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Universal law of gravitation
Beginner
Every mass attracts every other with a force that falls off as inverse square of distance.
F = Gm₁m₂/r²Every pair of masses attracts with a force F = Gm₁m₂/r², along the line joining them. It was Newton's insight that the same law governs falling apples and orbiting planets. The force is always attractive and falls off as the square of the distance.
Earth–Moon: F ≈ 2×10²⁰ N with M = 6×10²⁴ kg, m = 7.3×10²² kg, r = 3.84×10⁸ m.
r is the distance between centres, not surfaces.
In more detail
Newton's law of universal gravitation states that every pair of masses attracts with force F = Gm1m2/r², directed along the line joining them. The force falls off with the square of distance.
Real-world uses
- Satellite orbits are calculated from this law.
- Tidal forces on oceans come from the gravitational pull of the Moon and Sun.
- Engineers planning a satellite launch use the inverse-square law to find how the pull of Earth weakens with distance.
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Frequently asked questions
Does gravity act between everyday objects?
Yes, but it is so weak for everyday masses that we barely notice it.
Why does the force fall off with distance squared?
Because the gravitational influence spreads over a sphere whose area grows with the square of the radius.
Does doubling the distance halve the gravitational force?
No. Doubling the distance cuts the force to one quarter, because the force falls off as the inverse square of the separation.
Related topics in Gravitation & Orbits
Gravitational constant G · Acceleration due to gravity · Variation of g with altitude