are accustomed to viewing. While the near side of the moon is smoothed by maria &mdash large dark plains created by solidified lava flows &mdash and light lunar highlands, the far side is heavily cratered.

Although you can't see the back side of the moon from Earth, NASA and other space agencies have glimpsed it with satellites.

"It is surprising how much brighter Earth is than the moon," Adam Szabo, project scientist for NASA's Deep Space Climate Observatory satellite at Goddard Space Flight Center in Greenbelt, Maryland, said in a statement after the satellite captured the moon crossing Earth's face. "Our planet is a truly brilliant object in dark space compared to the lunar surface."

### The moon's changing orbit

The rotational period of the moon wasn't always equal to its orbit around the planet. Just like the gravity of the moon affects ocean tides on the Earth, gravity from Earth affects the moon. But because the moon lacks an ocean, Earth pulls on its crust, creating a tidal bulge at the line that points toward Earth.

Gravity from Earth pulls on the closest tidal bulge, trying to keep it aligned. This creates tidal friction that slows the moon's rotation. Over time, the rotation was slowed enough that the moon's orbit and rotation matched, and the same face became tidally locked, forever pointed toward Earth.

The moon is not the only satellite to suffer friction with its parent planet. Many other large moons in the solar system are tidally locked with their partner. Of the larger moons, only Saturn's moon Hyperion, which tumbles chaotically and interacts with other moons, is not tidally synchronized.

The lunar rotation determined whether the infamous Man in the Moon, a face-like pattern of dark maria on the Earth-facing side, wound up pointing toward our planet. Gravity created an Earth-side bulge in the moon, slowing down its rotation in the past to create the synchronous rotation and keeping the longer lunar axis toward our world.

Recent research suggested that the side of the moon facing Earth was determined by how quickly the lunar rotation slowed. Because the moon lost speed slowly, there was about a two-to-one chance that the Man in the Moon would wind up facing Earth rather than keeping a space-bound view.

"The real coincidence is not that the man faces Earth," Oded Aharonson, a planetary science researcher at the California Institute of Technology who studied why the Man in the Moon stares down at Earth, said in a statement. Instead, the real coincidence is that the moon's slowdown was just enough to load the coin.

The situation is not limited to large planets. The dwarf planet Pluto is tidally locked to its moon Charon, which is almost as large as the former planet.

Earth (and other planets) do not escape completely unscathed. Just as the Earth exerts friction on the spin of the moon, the moon also exerts friction on the rotation of the Earth. As such, the length of day increases a few milliseconds every century.

"The moon and Earth loomed large in each others skies when they formed," then-graduate student Arpita Roy said in a statement.

"At the time of the dinosaurs, Earth completed one rotation in about 23 hours," Daniel MacMillan, of NASA's Goddard Space Flight Center in Greenbelt, Maryland, said in a statement. "In the year 1820, a rotation took exactly 24 hours, or 86,400 standard seconds. Since 1820, the mean solar day has increased by about 2.5 milliseconds."

On June 30, 2012, an extra second was added to all of the clocks on Earth because of this phenomenon.

## Benefits

A satellite in geosynchronous orbit can see one spot of the planet almost all of the time. For Earth observation, this allows the satellite to look at how much a region changes over months or years. The drawback is the satellite is limited to a small parcel of ground if a natural disaster happens elsewhere, for example, the satellite won't be able to move there due to fuel requirements.

This is a large benefit for the military. If, for example, the United States is concerned about activities in a certain region of the world &mdash or it wants to see how its troops are doing &mdash a geosynchronous orbit allows constant pictures and other surveillance of one particular region. An example of this is the United States' Wideband Global SATCOM 5, which launched in 2013. Joining a "constellation" of four other WGS satellites, it extends the military's communications system to provide blanket coverage over virtually the entire planet. The network serves troops, ships, drones and civilian leaders and is supposed to provide communications for ground personnel.

