(Henry Spencer) wrote in message ...
In article ,
Bill Bogen wrote:
It's the "lose some velocity" part that's hard...

But an object _could_ (very small chance, I admit) be in heliocentric
orbit and yet pass over the Earth at just the right speed to enter a
circular polar orbit at 20310.8 km radius, could it not?

Unfortunately, no, because Earth's gravity will accelerate it as it
approaches. If it arrives from infinity, its speed must be at least
escape velocity (for that distance), which is about 1.4x circular-orbit
velocity.

So it doesn't arrive from infinity but rather from an orbit closer to
the Sun so Earth accelerates it to just the right velocity for a
circular polar orbit.

snip
In general, three-body systems which are not "hierarchical" -- one close
pair plus a distant third -- over time have a strong tendency to lose one
body by ejection.

And yet Jupiter has a number of moons in pretty stable orbits, over
millenia.

Those cases are not really three-body systems, because Jupiter dominates
the situation so overwhelmingly. Interactions between the moons are minor
by comparison. (Sometimes they are non-trivial -- e.g. the resonance with
Europa and Ganymede that maintains the slight eccentricity of Io's orbit
and hence its internal tidal heating -- but not to the extent of actually
altering another moon's orbit substantially.)

But if Cynthia is 25 times closer to the Earth than to Luna, wouldn't
Earth's influenece overwhelm Luna's?