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 | | From: | Wayne Throop | | Subject: | Re: can a moon sustain life in a solar system? | | Date: | Sat, 22 Jan 2005 20:05:12 GMT |
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 | : "Gene Ward Smith"
: I'm still curious about this question: given a star of the mass of the
: Sun, a planet of N^3 lunar masses orbiting at a distance of N times
: the lunar distance from an earth-mass planet in reasonably circular
: orbits, what can be said about the long-term stablility of the
: resulting 3-body system?
( I assume you mean "an earth-mass planet orbiting a planet of N^3
lunar masses at N times lunar distance, the pair orbiting about 1au
from the star". Unless I'm not understanding the discussion upthread. )
IIRC a rule of thumb is that the earthlike planet would have to be
close enough to the gas giant (or far enough from the star, but that's
a fixed distance onaccounta requirement for insolation) so that the
stellar tides would be pulling the planets apart less strongly than
the gravitational acceleration of the GG on the ELP. The distance
would actually have to be quite a bit smaller than to make these equal
iirc, but it's a finger-to-the-wind initial estimate on an upper bound,
I guess. If I've done my arithmetic right, that point is about 1e10
meters from a jupiter-mass GG, which seems more than large enough to
fit the situation above. No, wait, we want a Uranus-sized GG... um,
that one doesn't seem to fit.
As always, my arithmetic is slapdash and to-be-skeptical-about,
but that's what I get.
Interestingly, though I haven't shown it analytically, I think one of
the crazy Velkovskian/Saturnian orbits that have been proposed would
actually have been stable. It doesn't behave as the Saturnians require,
so their scheme still doesn't hold water (or much of anything else),
but it'd be stable (naict by numerical integration), the ELP isn't at
the GG lagrange point, and has the distance between the GG and ELP too
large for the above rule of thumb.
See http://sheol.org/throopw/grubaugh-synch-retro.html
( You folks via sci.astro should excuse the crudity of the presentation. )
( Well, other folks should excuse it too. )
"The solar system consists of the sun, jupiter, and some debris."
--- attribution lost...
Wayne Throop throopw@sheol.org http://sheol.org/throopw
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