Communications for civilians also benefit from geosynchronous orbit. There are numerous companies that provide telephone, Internet, television and other services from satellites in that orbital slot. Because the satellite is constantly hovering over one spot on the ground, communications from that location are reliable as long as the satellite is well connected to the location you want to communicate with.

## 4.2 Synodic Month

The most familiar lunar cycle is the synodic month because it governs the well-known cycle of the Moon's phases. The Moon has no light of its own but shines by reflected sunlight. As a consequence, the geometry of its orbital position relative to the Sun and Earth determines the Moon's apparent phase.

The mean length of the synodic month is 29.53059 days (29d 12h 44m 03s). This is nearly 2.21 days longer than the sidereal month. As the Moon revolves around Earth, both objects also progress in orbit around the Sun. After completing one revolution with respect to the stars, the Moon must continue a little farther along its orbit to catch up to the same position it started from relative to the Sun and Earth. This explains why the mean synodic month is longer than the sidereal month.

According to astronomical convention, New Moon is defined as the instant when the geocentric ecliptic longitudes of the Sun and Moon are equal. When the synodic month is measured from New Moon to New Moon, it is sometimes referred to as a lunation, and we will follow that usage here. Historically, the phases of the Moon have been used as the basis of lunar calendars by many cultures around the world. The major problem with such calendars is that the year, based on the solar calendar, is not evenly divisible by a whole number of lunations. Consequently, most lunar calendars are actually lunisolar calendars (e.g., Chinese, Hebrew, and Hindu) that include intercalary months to keep the seasons in step with the year.

The duration of the lunation actually varies from its mean value by up to seven hours. For instance, Table 4-1 contains details for all lunations in 2008. The first column lists the decimal date of every New Moon throughout the year (Terrestrial Dynamical Time), while the second column gives the duration of each lunation. The third column is the difference between the actual and mean lunation. The first lunation of the year (Jan 08) was 03h 23m longer than the mean. Continuing through 2008, the length of each lunation drops and reaches a minimum of 05h 48m shorter than the mean value (Jun 03). The duration now increases with each succeeding lunation until the maximum value of the year is reached of 06h 49m longer than the mean (Dec 27).

 Table 4-1 New Moon and Lunation Length in 2008 Date of New Moon (Dynamical Time) Length of Lunation Difference From Mean Lunation Moon's True Anomaly 2008 Jan 08.4849 29d 16h 07m +03h 23m 242.4° 2008 Feb 07.1567 29d 13h 30m +00h 46m 280.0° 2008 Mar 07.7190 29d 10h 41m -02h 03m 310.8° 2008 Apr 06.1642 29d 08h 23m -04h 21m 332.7° 2008 May 05.5134 29d 07h 04m -05h 40m 349.4° 2008 Jun 03.8081 29d 06h 56m -05h 48m 4.4° 2008 Jul 03.0970 29d 07h 54m -04h 50m 20.1° 2008 Aug 01.4261 29d 09h 45m -02h 59m 39.2° 2008 Aug 30.8327 29d 12h 14m -00h 30m 64.9° 2008 Sep 29.3426 29d 15h 02m +02h 18m 98.7° 2008 Oct 28.9687 29d 17h 41m +04h 57m 133.4° 2008 Nov 27.7053 29d 19h 28m +06h 44m 161.9° 2008 Dec 27.5163 29d 19h 33m +06h 49m 186.6°

What is the cause of this odd behavior? The last column in Table 4-1 gives a clue it contains the Moon's true anomaly at the instant of New Moon. The true anomaly is the angle between the Moon's position and the point of perigee along its orbit. In other words, it is the orbital longitude of the Moon with respect to perigee. Table 4-1 shows that when New Moon occurs near perigee (true anomaly = 0°), the length of the lunation is at a minimum (e.g., Jun 03). Similarly, when New Moon occurs near apogee (true anomaly = 180°), the length of the lunation reaches a maximum (e.g., Dec 27).

