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View Full Version : Could planets form within the same orbit around a star?



banquo's_bumble_puppy
2006-Feb-15, 12:46 PM
Could planets form within the same orbit around a star? Say - a planet the same distance from it's sun, but on the opposite side?

Fr. Wayne
2006-Feb-15, 01:25 PM
Quite possible in another star system. Here we have Earth and Moon in practically the same orbit, although men of science prefer to call the Moon, a moon because of size.

Kullat Nunu
2006-Feb-15, 01:38 PM
No, such system would be unstable. However, a Trojan planet orbiting 60 degrees before or after the larger planet might be possible, provided it is tiny compared to the larger planet. I don't know if it is possible to have a Epimetheus/Janus style co-orbital system, where the planets regularly swap their orbits.

baric
2006-Feb-15, 01:50 PM
Quite possible in another star system. Here we have Earth and Moon in practically the same orbit, although men of science prefer to call the Moon, a moon because of size.

1. The moon orbits around the Earth, so therefore it's orbit around the Sun is going to be very similar to that of Earth.

2. General consensus is that the Moon did not form as a separate planet, but as the coalesced remnants of a planetary impact.

Doodler
2006-Feb-15, 08:24 PM
No, such system would be unstable. However, a Trojan planet orbiting 60 degrees before or after the larger planet might be possible, provided it is tiny compared to the larger planet. I don't know if it is possible to have a Epimetheus/Janus style co-orbital system, where the planets regularly swap their orbits.

At planetary scales, that would cause some hardcore seismic activity around the time of the swap, wouldn't it?

As for a trojan, that would be a neat trick. One of the features of planetary formation is that the main body in an orbital region tends to clean house and absorb the bulk of the debris in the area. Secondly, you're also dealing with a young system where orbital paths are not yet stable, even this solar system has signs of a LOT of migrations and path shifts in from the early days. Any trojan set up that would form would almost need to migrate into being, rather than form there.

tony873004
2006-Feb-15, 08:51 PM
Actually, for a trojan system, one planet doesn't need to be smaller than the other. They can be the same mass. The only condition is that the ratio of their total combined mass vs. the star's mass must not exceed a certain value. Off the top of my head, i think it's about 1:25.

Kullat Nunu
2006-Feb-15, 09:04 PM
That value is correct. However, the Trojan object must be negligible in mass compared to the two others.

See the story of Theia (http://en.wikipedia.org/wiki/Theia_%28planet%29).

Ara Pacis
2006-Feb-15, 11:52 PM
Well, in a protoplanetary disc, the coalescence of one rock might cause the formation of another rock at the Solar L3 point. However, the distribution of material might mean that they keep pace or that one surpasses the other in size. So, which one is the primary and which one is the Lagrange object?

tony873004
2006-Feb-16, 01:07 AM
I think that Theia theory gets it wrong. Janus is 3.6 times as massive as Epimetheus, and they maintain stable horseshoe orbits.

According to:
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002AJ....124..592L&db_key=AST&

We show analytically that an equilateral configuration consisting of a star and two equal-mass planets is linearly stable for mass ratios mu=2mpl/(2mpl+M*)<0.03812.

I also tested this numerically.

In Gravity Simulator, here's an Earth-massed body in Jupiter's Lagrange 4 point. Jupiter is tracing the purple oval in the bottom right of the image, while the Earth-mass object is tracing the smaller oval in the top right corner of the image. This image is a rotating frame, attempting to keep Jupiter still. That's why it traces an oval instead of appearing to orbit the Sun. It is an oval rather than a point because Jupiter speeds up and slows down from its average speed due to a small amount of eccentricity in its orbit. I ran this simulation for a few hundred years, and the Earth-massed object still seems very stable in its Lagrange 4 point.

I also tried it after increasing the the trojan Earth's mass to .1 Jupiter masses, .5 Jm, and equal to Jupiter's mass. They all give the same results. Even a Jupiter-massed planet in Jupiter's Lagrange 4 or 5 would be stable. I ran the Jupiter-massed scenerio for 30,000 years and it show no sign of instablilty. The two masses have a small periodic affect on each other's eccentricities.

http://orbitsimulator.com/orbiter/earthtrojan.GIF

Fr. Wayne
2006-Feb-16, 02:44 AM
Nice colors and visuals! Does article in Universe Today for Feb 15th add anything here. Hmm?

Planetwatcher
2006-Feb-16, 10:28 AM
Originally Posted by Kullat Nunu
No, such system would be unstable. However, a Trojan planet orbiting 60 degrees before or after the larger planet might be possible, provided it is tiny compared to the larger planet. I don't know if it is possible to have a Epimetheus/Janus style co-orbital system, where the planets regularly swap their orbits.

This is quite correct. Two planets in an orbit exactly opposite to each other would be in each other's L3 Lagrange Point.

I would think that planets of simular size at a 120 degree interval might work. In which case you could have up to three planets. But again I think they would have to be simular in size.

Kullat Nunu
2006-Feb-16, 12:02 PM
I think that Theia theory gets it wrong. Janus is 3.6 times as massive as Epimetheus, and they maintain stable horseshoe orbits.

Janus/Epimetheus system is different from the proposed Earth/Theia system. I believe that such co-orbital systems are easily perturbed, which could easily lead to a collision course.

tony873004
2006-Feb-17, 01:28 AM
They can be perturbed from outside influences, but they won't perturb each other out of their orbits. It was the conclusion of the Theia article, that it grew large enough that the Earth : Theia mass ratio made the system unstable.

But the conclusion of the author of the paper I linked to, and the conclusion of the numeric solution I performed is that the Earth : Theia mass ratio is irrelavant. The only relavant ratio is the (Earth mass + Theia mass) : Sun mass.