Newton's law of universal gravitation
Is the force that pulls an apple down the same force that holds the Moon?
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Explain
Everything pulls on everything.
Big things pull the most.
Newton realised that the same gravity pulls apples down and holds the Moon. It is universal, which means it works everywhere.
Every mass pulls on every other mass. More mass makes the pull stronger, and more distance makes it weaker.
You pull on the Earth too, but it is so massive that you can't move it much.
F = G m₁ m₂ / r². Doubling one mass doubles the force. Doubling the distance makes the force 4 times smaller. This is called an inverse-square law.
G is very small, which is why you don't feel a pull from the people next to you.
Worked example: using Earth (6 × 10²⁴ kg), the Moon (0.07 × 10²⁴ kg) and r = 3.84 × 10⁸ m gives about 1.9 × 10²⁰ N.
- More mass, more pull
- More distance, less pull
- All things attract
Want the full story?
r is the distance between the centres of the objects. The calculator uses big units so that the numbers fit: 10²⁴ kg, 10⁸ m and 10²⁰ N. Newton's law is very accurate, but Einstein's general relativity improves on it where gravity is very strong.
The Formula
gravity force = G × mass one × mass two ÷ distance squared
- the gravity force between two objects, measured in newtons (N)
- the gravitational constant, 6.67 × 10⁻¹¹, measured in newton metres squared per kilogram squared (N m²/kg²)
- the two masses, measured in kilograms (kg)
- the distance between their centres, measured in metres (m)
Try the numbers
Gravity force: 25.03 × 10²⁰ N
Try it at home
Ask a grown-up to help
You need a heavy ball, a blanket, a marble.
You need: a heavy ball, a blanket, a marble.
Press a heavy ball into a blanket. Marbles roll in.
- Stretch a blanket between chairs, or hold it with a friend.
- Put a heavy ball in the middle.
- Roll a marble around it.
What's happening: this is only a model. Mass bends the blanket, and the marble curves towards it, a bit like the Moon curving around Earth.
Physics is life
Your body
Earth pulls on your body.
Daily life
You pull on the Earth too.
Nature
The Moon pulls the seas.
Space
Gravity works across all of space.
Quick check
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Words to know
Gravity: The pull between all things that have mass.