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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 thesurface - this is a wrong formula.

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 mass of the Earth, 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, the acceleration of gravity is equal to the force of gravity acting on the unit mass object.

Acceleration of gravity is made up of two components: the 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