Newton's Law of Gravitation
Simple Explanation
Newton's law of gravitation says every two masses in the universe attract each other with a force that increases with both masses, and decreases sharply — as the inverse square — with the distance between them. This single law explains everything from a dropped apple to the orbits of planets.
Why Do We Need It?
This was one of the first laws to show that the same physics governing everyday falling objects on Earth also governs the motion of the Moon and planets — unifying "earthly" and "heavenly" physics for the first time.
Formula
Newton's Law of Gravitation
F = G m₁m₂ / r²
Every pair of masses in the universe attracts each other with a force that grows with both masses, and shrinks rapidly (as the inverse square) with the distance between their centres.
- F
- — gravitational force between the two masses, in newtons (N)
- G
- — the universal gravitational constant, 6.67 × 10⁻¹¹ N·m²/kg²
- m₁, m₂
- — the two masses, in kilograms (kg)
- r
- — the distance between the centres of the two masses, in metres (m)
When to use it: Whenever the gravitational force of attraction between two known masses at a known separation needs to be found.
Worked Example
Find the gravitational force between two masses
Two masses of 50 kg and 80 kg are 2 m apart. Using G = 6.67 × 10⁻¹¹ N·m²/kg², find the gravitational force between them.
Why Does This Work?
The inverse-square dependence on distance comes from how gravity's influence spreads out over the surface of an ever-larger sphere as distance increases — the same force is "spread thinner" over a much bigger area, which is why doubling the distance cuts the force to a quarter.
Real-Life Example
Why gravitational force between everyday objects is unnoticeable
Two people standing near each other are gravitationally attracted to each other, yet no one ever notices this pull.
Because G is such an extremely tiny number, the gravitational force between ordinary-sized masses (a few tens of kilograms) is far too small to feel — gravity only becomes noticeable when at least one mass is enormous, like a planet.
Practice
If the distance between two masses is doubled, what happens to the gravitational force between them?
MediumCommon mistake
Forgetting to square the distance r before dividing — the law uses r², not r, so halving the distance quadruples the force, not just doubles it.
Quick Review
- F = Gm₁m₂/r²
- Gravitational force increases with both masses, and decreases as the inverse square of distance.
- G is an extremely small constant, which is why gravity between everyday-sized objects is unnoticeable.