Newtonian Gravitation Force
Newtonian Gravitation Force
Every pair of masses attracts with a force set by Newton’s law of gravitation — the force that holds orbits and weighs objects on Earth.
The force is F = G·m_1·m_2/r². where G is the gravitational constant, m_1 and m_2 the masses and r their separation.
Inputs
G := 6.674e-11 N·m^2/kg^2=6.67e-11 m^3/kg/s^2
m_1 := 5.972e24 kg=5.97e+24 kg
m_2 := 1000 kg=1000 kg
r := 6.371e6 m=6.37e+06 m
Apply Newton’s law of gravitation.
F := G·m_1·m_2/r^2=9819.53 N
Results
For a mass at Earth’s surface this returns its weight (≈ 9.8 kN per tonne). The inverse-square law makes the force fall off rapidly with distance.
Assumptions & limitations
- Point masses (or spherical bodies).
- Separation measured centre-to-centre.
- Non-relativistic.