# Gravitational force

F = G * (m_1 * m_2)/d^2
Newton's Universal Law of Gravitation.
Enter 'x' in the field to be calculated.
in N.m²/kg²

## Newton's Universal Law of Gravitation

According to the universal law of gravitation formulated by Isaac Newton in 1687, two bodies of mass m_1 and m_2 spaced at distance d, exert one on the other a force of attraction according to the following laws :
• The forces exerted by body 1 on body 2 (\vecF_12) and vice versa by body 2 on body 1 (\vecF_21) are vector opposite,

\vecF_12 = - \vecF_21,

• These forces have the same intensity F equal to,

F = G * (m_1 * m_2)/d^2

F is the force of attraction between the two bodies in Newton,
m_1 is body mass 1 in kg,
m_2 is body mass 2 in kg,
d is the distance between the two bodies in meter
G is the universal gravitational constant whose value is,
G = 6.674 . 10^(-11) N.m^2.kg^(-2)

## Example 1. Gravitation force between Earth and Moon

Let's calculate the gravitational force between the Earth and the Moon, first with the formula then with the calculator above.

F = G * (m1 * m2) / d^2 = (6.674 × 10^-11 N.m^2/(kg^2)) * (7.342 × 10^22 kg) * (5.972 × 10^24 kg) / (3.844*10^8 m)^2 = 1.98*10^20 N

To evaluate this force with the calculator, enter the following values,

Gravitational force F : input x or leave empty (this is the variable to calculate).

Unit of F : choose N (Newton) or whatever appropriate unit.

Mass m1 : input 1

m1 unit : choose ME (or mass of the Earth, equal to 5.972 × 10^24 kg)

Mass m2 : input 1

m2 unit : choose MM (or mass of the Moon, equal to 7.342 × 10^22 kg)

Distance d : input 1

d unit : choose EM-dist (or Earth-Moon distance, equal to 3.844*10^8 m)

Gravitational constant G : input 6.674.10^-11 N.m2/kg2

The Earth-Moon gravitation force is approximately F = 1.98*10^20 N
Here is the resulting calculator : Earth-Moon gravitation force

## Exemple 2 : Gravitational force between the Earth and artificial satellite

A satellite of mass m1 = 1000 kg orbits around the Earth, which has a mass of m2 = 5.972 × 10^24 kg. The distance between the center of mass of the Earth and the satellite is d = 7500 kilometers.

Let's calculate the gravitational force between the Earth and the satellite.

F = G * (m1 * m2) / d^2 = (6.674 × 10^-11 N.m^2/(kg^2)) * (1000 kg) * (5.972 × 10^24 kg) / (7500000 m)^2 = 7088 N

Therefore, the gravitational force between the Earth and the satellite is F = 7088 N.

To check this calculation, you may use the above calculator with the following inputs,

Gravitational force F : input x or leave empty (this is the variable to calculate).

Unit of F : choose N (Newton) or another unit.

Mass m1 : input 1

m1 unit : select ME (or mass of the Earth, equal to 5.972 × 10^24 kg)

Mass m2 : input 1000

Unit of m2 : select kg

Distance d : input 7500

Unit of d : select km

Gravitational constant G : input 6.674 . 10^-11 N.m2/kg2

This will lead to the following calculator, Gravitational force Earth-Satellite = 7088 N