It sounds like this“The Moon is 60 times further away, so Earth's pull is 60 times weaker.”
Thinking gravity weakens in step with distance
Why it feels right
Proportions are how we think about most things. Twice as far, twice as long a walk. So when someone says gravity gets weaker with distance, the plain reading is 'twice as far, half as strong'. It is the simplest rule that fits, so people reach for it without noticing there are other possibilities. Many things in the world really do work that way, which makes it feel like the default.
Why it’s wrong
Gravity follows an inverse-square law: 60 times the distance means 60 x 60 = 3,600 times weaker, not 60. Doubling the distance cuts the pull to a quarter.
A worked example
Light, sound and gravity all spread out in three dimensions. Picture a torch shining on a wall. At 1 metre it lights a patch. At 2 metres the same light covers a patch twice as wide and twice as tall, which is four times the area, so each part gets a quarter of the brightness. Gravity's pull thins out the same way.
So take the pull at the ground, one Earth radius from the centre, as 1. At 2 radii it is 1/4. At 3 radii, 1/9. At 10, 1/100. At 60, where the Moon is, 1/3,600.
A straight-line rule would have said 1/60 at the Moon, which is 60 times too strong. A Moon feeling that much pull would race round Earth in about 3.5 days instead of 27. The inverse-square rule is what makes the Moon's real speed come out right, and that is how Newton knew he had the rule correct.
How to catch yourself
- You scale gravity, light or sound in direct proportion to distance.
- You find an inverse-square result surprisingly small.
- You say 'twice as far' means 'half as strong' without checking how the thing spreads out.
What to hold instead
Gravity follows an inverse-square law: multiply the distance by 2 and the pull falls to a quarter; by 10 and it falls to a hundredth; by 60 and it falls to 1 part in 3,600. The pull spreads over an area that grows with the square of the distance, and that is why it thins so fast.
Where you’ll meet it
- Working out why the pull at the Moon is so small yet enough to hold it.
- Understanding why a lamp ten times further away looks a hundred times dimmer.
- Estimating how a radio or Wi-Fi signal falls off with distance.
Questions people ask
- What is the inverse-square law?
- A rule where the strength of something falls with the square of the distance: twice as far, a quarter as strong; three times as far, a ninth. Gravity, light, sound and electric force all follow it, because each spreads out over a surface that grows with the square of the distance.
- How strong is Earth's gravity at the Moon?
- About 0.0027 metres per second every second, roughly 1 part in 3,600 of its value at the surface. That comes from the Moon's distance of about 60 Earth radii, squared.