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Forum » SpaceEngine » Science and Astronomy Discussions » Planetary migration as a star loses its mass? (What is the predicted scale of the effect?)
Planetary migration as a star loses its mass?
Gondor2222Date: Friday, 16.08.2013, 08:56 | Message # 1
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I'm trying to create a few rough "snapshots" of the solar system as it may look at various points in the future but I am unable to find estimates for how much the planets would orbit outwards. Can anyone provide a general equation for the change in semimajor axis size expected for a sufficiently slow mass loss of a parent star OR at least estimates for the following cases for our sun due to the sun's mass loss and expansion?:

  • Migration by start of red giant phase (~6 billion years from now)
  • Migration by the time the star is just about to have a helium flash (~7 billion years from now)
  • Migration after planetary nebula escapes past orbits of planets. (~8 billion years from now)

Ignore perturbations by passing stars from galaxy collisions, Mercury-Jupiter resonance disturbing inner system, etc. please.
 
WatsisnameDate: Friday, 16.08.2013, 20:08 | Message # 2
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Gondor, you may try using this Simulator for Circumstellar Habitable Zones, which contains simple model for planetary migration due to stellar evolution. I don't know if it accounts for gas drag; probably not. Tidal effects are important also, but let's ignore these.

Mass loss and thus migration is negligible until the period from about 7 to 8 billion years from now, when the Sun moves up Red Giant Branch. It then proceeds rapidly as it nears Helium Flash event. Brief pause for the Asymptotic Giant Branch, and then rapid migration again as outer layers are shed as planetary nebula.

Mercury and Venus undoubtedly get destroyed, and Earth's fate is uncertain. Mars probably survives.





 
Gondor2222Date: Saturday, 17.08.2013, 00:52 | Message # 3
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According to the simulator (the numbers it gives, not its description), the factor of increase in the semimajor axes is inversely proportional to the factor of decrease in the star's mass.
 
WatsisnameDate: Saturday, 17.08.2013, 09:01 | Message # 4
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That's exactly correct. smile In pretty math speak, it's


Hopefully that helps you calculate distances of planets at the moments of interest, with simulation giving you the mass of the sun at those times. It won't be perfect, but should give a good general sense.





 
Gondor2222Date: Saturday, 17.08.2013, 09:45 | Message # 5
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And does gas drag tend to make a planet spiral inwards by reducing net centrifugal force? Am I correct in assuming that for a small enough constant amount of gas drag a planet's orbit would form a spiral that semi-locally resembles a circle like:

? (With a far tighter spiral of course)
Also, what is the typical outward velocity of a planetary nebula? I.e. does it move slow enough to allow for significant decay in a planet's orbit?


Edited by Gondor2222 - Saturday, 17.08.2013, 09:48
 
WatsisnameDate: Saturday, 17.08.2013, 12:07 | Message # 6
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Quote (Gondor2222)
And does gas drag tend to make a planet spiral inwards by reducing net centrifugal force?


Mmm, I wouldn't describe it that way; it confuses the physics involved.

Any phenomenon whose explanation invokes centrifugal force may instead be more directly explained by centripetal force. The centripetal force is the real force, whereas centrifugal is the perceived force due to observer being in a non-inertial reference frame. So there is no need to use centrifugal force to explain the effect of gas drag; or even to explain planetary orbits at all. A planet is held in orbit because gravity, a centripetal force, pulls its otherwise straight-line trajectory into an ellipse. A planet experiencing gas drag spirals in because it loses orbital energy via friction with the gas. You can think of it as an object moving through fluid.

I can't see your image by the way. It appears to be a wolfram alpha link, but the page doesn't exist. But yeah, your description sounds right. It'd be analogous to the orbit of a decaying satellite, except satellites encounter exponentially more drag as their orbits decay and so their spirals widen significantly.

Quote (Gondor2222)
Also, what is the typical outward velocity of a planetary nebula? I.e. does it move slow enough to allow for significant decay in a planet's orbit?


Outward velocity of planetary nebula is complex and non-constant. That being said the migration due to gas drag from planetary nebula is probably insignificant compared to migration due to mass loss during the same phase.

I also have to say that you might be putting way more thought than necessary into figuring this all out. The migration of planetary orbits through stellar evolution is really complex stuff! People investigate it with detailed models and simulations and even then the results have large uncertainties. I would recommend just sticking with the results we found above; they're not bad as a first approximation. smile





 
Forum » SpaceEngine » Science and Astronomy Discussions » Planetary migration as a star loses its mass? (What is the predicted scale of the effect?)
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