Two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Symbols
F
gravitational force
[N]
G
gravitational constant (≈6.67⋅10−11)
[N·m²/kg²]
m1,m2
masses of the bodies
[kg]
r
distance between the bodies
[m]
Where it comes from
Every pair of bodies attracts each other. The force falls off quickly with distance (as the square) — doubling the separation weakens it fourfold. Bodies much smaller than the distance between them are treated as point masses.
When to use it
Interactions of masses (planets, satellites, falling bodies). This law gives rise to g=GM/R2 and the cosmic velocities.
Example
Find the attractive force between two 1000 kg masses 2 m apart.