This relationship is quite apparent when viewed graphically. Figure 4-1 plots the difference from mean lunation (histogram) and the Moon's true anomaly (diagonal curves) for every New Moon from 2008 through 2010. The left-hand scale is for the difference from mean lunation, while the right-hand scale is for the true anomaly. The shortest lunations are clearly correlated with New Moon at perigee, while the longest lunations occur at apogee. From the figure, the length of this cycle appears to be about 412 days. The reason why must wait until the next section.

The Moon's orbital period with respect to perigee is the anomalistic month and has a duration of approximately 27.55 days. The lock-step rhythm between the lunation length and true anomaly can be explained with the help of the anomalistic month and Figure 4-2. It illustrates the Moon's orbit around Earth and Earth's orbit around the Sun. The relative sizes and distances of the Sun, Moon, and Earth as well as the eccentricity of the Moon's orbit are all exaggerated for clarity. The major axis of the Moon's orbit marks the positions of perigee and apogee.

Two distinct cases-each consisting of two revolutions of the Moon around Earth-are depicted in Figure 4-2. The first case covers the New Moon geometry around perigee. The orbit marked A shows New Moon taking place near perigee at position a1. One anomalistic month later (orbit B), the Moon has returned to the same position relative to perigee (marked b1). However, Earth has traveled about 30° around its orbit so the Sun's direction relative to the Moon's major axis has shifted. The Moon must travel an additional distance of Δb in its orbit before reaching the New Moon phase at b2. This graphically demonstrates why the synodic month is longer (

1.98 days) than the anomalistic month.

The second case takes place about half a year later. New Moon then occurs near apogee (orbit C, position c1). After one anomalistic month, the Moon has returned to the same location with respect to apogee (orbit D, position d1). Once again, Earth has traveled about 30° around its orbit so the Moon must revolve an additional distance of Δd before reaching the New Moon phase at position d2.

An inspection of orbits B and D reveals that the orbital arc Δd is longer that Δb. This means that the Moon must cover a greater orbital distance to reach New Moon near apogee as compared to perigee. Furthermore, the Moon's orbital velocity is slower at apogee so it takes longer to travel a given distance. Thus, the length of the lunation is shorter than average when New Moon occurs near perigee and longer than average when New Moon occurs near apogee. Earth's elliptical orbit around the Sun also factors into the length of the lunation. With an eccentricity of 0.0167, Earth's orbit is about one third as elliptical as the Moon's orbit. Nevertheless, it affects the length of the lunation by producing shorter lunations near aphelion and longer lunations near perihelion.

During the 5000-year period covered in this catalog, there are 61841 complete lunations. The shortest lunation began on -1602 Jun 03 and lasted 29.26574 days (29d 06h 22m 40s 6h 21m 23s shorter than the mean). The longest lunation began on -1868 Nov 27 and lasted 29.84089 days (29d 20h 10m 53s 7h 26m 50s longer than the mean). Thus, the duration of the lunation varies over a range of 13h 48m 13s during this time interval.

The histogram presented in Figure 4-3 shows the distribution in the length of the lunation over 5000 years. To create the histogram, the durations of individual lunations were binned into 30-minute groups. It might seem reasonable to expect a simple bell-shaped Gaussian curve. However, the results are surprising because the distribution in lunation length has two distinct peaks. This bifurcation can be understood if the lunation length, which depends primarily on the Moon's distance, is considered as a series of sine functions. The extremes of a sine function always occur more frequently than the mean, which is just what is seen in Figure 4-3. For a more detailed discussion, see Meeus (1997).

## Strange Extrasolar Planet Orbits Explained

Image credit: NWU
The peculiar orbits of three planets looping around a faraway star can be explained only if an unseen fourth planet blundered through and knocked them out of their circular orbits, according to a new study by researchers at the University of California, Berkeley, and Northwestern University.

