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

Enter a value for all fields

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**) Semi-major axis of the orbit of the planet about the star. - (
**e**) Eccentricity of the orbit of the planet about the star. - (
**m**) Mass of the planet (or smaller object). - (
**M**) Mass of the star (or larger object).

**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 formula for the Hill Sphere Radius is:

`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)

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