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Thread: Trojan gas giants?

  1. #1
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    Trojan gas giants?

    How's that for ridiculous sci-fi?

    Lets say there's a star similar to our sun. In a low-eccentricity orbit around that star is a very massive jovian. Say, about, 11 Jupiters. Could a significantly smaller gas giant, say, a Uranus-sized planet, be able to remain in one of the trojan lagrangian spots of the 11-jupiter-mass planet's orbit?

  2. #2
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    The classic three-body problem has a stable solution if the central mass is more than about 25 times the mass of the second mass and if the third body is of negligible mass. You can look that up easily in many places; for example,

    http://www.cdeagle.com/ommatlab/crtbp.pdf

    Now, if the third body has a non-negligible mass, the analysis is more difficult. I recall a thread on the BAUT fora a few years ago which discussed this very problem. As I recall, tony873004 provided some very nice numerical results -- can he or anyone else find this thread? -- which suggested that as long as the combined mass of bodies two and three is less than about 4 percent of the central body, the orbit is _relatively_ stable on reasonably long time scales.

    Since the mass of the Sun is of order 1000 times that of Jupiter, a system consisting of a) a solar-mass star, b) a planet 11 times Jupiter's mass and c) another planet of roughly Jupiter's mass, would satisfy the condition mentioned above: total mass of bodies two and three is less than about 4 percent that of the central star.

  3. #3
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    Actually, the third body is a Uranus mass object, which should probably work out in its favor?

  4. #4
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    Quote Originally Posted by PlutonianEmpire View Post
    How's that for ridiculous sci-fi?

    Lets say there's a star similar to our sun. In a low-eccentricity orbit around that star is a very massive jovian. Say, about, 11 Jupiters. Could a significantly smaller gas giant, say, a Uranus-sized planet, be able to remain in one of the trojan lagrangian spots of the 11-jupiter-mass planet's orbit?
    1:1 resonances are considered an open possibility that some planet searchers are looking for. So I don't think it's ridiculous. The mass ratios they talk about are much closer than your example.

  5. #5
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    Quote Originally Posted by StupendousMan View Post
    Now, if the third body has a non-negligible mass, the analysis is more difficult. I recall a thread on the BAUT fora a few years ago which discussed this very problem. As I recall, tony873004 provided some very nice numerical results -- can he or anyone else find this thread? -- which suggested that as long as the combined mass of bodies two and three is less than about 4 percent of the central body, the orbit is _relatively_ stable on reasonably long time scales.
    These might be relevant.

    http://www.bautforum.com/showthread.php/38142.html
    http://www.bautforum.com/showthread.php/36345.html

    I tried searching google with the terms tony873004 site:bautforum.com, and added phrases like 3-body, jupiter, trojan. Guaranteed to find plenty interesting threads!
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  6. #6
    Quote Originally Posted by StupendousMan View Post
    As I recall, tony873004 provided some very nice numerical results -- can he or anyone else find this thread? -- which suggested that as long as the combined mass of bodies two and three is less than about 4 percent of the central body, the orbit is _relatively_ stable on reasonably long time scales...
    http://www.bautforum.com/showthread....Earth-changes?

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