The conclusion is based on computer extrapolations from 13 years of observations of planet motions around the star Upsilon Andromedae. It suggests that the non-circular and often highly elliptical orbits of many of the extrasolar planets discovered to date may be the result of planets scattering off one another. In such a scenario, the perturbing planet could be shot out of the system entirely or could be kicked into a far-off orbit, leaving the inner planets with eccentric orbits.

“This is probably one of the two or three extrasolar systems that have the best observations and tightest constraints, and it tells a unique story,” said Eric Ford, a Miller postdoctoral fellow at UC Berkeley. “Our explanation is that the outer planet’s original orbit was circular, but it got this sudden kick that permanently changed its orbit to being highly eccentric. To provide that kick, we’ve hypothesized that there was an additional planet that we don’t see now. We believe we now understand how this system works.”

If such a planet had caromed through our solar system early in its history, the researchers noted, the inner planets might not now have such nicely circular orbits, and, based on current assumptions about the origins of life, Earth’s climate might have fluctuated too much for life to have arisen.

“While the planets in our solar system remain stable for billions of years, that wasn’t the case for the planets orbiting Upsilon Andromedae,” Ford said. “While those planets might have formed similarly to Jupiter and Saturn, their current orbits were sculpted by a late phase of chaotic and violent interactions.”

According to Ford’s colleague, Frederic A. Rasio, associate professor of physics and astronomy at Northwestern, “Our results show that a simple mechanism, often called ‘planet-planet scattering’ – a sort of slingshot effect due to the sudden gravitational pull between two planets when they come very near each other – must be responsible for the highly eccentric orbits observed in the Upsilon Andromedae system. We believe planet-planet scattering occurred frequently in extrasolar planetary systems, not just this one, resulting from strong instabilities. So, while planetary systems around other stars may be common, the kinds of systems that could support life, which, like our solar system, presumably must remain stable over very long time scales, may not be so common.”

The computer simulations are reported in the April 14 issue of the journal Nature by Ford, Rasio and Verene Lystad, an undergraduate student majoring in physics at Northwestern. Ford was a student of Rasio’s at the Massachusetts Institute of Technology before pursuing graduate studies at Princeton University and arriving at UC Berkeley in 2004.

The planetary system around Upsilon Andromedae is one of the most studied of the 160-some systems with planets discovered so far outside our own solar system. The inner planet, a “hot Jupiter” so close to the star that its orbit is only a few days, was discovered in 1996 by UC Berkeley’s Geoff Marcy and his planet-hunting team. The two outer planets, with elongated orbits that perturb each other strongly, were discovered in 1999. These three, huge, Jupiter-like planets around Upsilon Andromedae comprised the first extrasolar multi-planet system discovered by Doppler spectroscopy.

Because of the unusual nature of the planetary orbits around Upsilon Andromedae, Marcy and his team have studied it intensely, making nearly 500 observations – 10 times more than for most other extrasolar planets that have been found. These observations, the wobbles in the star’s motion induced by the orbiting planets, allow a very precise charting of the planets’ motions around the star.

“The observations are so precise that we can watch and predict what will happen for tens of thousands of years in the future,” Ford said.

Today, while the innermost planet huddles close to the star, the two outer planets orbit in egg-shaped orbits. Computer simulations of past and future orbital changes showed, however, that the outer planets are engaged in a repetitive dance that, once every 7,000 years, brings the orbit of the middle planet to a circle.

“That property of returning to a very circular orbit is quite remarkable and generally doesn’t happen,” Ford said. “The natural explanation is that they were once both in circular orbits, and one got a big kick that caused it to become eccentric. Then, the subsequent evolution caused the other planet to grow its eccentricity, but because of the conservation of energy and angular momentum, it returns periodically to a very nearly circular orbit.”

