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I'm trying to understand the Hill Sphere formula. (Yes, I've already been to Wikipedia.)

I notice that it doesn't take the mass of the satellite into consideration. Is that because the mass of the satellite has no effect, or is it a simplification based on the assumption that the mass of the satellite is very small with respect to the masses of the other two bodies? How would it apply to twin planets?

I found https://www.physicsforums.com/showpost.php?p=1225193&postcount=10" which seems to indicate satellite mass does matter. If so, how should the formula be altered to include the effect of a large satellite?

Also, what about the relative masses of the other two bodies? Is

(I'm looking for a way to calculate

Thank you for your assistance.

I notice that it doesn't take the mass of the satellite into consideration. Is that because the mass of the satellite has no effect, or is it a simplification based on the assumption that the mass of the satellite is very small with respect to the masses of the other two bodies? How would it apply to twin planets?

I found https://www.physicsforums.com/showpost.php?p=1225193&postcount=10" which seems to indicate satellite mass does matter. If so, how should the formula be altered to include the effect of a large satellite?

Also, what about the relative masses of the other two bodies? Is

**m**assumed to be a very small fraction of**M**? If, for example, you were looking at a planet orbiting one star of a binary system, would the formula need to be altered in any way?(I'm looking for a way to calculate

*reasonable*outer limits for stable orbits in a variety of hypothetical situations. I don't need a high degree of accuracy. For example, although it would be nice to include eccentricity, the cases I'm interested in are sufficiently near to circular for that to be a reasonable approximation.)Thank you for your assistance.

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