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Thread: Planetary Orbits

  1. #1

    Planetary Orbits

    Let's say, for the sake of argument, that Venus was in the orbit of Earth (and also had a moon like ours). Let's also say that Mars was a superterra with twice the mass of Earth (and its own moon/s), but in the same orbit. Earth and its moon exist somewhere between these two. What should its orbit be?

    I'm trying to be more specific as to a question I had asked before involving having three inhabitable planets in our solar system: http://www.bautforum.com/showthread....tem?highlight=

    I wanted to use this for a scifi setting I'm planning to write, but I wasn't sure where to put the orbits of three Earth-like worlds.

    Thanks in advance!

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    You could have three Earth-like moons orbiting a Jupiter-like object, which itself is in an Earth-like orbit around a Sun-like star. This would get you over the issues of orbit stability of three planets in similar orbits.
    Forming opinions as we speak

  3. #3
    Quote Originally Posted by antoniseb View Post
    You could have three Earth-like moons orbiting a Jupiter-like object, which itself is in an Earth-like orbit around a Sun-like star. This would get you over the issues of orbit stability of three planets in similar orbits.
    Wouldn't the radiation coming off the Jupiter-like object cause a problem, though? I suppose they could be far enough away for it to not be a problem, but I'm not sure how for that would need to be.

    I had originally not wanted Earth to be too far from its current place, but I'm really not sure how much farther from the sun Venus would need to have been to have an Earth-like habitable environment. I'm fairly sure if it was too close to Earth there would be issues with their orbits, but I'm not sure how the dynamics would work. Similarly having Minerva (Mars but with water), is something I want to sound plausible.

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    An Earth-like planets atmosphere and magnetic field would protect it from the Jupiter-like planet's radiation belts even if it were in the heaviest part of it... but the planets would need to be further out, because if they were too close, like Io, they'd be too volcanic/seismic for any reasonable civilization to cope with.
    Forming opinions as we speak

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    Io is volcanic NOT because of being close to Jupiter (that is quite irrelevant) but because it is perturbed by the resonance with Europa (and Callisto).

    Having more than one Earth sized satellite gets inconveniently strong tidal forces even with nonresonant orbits. With the exception of having the same orbit.

    Does someone know the exact stability condition for a four body system where the trojan and the achaian have nonnegligible masses relative to the secondary and therefore perturb each other?

  6. #6
    Quote Originally Posted by antoniseb View Post
    An Earth-like planets atmosphere and magnetic field would protect it from the Jupiter-like planet's radiation belts even if it were in the heaviest part of it... but the planets would need to be further out, because if they were too close, like Io, they'd be too volcanic/seismic for any reasonable civilization to cope with.
    True, especially if the inner one had the relative orbit of Callisto. Themisto and Leda orbits could work for the other two. Do you think Io, Europa and Ganymede would also work? If this planet is in the habitable zone, it could easily have captured any number of protoplanets. Should there also be some further out? and what other planets in separate orbits might make sense?

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    How about habitable Trojan and Achaian?

  8. #8
    Quote Originally Posted by chornedsnorkack View Post
    How about habitable Trojan and Achaian?
    If they can work. My line of thought was: Earth is habitable. Venus is nearly the same mass as Earth. If Venus was in Earth's orbit it would probably be habitable.

    My problem is that if Venus was in Earth's obit, and Earth was still around, then I'm not sure where Earth would be. Similarly if Mars was larger - the same mass as Earth or a bit more - it too could be habitable. It just seemed a bit easier figuring out the orbits for planets in separate orbits than to figure out how it would work with them being moons of the same planet.

  9. #9
    Quote Originally Posted by chornedsnorkack View Post
    Io is volcanic NOT because of being close to Jupiter (that is quite irrelevant) but because it is perturbed by the resonance with Europa (and Callisto).

    Having more than one Earth sized satellite gets inconveniently strong tidal forces even with nonresonant orbits. With the exception of having the same orbit.

    Does someone know the exact stability condition for a four body system where the trojan and the achaian have nonnegligible masses relative to the secondary and therefore perturb each other?
    Io's proximity to Jupiter is not irrelevant. Tidal force is inversely proportional to the cube of the distance to Jupiter.

    What is "achaian"? I've never heard that term. By the context of your sentence, I'm guessing it means the primary planet?

    You could place Venus and Earth in the same orbit, 60 degrees apart, provided that the mass of (Earth + Venus) is less than about 4% of the mass of the Sun. You could also make Venus and Earth orbit each other, but the evolution of this system might leave present-day Earth with a very long day.