Previously, astronomers had proposed two possible scenarios for the formation of Upsilon Andromedae’s planet system, but the observational data was not yet sufficient to distinguish the two models. Another astronomer, Renu Malhotra at the University of Arizona, had previously suggested that planet-planet scattering might have excited the eccentricities in Upsilon Andromedae. But an alternative explanation claimed that interactions among the planets and a gas disk surrounding the star could also have produced such eccentric orbits. By combining additional observational data with new computer models, Ford and his colleagues were able to show that interactions with a gas disk would not have produced the observed orbits, but that interactions with another planet would naturally produce them.

“The key distinguishing feature between those theories was that interactions with an outer disk would cause the orbits to change very slowly, and a strong interaction with a passing planet would cause the orbits to change very quickly compared to the 7,000-year time scale for the orbits to evolve,” Ford said. “Because the two hypotheses make different predictions for the evolution of the system, we can constrain the history of the system based on the current planetary orbits.”

Ford said that as the planets formed inside a disk of gas and dust, the drag on the planets would have kept their orbits circular. Once the dust and gas dissipated, however, only an interaction with a passing planet could have created the particular orbits of the two outer planets observed today. Perhaps, he noted, the perturbing planet was knocked into the inner planets by interactions with other planets far from the central star.

However it started, the resulting chaotic interactions would have created a very eccentric orbit for the third planet, which then also gradually perturbed the second planet’s orbit. Because the outer planet dominates the system, over time it perturbed the middle planet’s orbit enough to deform it slowly into an eccentric orbit as well, which is what is seen today, although every 7,000 years or so, the middle planet returns gradually to a circular orbit.

“This is what makes the system so peculiar,” said Rasio. “Ordinarily, the gravitational coupling between two elliptic orbits would never make one go back to a nearly perfect circle. A circle is very special.”

“Originally the main objective of our research was to simulate the Upsilon Andromedae planetary system, essentially in order to determine whether the outer two planets lie in the same plane like the planets in the solar system do,” said Lystad, who started working with Rasio when she was a sophomore and did many of the computer integrations as part of her senior thesis. “We were surprised to find that, for many of our simulations, it was difficult to tell whether the planets were in the same plane due to the fact that the middle planet’s orbit periodically became so very nearly circular. Once we noticed this strange behavior was present in all of our simulations, we recognized it as an earmark of a system that had undergone planet-planet scattering. We realized there was something much more interesting going on than anyone had found before.”

Understanding what happened during the formation and evolution of Upsilon Andromedae and other extrasolar planetary systems has major implications for our own solar system.

“Once you realize that most of the known extrasolar planets have highly eccentric orbits (like the planets in Upsilon Andromedae), you begin to wonder if there might be something special about our solar system,” Ford said. “Could violent planet-planet scattering be so common that few planetary systems remain calm and habitable? Fortunately, astronomers – led by Geoff Marcy, a professor of astronomy at UC Berkeley – are diligently making the observations that will eventually answer this exciting question.”

The research was supported by the National Science Foundation and UC Berkeley’s Miller Institute for Basic Research.

## Orbit Simulator

The above demo shows how a body behaves when under the influence of the gravity of a much more massive object. In our example, we have chosen this to be a moon orbiting a planet, but it could equally be a planet orbiting a star.

You can click anywhere on the demo to reposition the moon. And clicking and dragging from within the moon will display an arrow. The length and direction of this arrow gives the moon an initial velocity, which affects the overall shape of the orbit.

Newton's law of gravitation tells us that the force acting on the moon will be [ F = frac<>> ]

Where ( M ) and ( m ) are the masses of the planet and moon respectively ( G ) is the universal gravitational constant, which has a value of ( 6.67384 imes mathrm <10^<-11>m^3 kg^ <-1>s^<-2>> ) ( r ) is the distance between the centers of each body, and ( hat ) is the unit vector pointing along the direction or ( r ).

The planet will also experience a force equal in magnitude but opposite in direction to the one the moon experiences. However, because the planet is much more massive than the moon, the acceleration will be much lower, and for the sake of simplicity, is ignored in this demonstration.