Gravitational force
Newton's Universal Law of Gravitation.
Enter 'x' in the field to be calculated.
Answer
_____ Steps _____
Formula
`F = G*(m_1*m_2)/d^2`
Inputs and conversions to SI Units
`m_1` = 1 ME = 5.9742E+24 kg convert
`m_2` = 1 MM = 7.34767309E+22 kg convert
`d` = 1 EM-dist = 384400000 m convert
`G` (in `N.m^2.kg^-2`) = 6.674E-11
Apply the formula
`F` = 1.9826635727878E+20 N convertDo you have any suggestions to improve this page ?
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