    On this page: http://orbitsimulator.com/formulas/
    are some astronomy calculators I made. Halfway down the page are two called "interior reach" and "exterior reach". You can use these to determine the stability of orbits between the planets.

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    Quote Originally Posted by tony873004 View Post
    Io's proximity to Jupiter is not irrelevant. Tidal force is inversely proportional to the cube of the distance to Jupiter.
    Yes, but if Io had exactly circular, zero eccentricity orbit, then the tidal force would be exactly constant in strength and direction, and only direct influence of Europa and Ganymede would cause some vatiable tidal force.
    Quote Originally Posted by tony873004 View Post
    What is "achaian"? I've never heard that term. By the context of your sentence, I'm guessing it means the primary planet?
    Trojans are 60 degrees behind the secondary on its orbit, achaians 60 degrees ahead of the secondary on the same orbit, thus 120 degrees ahead of trojans.
    Quote Originally Posted by tony873004 View Post
    You could place Venus and Earth in the same orbit, 60 degrees apart, provided that the mass of (Earth + Venus) is less than about 4% of the mass of the Sun. You could also make Venus and Earth orbit each other, but the evolution of this system might leave present-day Earth with a very long day.
    It would leave both with the day length required by their initial angular momenta and masses. Pluto and Charon have 6 day long day and are not evolving anywhere; you might have one orbit with 2 planets tidally locked to each other with 1 day day on both (around 50 000 km distance) AND 60 degrees away on the same orbit (150 million km away) another similar pair, for a total of 4 habitable planets sharing the same year length and insolation.

    That much is plain; but back to 4 body system.

    Jupiter achaians and Jupiter trojans are both of negligible mass; so they do not disturb each other and each group can orbit as if the other Lagrange point were completely vacant.

    But what if one of the Lagrange points does have a body of somewhat appreciable mass? Like, a habitable planet while the secondary is a gas giant?

    How massive object relative to the secondary can exist at one Lagrange point, 120 degrees away from the other, before it makes the other Lagrange point unstable?

  11. #11
    Quote Originally Posted by tony873004 View Post
    Io's proximity to Jupiter is not irrelevant. Tidal force is inversely proportional to the cube of the distance to Jupiter.

    What is "achaian"? I've never heard that term. By the context of your sentence, I'm guessing it means the primary planet?

    You could place Venus and Earth in the same orbit, 60 degrees apart, provided that the mass of (Earth + Venus) is less than about 4% of the mass of the Sun. You could also make Venus and Earth orbit each other, but the evolution of this system might leave present-day Earth with a very long day.

    On this page: http://orbitsimulator.com/formulas/
    are some astronomy calculators I made. Halfway down the page are two called "interior reach" and "exterior reach". You can use these to determine the stability of orbits between the planets.
    Could you give an example of how those are supposed to work? I tried out the period calculator for 1 AU, 1 M_Earth (1 Earth Mass?), and put the result in years (yr) and got 577.0121236653212. What does this mean? Earth's year isn't 577 days long...

    I don't mind a common barycenter, but I'd prefer to have the worlds further apart.

  12. #12
    Io's orbit is not circular, and that's where the energy comes from. The tidal force from Jupiter varies with time over the course of the orbit, flexing the moon. If you compare the force (F=GMm/r^2) between Jupiter and Io at r=perijove and r=apijove you'll find a difference of about 10^21 Newtons. This difference would be significantly less if Io were further from Jupiter.

    If you compare the force between Io and Europa at their closest approach (r=subtract their sma's) vs. their furthest approach (add their sma's) from each other, you'll find a difference of about 4*10^18 N. That's 3 orders of magnitude less. The importance of the resonances from Europa and Ganymede are that they prevent Io's orbit from circularizing.

    Thanks, I never heard of Achaian. I've heard of Trojan and Greek asteroid groups orbiting with Jupiter.

    You can put 3 planets spaced 60 degrees apart (0, 60, 120, etc.). Their mass ratio doesn't matter. They could all have the same mass, provided that their combined mass is less than about 4% of the Sun. There was a nice thread on this forum a few years ago on this topic, but I can't seem to find it now.

  13. #13
    Quote Originally Posted by Indagare View Post
    Could you give an example of how those are supposed to work? I tried out the period calculator for 1 AU, 1 M_Earth (1 Earth Mass?), and put the result in years (yr) and got 577.0121236653212. What does this mean? Earth's year isn't 577 days long...

