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A What keeps Rhea stable? Simulation shows Titan-assist escape [solved]

  1. Feb 5, 2017 #1

    D O

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    Hi everyone,

    I have created a simulation of the major bodies in the Solar System, using the exact positions, velocities, and masses etc. at midnight on Jan 10 (as provided by the NASA HORIZONS project). Using Newtonian gravity I numerically simulate the forces between all the bodies (with a very small time interval; about 0.1 seconds) and can focus the centre of the images produced (in a stop-time sort of way) on any planet I want.

    So far I have been very successful; behaviour is as expected - I get the 1:2:4 resonance of the Galilean moons etc.
    However, the Saturn system seems to have strange behaviour; Rhea is significantly affected by Titan (the only other moon I simulated in the Saturn system), and is perturbed to a higher and higher orbit, eventually passing right around Titan in a gravity assist. Rhea then shoots out of the Saturn system like a rocket and orbits the Sun.

    The image shows Rhea (grey), having passed Titan (yellow), on its way out of Saturn (the big yellow ball). The time after the epoch (Jan 10 00:00) is t=1381376 seconds. This would put the picture on the 25th January 2017. I think I would have been aware of such an event if it had happened in real life!

    An animation of the event is available at https://www.outpig.com/files/saturn.mp4

    The bodies I have simulated are:
    Sun, Mercury, Venus, Earth (Moon), Mars, Jupiter (Io, Europa, Ganymede, Callisto), Saturn (Titan, Rhea), Uranus (Titania, Oberon), Neptune (Triton), and Pluto (Charon) for old times' sake ;).

    My reasoning behing these choices was to try to select the bodies I think have the greatest effect on those already picked; I used a list of Solar System major bodies by mass (from Wikipedia) and left out Eris etc. in lieu of Pluto and Charon. For moons, I'm happy with the Jupiter system, but I think the moons in the Saturn system are much closer in mass at the top end.

    My initial thoughts are: Is the behaviour caused by leaving out some important stabilising moon/s? Iapetus, Dione, Tethys, and Enceladus all seem to have mass significant enough to have some influence.

    Rhea is not too close to Saturn so I would not have thought the rings (which I have not modelled) would have anything to do with it, but then I am not familiar with the effects the rings have on the moons and vice versa.

    Just to clarify: I have modelled all the planets as point masses; there is no rotation, atmospheres, tidal forces etc. in the simulation. The sizes of the moons on the images produced have been magnified by 4x so they are visible; this has no effect on the physics (there is no collision detection etc.)
    The images produced are viewed looking top-down on the Solar System (projection onto plane of Earth's orbit, I believe), and are snapshotted at time intervals of 1024 seconds. If the lines look a bit segmented, that is to do with this time interval and does not reflect the accuracy of the underlying simulation.

    I can provide further details upon request. Any ideas?

    Dan O
  2. jcsd
  3. Feb 6, 2017 #2


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    Which integration method did you use?
    What happens if you remove Titan?

    Are you sure you got all masses right? The curvature of the outbound Rhea trajectory looks like your Titan mass is maybe 10% of the Saturn mass, the correct value is about 0.02%.

    If it is not a wrong mass I would expect a problem with the integration method.

    The influence of Titan should be small.
  4. Feb 6, 2017 #3

    D O

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    Thanks for the help! I removed Titan and the orbit was elliptical and worked fine. You're right - I checked the masses, and they are 1000 times too big for both Rhea and Titan. This was because for some reason the mass data for those moons were provided in grams, not kilograms.

    After modifying the code for parsing the data, the system is stable.
  5. Feb 6, 2017 #4


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    I would guess you got the mass of Titan wrong.
    What is the starting time and date of your simulation?
  6. Feb 6, 2017 #5


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  7. Feb 6, 2017 #6


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    I see you already figured it out.
    I noticed that too, that all Saturn's moons are given in grams on the Horizons page, while everything else in the solar system is kg.
  8. Feb 6, 2017 #7

    D O

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    Thanks for helping anyway! Yes, that looks like the result I am now getting.
    I sent an email to the Horizons team and they said they would change them from g to kg for Saturnian cases.
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