Space · Model
Gravity between Earth, Moon and Sun
The Earth pulls the Moon with two hundred billion billion newtons and the Moon has not moved any closer in four billion years. Both of those statements are true, and understanding why is most of what orbits are.
Start here
The Moon has been falling towards us since before there were fish.
The Earth’s gravity reaches the Moon and pulls on it hard — about 2 × 10^20 N, every second of every day. The Moon is 384 400 km away and has stayed at roughly that distance for four billion years.
Why has it not arrived?
It is falling, and missing. The Earth pulls the Moon with about 2 × 10^20 N, which is enormous, and the Moon is moving sideways at about 1 km/s. Left alone the pull would bring it straight down; left alone the sideways motion would take it off into space in a straight line. The two together curve its path into an orbit, and the Moon spends every moment falling towards a planet that keeps curving away underneath it. Nothing pushes outwards and nothing balances anything.
Gravity is an attraction between any two masses. It never pushes, it never switches off, and it acts across empty space with nothing in between. Every object in the universe is pulling on every other object, including you and this page.
Two things set how strong the pull is. Bigger masses pull harder — both masses count, not just the larger one. And distance weakens it fast: double the separation and the pull falls to a quarter, treble it and the pull falls to a ninth. That is called an inverse square law, and it is why gravity dominates at the scale of planets and is undetectable between two people standing next to each other.
A gravitational pull always comes as a pair of equal and opposite forces. The Sun pulls the Earth and the Earth pulls the Sun, with exactly the same number of newtons. What differs is the result: the same force barely stirs a body 330 000 times the mass of the Earth and swings a smaller one right round it.
At the bench · four gravitational pulls, and what distance does to them
Double the distance, quarter the pull.
Change a control to begin
Choose a pull and then move the two bodies further apart. Every bar is the same pull at a different separation, and the drop-off is steeper than most people expect.
Commit first. The Sun pulls the Earth. How hard does the Earth pull the Sun?
The pull you are looking at
× 1
The same pull at one, two, three and four times the real separation
The pull
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At the real distance
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At × 1 the distance
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The partner pull
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Key fact
Gravity is an attraction between any two masses. It gets stronger with either mass and weaker with distance as an inverse square — double the distance, quarter the pull. The two forces in a gravitational pair are always equal and opposite. An orbit is a body falling towards another and moving sideways fast enough to keep missing it.
Think again
“The Moon is held up by a balance between gravity pulling in and a force flinging it out.”
There is no outward force. If the pull were balanced the Moon would travel in a straight line, and a straight line leaves the Earth behind. Gravity is unbalanced, constantly, and that is precisely why the Moon’s path curves. The outward feeling you get on a fairground ride is your body carrying on straight while the ride turns you — nothing is pulling you outwards there either.
“There is no gravity in space.”
Gravity is what holds every moon to its planet, every planet to its star and every star to its galaxy — all of which happens in space. It gets weaker with distance and never reaches zero. What astronauts experience is not the absence of gravity but free fall: they and their spacecraft are falling together, so nothing presses them against anything, and the sensation of weight vanishes while the pull continues.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Read the model
Two spacecraft drift apart until they are three times as far from each other as they started. What has happened to the gravitational pull between them?
Rung 2 · The one that catches people
The Sun pulls the Earth with about 3.5 × 10^22 N. How hard does the Earth pull the Sun?
Rung 3 · Explain
Explain why the Moon stays in orbit rather than falling into the Earth or flying off into space.
Rung 4 · Take it somewhere new
The Sun pulls the Moon about twice as hard as the Earth does. Explain why the Moon still orbits the Earth rather than being pulled away.
Key note
Gravity is an attractive force between any two masses, acting across empty space. It is stronger for larger masses and falls off as an inverse square with distance, so twice as far apart means a quarter of the pull. The forces come in equal and opposite pairs: the Sun pulls the Earth exactly as hard as the Earth pulls the Sun. An orbit is the result of a gravitational pull and a sideways motion together — the orbiting body is permanently falling and permanently missing.
Going further
The Moon does not go round the Earth so much as the two go round each other, about a point called the barycentre. Because the Earth is eighty-one times the more massive, that point lies inside the Earth, about 1700 km below the surface — so the wobble is real but hidden. For Pluto and Charon the barycentre is outside both bodies, and the pair genuinely circle a point in empty space.
The same pull, arriving slightly harder on the near side of the Earth than the far side, is what raises the tides. The difference between those two pulls is what does the work, which is why the Moon — far smaller than the Sun but far closer — has more than twice the tidal effect. When the two line up you get the large spring tides, and when they pull at right angles you get the small neap ones.
Before this lesson
Connects to
At GCSE this becomes
- Circular motion at constant speed with a changing velocity, gravity as the centripetal force, and orbital radius against orbital speed.
Where to next
Ask Mr Badmus AI
Wondering why an orbit is not a balance of forces?
The bench is a teaching model. Forces are calculated from Newton’s law of gravitation using accepted masses and mean separations, and are rounded to three significant figures: Earth–Moon 1.98 × 10^20 N, Sun–Earth 3.54 × 10^22 N and Sun–Moon 4.36 × 10^20 N. Real separations vary over each orbit, so the true forces vary by a few per cent through the month and the year. The separation multiplier is a thought experiment: moving these bodies apart would change their orbits entirely.
Lesson content © MrBadmusAI.