    I don't mind a common barycenter, but I'd prefer to have the worlds further apart.
    577 years is correct. If Earth were deep in interstellar space where the Sun and other planets couldn't perturb objects in orbit around Earth, then an object that orbited Earth with a semi-major axis of 1 AU, would have a period of 577 years.

    Instead, try entering 1 AU and 1 Sun mass, and you will find that this object has a period of 1 year.


    As for interior and exterior reach formulas:

    For interior reach, choose a value of 1 for aG, 0 for eG, 3 for nint, 1 Earth mass for mG, and 1 Sun mass for Mstar. You should get 0.97AU for your answer.


    For exterior reach, choose a value of 1 for aG, 0 for eG, 3 for next, 1 Earth mass for mG, and 1 Sun mass for Mstar. You should get 1.03 AU for your answer.

    This means that Earth destabalizes the region around the Sun from 0.97 AU to 1.03 AU.

  14. #14
    Quote Originally Posted by tony873004 View Post
    577 years is correct. If Earth were deep in interstellar space where the Sun and other planets couldn't perturb objects in orbit around Earth, then an object that orbited Earth with a semi-major axis of 1 AU, would have a period of 577 years.

    Instead, try entering 1 AU and 1 Sun mass, and you will find that this object has a period of 1 year.


    As for interior and exterior reach formulas:

    For interior reach, choose a value of 1 for aG, 0 for eG, 3 for nint, 1 Earth mass for mG, and 1 Sun mass for Mstar. You should get 0.97AU for your answer.


    For exterior reach, choose a value of 1 for aG, 0 for eG, 3 for next, 1 Earth mass for mG, and 1 Sun mass for Mstar. You should get 1.03 AU for your answer.

    This means that Earth destabalizes the region around the Sun from 0.97 AU to 1.03 AU.
    Okay. What do the numbers in figure 2 mean, exactly?

  15. #15
    I don't know. I believe the author of the paper empirically derived that formula. I simply made a javascript calculator of his formulas. You adjust that number if you want your planets to have elliptical orbits. Leave it at 3 for circular orbits. The formula is in good agreement with another method I use to test stability. That method is to see whether a planet's semi-major axis changes by more than 1% after several hundred orbits.

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    Quote Originally Posted by tony873004 View Post
    Io's orbit is not circular, and that's where the energy comes from. The tidal force from Jupiter varies with time over the course of the orbit, flexing the moon. If you compare the force (F=GMm/r^2) between Jupiter and Io at r=perijove and r=apijove you'll find a difference of about 10^21 Newtons. This difference would be significantly less if Io were further from Jupiter.
    Tidal force varies with cube of distance, not square, because it is the difference of the gravitational acceleration across the size of the body where tides are raised.
    Quote Originally Posted by tony873004 View Post

    Thanks, I never heard of Achaian. I've heard of Trojan and Greek asteroid groups orbiting with Jupiter.

    You can put 3 planets spaced 60 degrees apart (0, 60, 120, etc.). Their mass ratio doesn't matter. They could all have the same mass, provided that their combined mass is less than about 4% of the Sun. There was a nice thread on this forum a few years ago on this topic, but I can't seem to find it now.
    Obviously if you put 3 planets, namely 2 massive ones 120 degrees apart from each other and a small test body in the middle, it would be unstable as 2 planets 120 degrees from each other would be in the absence of the third.

  17. #17
    Quote Originally Posted by chornedsnorkack View Post
    Obviously if you put 3 planets, namely 2 massive ones 120 degrees apart from each other and a small test body in the middle, it would be unstable as 2 planets 120 degrees from each other would be in the absence of the third.
    You're right, your reasoning makes sense. Also, I just simulated it. The middle massless body goes flying off, while the 2 massive bodies continue orbiting in 1:1 resonance to each other. So I guess the ratio only applies to a pair, rather than a triplet.

    Quote Originally Posted by chornedsnorkack View Post
    Tidal force varies with cube of distance, not square, because it is the difference of the gravitational acceleration across the size of the body where tides are raised.
    Right again. I forgot to compare the force on the near side to the force on the far side. Doing that, I get that the tidal force on Io due to Jupiter is 1.113x1018 N at perihelion and 1.086x1018 N . The difference is 2.659x1016 N.

    When Io and Europa are at their closest, I get a tidal force on Io from Europa of 1.372x1014 N. When they are at their farthest, I get a tidal force of 1.628x1012 , for a difference of 1.356x1014 N.

