LearnMechanics & orbitsNaked eye
Gravity
Every mass attracts every other mass with a force that falls off as the square of the distance between them.
Why it matters
It is the only force that matters at astronomical scales, because it never cancels — there is no negative mass to shield it the way opposite charges shield electricity.
The maths, in layers
1 · Intuition
Double the distance and the pull drops to a quarter, because the same influence is spread over a sphere four times the area.
2 · The equation
F = G·m₁·m₂ / r²
- F
- force between the two bodies, newtons
- G
- gravitational constant, 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²
- m₁, m₂
- the two masses, kilograms
- r
- distance between their centres, metres
What people usually get wrong
Astronauts float because there is no gravity in orbit.
Gravity at the ISS is about 90% of its strength at the ground. They float because they are falling — the station and everything in it are falling around the Earth together.
Rests on
Nothing. This is a starting point — you can begin here.
Leads to
- Kepler's lawsOrbits are ellipses with the Sun at one focus; a planet sweeps equal areas in equal times; and the square of the period is proportional to the cube of the semi-major axis.
- Escape velocityThe speed at which an object's kinetic energy exactly cancels the gravitational well it sits in, so it can leave and never return.
- TidesThe stretching a body feels because gravity pulls harder on its near side than its far side.
- BarycentreThe common centre of mass that two orbiting bodies both circle, rather than one circling the other.
- DifferentiationThe separation of a molten young world into layers by density — iron sinking to a core, lighter silicates floating to a crust.
- The discovery of NeptuneA planet found in 1846 by mathematics rather than by searching — predicted from discrepancies in Uranus's orbit, then located within one degree on the first night of looking.