# Hill Sphere Radius

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Equation / Last modified by KurtHeckman on 2019/04/22 23:14
r =
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KurtHeckman.Hill Sphere Radius
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8e39e8c8-be9f-11e7-abb7-bc764e2038f2

The Hill Sphere Radius calculator computes the radius from a planet where an object is no longer under the dominant influence of the gravity of the planet but is now under the dominant influence of the gravity of the star.

INSTRUCTIONS: Choose units and enter the following:

• (a)  This is the the semi-major axis of the orbit of the planet about the star.
• (e)  This is the eccentricity of the orbit of the planet about the star.
• (m)  This is the mass of the planet.
• (M)  This is the mass of the star.

Hill Sphere Radius (r): The calculator returns the radius in kilometers.  However, this can be automatically converted to other distance units (e.g. miles) via the pull-down menu.

#### The Math / Science

r = a(1-e)(m / (3M))^(1/3)

where:

• r = Hill Sphere Radius
• a = semi-major axis of the orbit
• e = eccentricity or the orbit
• m = smaller mass (e.g. planet)
• M = greater mass (e.g. Sun)

### Special Thanks

Thanks to Robert Frost, Instructor and Flight Controller at NASA for posting this formula on Quora.

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