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A planet orbits around its sun on an elliptic orbit, and loses mass slowly due to evaporation. How will the parameters of the orbital ellipse change as a function of time? Could we do a generalisation and mathematically model it?

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  • $\begingroup$ As a curiosity, is this a homework question, or for "worldbuilding" consideration, or?? $\endgroup$ – Fattie Oct 15 '16 at 11:39
  • $\begingroup$ @JoeBlow Nope this is not a HW question. If it were, I would have a used a HW tag. $\endgroup$ – Spoilt Milk Oct 15 '16 at 11:49
  • $\begingroup$ If you just mean in a Keplerian sense, as Earth gets lighter the orbital path would be identical but, let me think, slower, the year would be longer. Mass does not come in to Kepler's laws. $\endgroup$ – Fattie Oct 15 '16 at 12:05
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    $\begingroup$ @JoeBlow Not in a keplerian sense. $\endgroup$ – Spoilt Milk Oct 15 '16 at 12:14
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The mass of a planet does not affect its orbit significantly unless it is a very large planet. On the opposite end of the spectrum would be a very small mass planet that was evaporating, and that is essentially what a comet is. It's all Keplerian, though comets can have their orbits affected slightly by the tiny push they get from the evaporating gases. So it's not the change in mass, but how the evaporation actually happens, but this is a small effect. Even a large planet like Jupiter does not affect the Sun much (the Sun orbits around a point that is not even external to the Sun), so losing mass would not affect the orbit of Jupiter in any significant way either.

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  • $\begingroup$ So how does the evaporation happen and how is this measured and analysed? Even if the effect is small, how is it analysed? $\endgroup$ – Spoilt Milk Oct 15 '16 at 13:02
  • $\begingroup$ Evaporation of comets is what leads to their tails, which we have observed up close using space missions. We also track their trajectories, and note small deviations from Keplerian orbit, both from the gravity of other planets, and from impulses from the evaporation. The latter produce small unpredictable kicks, but again it is not the change in mass that matters, it is how evaporation can act like a very tiny jet engine. $\endgroup$ – Ken G Oct 15 '16 at 22:52
  • $\begingroup$ so would the comet follow a hyperbolic trajectory as it comes closer to the sun? $\endgroup$ – Spoilt Milk Oct 16 '16 at 5:21
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    $\begingroup$ To nitpick a point you made, the point the sun orbits (the barycenter of the solar system) is occasionally outside of the sun, when Jupiter and Saturn and some of the ice giants line up. $\endgroup$ – Cody Nov 14 '16 at 17:49
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    $\begingroup$ @Cody is correct. The solar system barycentre is frequently external to the Sun. $\endgroup$ – Rob Jeffries Nov 14 '16 at 23:58

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