    That's the point I was trying to make is that Jupiter flexes Io much more than Europa flexes Io. Additionally, Jupiter flexes Io more often than Europa does. Jupiter min to max is half of Io's period, while Europa's min to max is half of the Io/Europa synodic period.

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    Quote Originally Posted by Indagare View Post
    If they can work. My line of thought was: Earth is habitable. Venus is nearly the same mass as Earth. If Venus was in Earth's orbit it would probably be habitable.

    My problem is that if Venus was in Earth's obit, and Earth was still around, then I'm not sure where Earth would be. Similarly if Mars was larger - the same mass as Earth or a bit more - it too could be habitable. It just seemed a bit easier figuring out the orbits for planets in separate orbits than to figure out how it would work with them being moons of the same planet.
    It seems that if Venus was an Earth-Moon Trojan, then the Earth and moon would be a Venus Achian (or Greek). One issue is that L4 and L5 become unstable when M1 < 25M2, as we would have in the Earth-Venus case.

    The other Lagrange points for each would be disrupted by the presence of Venus-Earth. The equivalent of the L1-L2-L3 line would be rotated towards the Earth-moon, since it is heavier. For a system with masses similar to Venus and Earth-Moon the L1-L2 points would be 25.6 degrees from Earth and 34.4 degrees from Venus, and L3 would be 180 degrees from these.

    Alternatively, the Earth-like planet could have a Venus-like Theia in a horseshoe orbit that brings the planets close enough that their gravity swaps their orbital positions every few centuries. A comet on a path that would threaten to alter this balance and allow the planets to collide would be an interesting story line.

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    Quote Originally Posted by utesfan100 View Post
    It seems that if Venus was an Earth-Moon Trojan, then the Earth and moon would be a Venus Achian (or Greek). One issue is that L4 and L5 become unstable when M1 < 25M2, as we would have in the Earth-Venus case.

    The other Lagrange points for each would be disrupted by the presence of Venus-Earth. The equivalent of the L1-L2-L3 line would be rotated towards the Earth-moon, since it is heavier. For a system with masses similar to Venus and Earth-Moon the L1-L2 points would be 25.6 degrees from Earth and 34.4 degrees from Venus, and L3 would be 180 degrees from these.

    Alternatively, the Earth-like planet could have a Venus-like Theia in a horseshoe orbit that brings the planets close enough that their gravity swaps their orbital positions every few centuries. A comet on a path that would threaten to alter this balance and allow the planets to collide would be an interesting story line.
    Suppose we were considering the possibility of a Theia-Gaia pair in a horseshoe orbit prior to a collision forming the Earth-Moon system. Assuming an 8:1 mass ratio, is it possible to determine the mean number of years between orbital exchange given the mean angle of separation at closest approach?

  20. #20
    Quote Originally Posted by utesfan100 View Post
    Alternatively, the Earth-like planet could have a Venus-like Theia in a horseshoe orbit that brings the planets close enough that their gravity swaps their orbital positions every few centuries. A comet on a path that would threaten to alter this balance and allow the planets to collide would be an interesting story line.
    The comet would be an interesting story in itself. I'd imagine it would have to be at least the size of a large moon to deflect a Venus-Theia into a collision trajectory with a proto-Earth. Horseshoe orbits are quite stable.

    see http://www.scielo.br/pdf/cam/v24n1/06v24n1.pdf
    "Note that the trajectories in the range 0.9943 < r < 1.0057 AU, believed to
    be trajectories of collision with the Earth (previous section), are in fact stable
    horseshoe or even tadpole orbits. The actual minimum approximation one of
    these trajectories can get from the Earth is more than 10 degrees, without any chance
    of collision. This two bodies ‘‘repel’’ each other azimuthally and never come
    in close proximity. In fact, the width of the stable co-orbital region is delimited
    at least in the range 0.990 = r = 1.010 AU. Eventually, a collision between an
    asteroid and the Earth can occur for trajectories just outside of the border of the
    stable region[...]"

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    Quote Originally Posted by chornedsnorkack View Post
    Tidal force varies with cube of distance, not square, because it is the difference of the gravitational acceleration across the size of the body where tides are raised.


    Obviously if you put 3 planets, namely 2 massive ones 120 degrees apart from each other and a small test body in the middle, it would be unstable as 2 planets 120 degrees from each other would be in the absence of the third.
    I'm not sure if the latter statement is correct .
    A three body coorbital configuration (-60°,0°,60°) is dynamically stable , under the conditions : Sum Masses < 0.04 Mprimary .
    The planets will librate with a period depending upon the total mass of the three coorbitals ( and maybe depending upon the mass distribution ) . For an Earth-Earth-Earth configuration I get a period of about 190 years and a minimal distance of the two outermost of 1.226 AU .

