Gravitational acceleration

g=G\dfrac{M}{R^2}

Result unit: m/s²

What it describes

The acceleration imparted to a body by a planet's gravitational field at its surface.

g

gravitational acceleration

[m/s²]

G

gravitational constant

[N·m²/kg²]

M

mass of the planet

[kg]

R

radius of the planet

[m]

This is the law of gravitation divided by the mass of the falling body — which is why all bodies fall alike.

g

depends on the mass and radius of the planet, not on the mass of the falling body.

Finding

g

on any planet; the farther from the centre (larger

R

), the smaller

g

Find

g

on Earth (

M=5.97\cdot10^{24}

kg,

R=6.37\cdot10^{6}

m).

Substitution

G=6.67\cdot10^{-11}

Result

g=\dfrac{6.67\cdot10^{-11}\cdot5.97\cdot10^{24}}{(6.37\cdot10^{6})^2}\approx9.8

m/s².

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