- #1
Ryan H
- 15
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The Hill sphere of a celestial object is the area in which it is the dominating force in the area.
I was wondering how the formula was determined.
If the mass of the smaller body is m, and it orbits a heavier body of mass M with a semi-major axis a and an eccentricity of e, then the radius r of the Hill sphere for the smaller body is, approximately:
Equation: [tex]r \approx a(1-e)\sqrt[3]{m/3M}[/tex]
I believe I understand how to determine eccentricity and the semi-major axis, I'm just searching for how the whole thing comes together.
http://en.wikipedia.org/wiki/Hill_sphere"
The derivation on the wikipedia article didn't help much.
I was wondering how the formula was determined.
If the mass of the smaller body is m, and it orbits a heavier body of mass M with a semi-major axis a and an eccentricity of e, then the radius r of the Hill sphere for the smaller body is, approximately:
Equation: [tex]r \approx a(1-e)\sqrt[3]{m/3M}[/tex]
I believe I understand how to determine eccentricity and the semi-major axis, I'm just searching for how the whole thing comes together.
http://en.wikipedia.org/wiki/Hill_sphere"
The derivation on the wikipedia article didn't help much.
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