    Whats more : I've also simulated a configuration of (-60°,0°,60°) with masses : ( Mearth , 1 µgram , Mearth ) and got a dynamically stable system over more than 3000 years . This system has a libration period of ca. 160 years . The minimal distance becomes 0.5153 AU between the outermost planets . Also in this configuration the "test" mass seems to stay right in the middle of the outermost planets , without any sign of instability .

  22. #22
    Quote Originally Posted by frankuitaalst View Post
    Whats more : I've also simulated a configuration of (-60°,0°,60°) with masses : ( Mearth , 1 µgram , Mearth ) and got a dynamically stable system over more than 3000 years . This system has a libration period of ca. 160 years . The minimal distance becomes 0.5153 AU between the outermost planets . Also in this configuration the "test" mass seems to stay right in the middle of the outermost planets , without any sign of instability .
    I get the same results as you if the outer masses are 1 Earth mass, and the trio is orbiting the Sun at 1 AU. But when I make them 1 Jupiter mass, the middle test particle becomes unstable as chornedsnorkack mentioned. A pair of Jupiters is < 0.04 Msol. So I guess a new ratio is needed for 0,60,120 trios.

  23. #23
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    Quote Originally Posted by tony873004 View Post
    I get the same results as you if the outer masses are 1 Earth mass, and the trio is orbiting the Sun at 1 AU. But when I make them 1 Jupiter mass, the middle test particle becomes unstable as chornedsnorkack mentioned. A pair of Jupiters is < 0.04 Msol. So I guess a new ratio is needed for 0,60,120 trios.
    When I put 3 Jupiters masses at 1Au from Sol at -60,0,60 I get a pattern in which the Jupiters circle around the L4 L5 points in a tadpole orbit .
    The period for circling around the L4 resp L5 points is about 10 years . But I think this pattern is maintained , at least for more than 3000 years .
    Here's a picture of the orbits in rotating frame.

    In a second run I've increased the Jupiter masses to 10 MJup each ( their sum is about 0.03 MSun ) .
    This system is unstable . So you're right . The rule "< 0.04 Msun " doesn't apply here exactly .
    Attached Images Attached Images

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    Quote Originally Posted by Wot? View Post
    The comet would be an interesting story in itself. I'd imagine it would have to be at least the size of a large moon to deflect a Venus-Theia into a collision trajectory with a proto-Earth. Horseshoe orbits are quite stable.

    see http://www.scielo.br/pdf/cam/v24n1/06v24n1.pdf
    "Note that the trajectories in the range 0.9943 < r < 1.0057 AU, believed to
    be trajectories of collision with the Earth (previous section), are in fact stable
    horseshoe or even tadpole orbits. The actual minimum approximation one of
    these trajectories can get from the Earth is more than 10 degrees, without any chance
    of collision. This two bodies ‘‘repel’’ each other azimuthally and never come
    in close proximity. In fact, the width of the stable co-orbital region is delimited
    at least in the range 0.990 = r = 1.010 AU. Eventually, a collision between an
    asteroid and the Earth can occur for trajectories just outside of the border of the
    stable region[...]"
    With an 8:1 mass ratio leading to an Earth-Moon mass, the smaller Theia would be Mars sized. If the prior horseshoe orbit was oscillating at near the critical region it would not take as much energy to push it into the unstable region.

    Further, the stable region might become more complicated when orbital inclination and eccentricity are added to the model.

    I will admit that the collision region is a far narrower window than the unstable region, making a collision on the order of millions of years far more likely than centuries.

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    Quote Originally Posted by frankuitaalst View Post
    When I put 3 Jupiters masses at 1Au from Sol at -60,0,60 I get a pattern in which the Jupiters circle around the L4 L5 points in a tadpole orbit .
    The period for circling around the L4 resp L5 points is about 10 years . But I think this pattern is maintained , at least for more than 3000 years .
    Here's a picture of the orbits in rotating frame.

    In a second run I've increased the Jupiter masses to 10 MJup each ( their sum is about 0.03 MSun ) .
    This system is unstable . So you're right . The rule "< 0.04 Msun " doesn't apply here exactly .
    Since the Lagrange Points are already expanding to a tadpole orbit, I would suggest that this already shows the orbits to be unstable. I would expect this to be confirmed within your model by showing that the tadpole orbits are expanding with time.

