# Gravitational force

Newton's Universal Law of Gravitation.

**Enter 'x' in the field to be calculated.**

## 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 m_{1} : input **1**

• m_{1} unit : choose **ME** (or mass of the Earth, equal to `5.972 × 10^24` kg)

• Mass m_{2} : input **1**

• m_{2} 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 m_{1} = 1000 kg orbits around the Earth, which has a mass of m_{2} = 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 m_{1} : input **1**

• m_{1} unit : select **ME** (or mass of the Earth, equal to `5.972 × 10^24` kg)

• Mass m_{2} : input **1000**

• Unit of m_{2} : 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

## See also

Weight calculator

Unit conversion