Newton's law of universal gravitation — the force between any two masses, plus the acceleration each mass feels.
How to use this tool
Any units — kilograms, grams, pounds, or even whole Earth masses for planets and stars.
Gravitation uses the distance between centres, not surfaces — that matters for planets.
The big number is the attractive force in newtons, with the acceleration each mass feels underneath.
Earth (5.972 × 10²⁴ kg) and a 70 kg person 6,371 km apart give about 686 N — your weight.
Formula & worked example
Worked example: Earth (5.972 × 10²⁴ kg) and a 70 kg person at the surface (r = 6,371,000 m) attract with F = 6.67430 × 10⁻¹¹ × 5.972 × 10²⁴ × 70 ÷ (6,371,000)² ≈ 686 N. Dividing by 70 kg gives 9.8 m/s² — familiar gravity.
Limitations — read this before you rely on it
Newton's law is an excellent approximation for everyday and solar-system scales, but it breaks down near extremely dense or fast objects, where general relativity is needed, and it treats bodies as point masses — for a person standing on Earth, use the centre-to-centre distance.
Frequently asked questions
F = G × m₁ × m₂ ÷ r². Double either mass and the force doubles; double the distance and the force falls to a quarter — the inverse-square law.
The gravitational constant G is 6.67430 × 10⁻¹¹ N·m²/kg², measured by Cavendish-style experiments. It is tiny, which is why gravity between everyday objects is negligible.
Newton's third law: the force on each mass is equal and opposite. The lighter mass just accelerates more (a = F ÷ m), which is why an apple falls to Earth rather than Earth visibly rising to the apple.
Weight is the gravitational force on you at a planet's surface. On the Moon the same mass weighs about a sixth as much because the Moon is less massive — your mass itself never changes.
No — it means centre-to-centre distance. Standing on Earth, you are about 6,371 km from Earth's centre, not 0 km from its surface. For two nearby balls, centre-to-centre is what counts.