Gravitational force

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

See also

Weight calculator
Unit conversion

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