# Acceleration of gravity

Acceleration of gravity calculation on the surface of a planet. It's possible to calculate the acceleration above the surface by setting the sea level. But it won't be possible under the surface - this is a wrong formula.

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#### Timur

Created: 2015-12-02 20:11:20, Last updated: 2021-02-12 11:21:38

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Written under the influence of Larry Niven's story "There Is a Tide." Try to calculate the force of gravity on the surface of a spherical piece of a neutron star with a mass 500 000 times less than the Earth's mass but with a 3 meters diameter ...

### Theory

Acceleration of gravity g — an acceleration given to the body in a vacuum by the force of gravity, that is, the geometric sum of the planet's gravitational pull (or another celestial body) and inertial forces resulting from its rotation. According to Newton's second law, gravity's acceleration is equal to the force of gravity acting on the unit mass object.

Acceleration of gravity is made up of two components: gravitational acceleration and centrifugal acceleration. The calculator only calculates the gravitational acceleration.

The value of the gravitational acceleration on the surface can be approximated by imagining the planet as point mass M and calculating the gravitational acceleration at a distance of its radius R:

$g=G\frac{M}{(R+h)^{2}}$
where:
G — gravitational constant ($6.6742*10^{-11}$ m^3, s^-2, kg^-1).
h — altitude above sea level

#### Acceleration of gravity

Altitude above "sea level" of the planet (m)
Digits after the decimal point: 6
Acceleration of gravity (m/s^2)

Acceleration of gravity in g (1g - on the surface of the Earth)

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PLANETCALC, Acceleration of gravity