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    Quote Originally Posted by utesfan100 View Post
    Since the Lagrange Points are already expanding to a tadpole orbit, I would suggest that this already shows the orbits to be unstable. I would expect this to be confirmed within your model by showing that the tadpole orbits are expanding with time.
    Well , I paid attention to the evolution of the tadpole orbits when simulating the case of the three MJup bodies at 1Au . The tadpoles are there almost from the start of the simulation and do not seem to expand in time .
    Therefor I guess this system is dynamically stable , at least in the 3000 years I simulated .

    Edit : ran this system now for 20000 years . Tadpoles remain stable.
    Last edited by frankuitaalst; 2012-May-02 at 09:06 PM. Reason: addition

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    Quote Originally Posted by frankuitaalst View Post
    Well , I paid attention to the evolution of the tadpole orbits when simulating the case of the three MJup bodies at 1Au . The tadpoles are there almost from the start of the simulation and do not seem to expand in time .
    Therefor I guess this system is dynamically stable , at least in the 3000 years I simulated .

    Edit : ran this system now for 20000 years . Tadpoles remain stable.
    I am thinking the 4 body system can be stable when L4=L5. If one of these masses were 1.01% more than the other I suspect it would no longer be stable. The case where the central mass is negligible I think reflects that for MEarth at 120 degrees separation the force between the planets is negligible on the scales of 3000 years.

  28. #28
    Quote Originally Posted by utesfan100 View Post
    With an 8:1 mass ratio leading to an Earth-Moon mass, the smaller Theia would be Mars sized. If the prior horseshoe orbit was oscillating at near the critical region it would not take as much energy to push it into the unstable region.

    Further, the stable region might become more complicated when orbital inclination and eccentricity are added to the model.
    Yes, you're right that there are horsehoe orbits that are unstable due to lying ouside the stable 10% band, or have eccentric orbits or inclinations. But I suppose my thinking was that if a body can accrete enough material to be Venus-sized, or even Theia-sized, then it would presumably have inhabited a securely stable orbit as it grew. (It raises the question though of why, with all the stable Lagrange points there are in the solar system, nothing of any significant mass remains. Would the Late Heavy Bombardment be enough to dislodge them from the inner rocky Primaries, and planet migration account for those of the outer Gas Giants?)

  29. #29
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    Quote Originally Posted by Wot? View Post
    Yes, you're right that there are horsehoe orbits that are unstable due to lying ouside the stable 10% band, or have eccentric orbits or inclinations. But I suppose my thinking was that if a body can accrete enough material to be Venus-sized, or even Theia-sized, then it would presumably have inhabited a securely stable orbit as it grew. (It raises the question though of why, with all the stable Lagrange points there are in the solar system, nothing of any significant mass remains. Would the Late Heavy Bombardment be enough to dislodge them from the inner rocky Primaries, and planet migration account for those of the outer Gas Giants?)
    The question why there are not many bodies in the stable Lagrangian points has been investigated by a lot of scientists . The clue to the answer is that , altough the Lagrangian L4-L5 are stable for a 3 body system , the situation becomes very complicated for most planets due to the mutual interactions between the planets of the solar system . Exception is Jupiter which is massive enough to hold a lot of Trojans .
    The lifetime of Trojans around most other planets seems to be significantly smaller than the lifetime of our solar system , meaning that most of the Trojans have moved .

  30. #30
    Thank you.

    Can I press you further? Do you know what the mainstream opinion is for the idea of Theia as a Trojan co-orbital to a proto-Earth?

    It seems that Theia's accretion origins as a Trojan are, on the one hand, inhibited by the perturbing prescence of other planetary bodies, and, on the other hand, its proposed collision trajectory with proto-Earth cannot be caused by a simple dislodgement from L4/L5. Is it now considered that Theia originated from further afield than what one popular explanation suggests? (
    ***
    In other words, was Theia likely to be a protoplanet in its own right? or even an asteroid?
    http://news.nationalgeographic.com/n...collision.html

    If these difficulties with Theia are granted it would seem that Indagare's proposal of 3 planets sharing Earth's orbit are going to look a little unrealistic, making AntoniseB's suggestion the most likely. Otherwise I suppose you would have to propose a system where the disk around a protostar was in a tight, dense ring that only accreted into just 3 planets, all sharing the same orbit, which also seems unnaturally contrived.

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