This is a three-body gravity question
The "Hill Sphere" of the Earth is about 0.01AU. I would like an
Internet reference for the derivation of the Hill Sphere
approximation.
If there is no Internet reference, could you copy the derivation for
me from your hardcopy source to this site from whatever source is
available to you?

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Request for Question Clarification by pafalafa-ga on 21 Apr 2005 13:19 PDT

There's a detailed derivation of the Roche Limit here:

http://www.physicsdaily.com/physics/Roche_limit


which I gather is closely related to the Hill Sphere approximation.


Is this useful for your needs?


pafalafa-ga

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Clarification of Question by m4892-ga on 21 Apr 2005 16:47 PDT

The Roche Limit calculates tidal forces for a minor body nearing a major body.
The Hill sphere estimates the sphere of gravitational influence for
say, the Earth relative to the Sun. They are totally different.
I've tried finding the derivation of the Hill Sphere on the Internet
without success. Surely a derivation can be found in a good textbook
on orbital mechanics, something I don't have access to.

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Request for Question Clarification by pafalafa-ga on 21 Apr 2005 17:21 PDT

On option for you is to make use of amazon.com's "Look Inside the Book" feature.

Once you are registered at the amazon site (no charge), search on [
"hill sphere" approximation ] (just as shown, with quote marks
included), and one of the first books that shows up is:

Solar System Dynamics
by Carl D. Murray

page 116 of this book appears to have a derivation, if I am reading it right.  

Let me know how it works out.

paf

The comment equating "Hill Sphere" to "Roche LIMIT" was almost
correct, save for one small detail: the "Hill Sphere" and "Roche
SPHERE" are the same thing.

See http://en.wikipedia.org/wiki/Hill_sphere for a formula to
approximate the radius of the Hill Sphere - located in the "formula
and examples" section.

There doesn't appear to be a derivation, though there is some
explanation that may be useful.

Thanks for the comment relating the Roche Sphere and the Hill Sphere.
I finally bought the book:
"Solar System Dynamics", which does have the H S derivation. No
Internet derivations to be had.