Gravitational Acceleration Formula

The law of universal gravitation says that the intensity of the forces of attraction between two bodies was proportional to their masses and to the distance between them. Gravity acceleration is the specific gravitational force acting on one body in the gravitational field of the other, like the gravitational force per unit mass of the body experiencing it.

Gravity acceleration= universal gravitational constant * planet mass / planet radius.

The equation is written

g = G*M/R²

We have:

g = gravity acceleration

G = universal gravitational constant

M = planet mass

R = planet radius.

Gravitational acceleration Questions:

1) Determine gravitational acceleration on planet earth, whose mass is 6*10²⁴ kg and radius is approximately 6378 km at the equator.

Answer: First calculate the gravity acceleration using the formula above, where M = 6*10²⁴kg, R = 6378000m and G = 6.67*10^-11 Nm²/kg².

g = G*M/R²

g = 6.67*10^-11 Nm²/kg²*6*10²⁴kg/(6378000m)²

g = 9.807m/s².

2) Determine the gravitational acceleration of the moon, whose mass is 7.34*10²² kg and radius is approximately 1740 km.

Answer: First calculate the gravity acceleration using the formula above, where M = 7.34*10²²kg, R = 1740000m and G = 6.67*10^-11 Nm²/kg².

g = G*M/R²

g = 6.67*10^-11Nm²/kg²*7.34*10²²kg/(1740000m)²

g = 1.62 m/s².