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# 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

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)

#### Astronomy Calculators

- Astronomy Calculator: This contains over 30 functions useful to astronomers and and astronomy students.
- Kelper's Third Law Calculator: This contains the Kepler's Third Law solved for each parameter.
- Force of Gravity: This compute the force of gravity between two bodies.
- Schwarzschild Radius
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- Mass of a Black Hole

### Special Thanks

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

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**Hill Sphere Radius**, is listed in 1 Collection.