cognoscJoin the beta

Why doesn't the Moon fall onto Earth?

The Moon is falling right now. Guess why it never hits us, then see the sideways speed that makes an orbit, and why no force balances gravity.

The steps5 · 27 min
  1. 1Gravity weakens with distance but never stops5 min
  2. 2The Moon is falling, and missing6 min
  3. 3Speed sets the orbit, and nothing balances gravity6 min
  4. 4Earth is pulled too: both circle a shared point5 min
  5. 5One law for the apple and the Moon5 min
Free, no card
What it takes apart

Sound like you?

The ideas people most often get wrong on the way, in their own words. Each step starts from one of them.

“The Moon is too far away for Earth's gravity to reach it, so it just floats there.”Taken apart in step 1Thinking gravity stops at some distance“The Moon is 60 times further away, so Earth's pull is 60 times weaker.”Taken apart in step 1Thinking gravity weakens in step with distance“If the Moon were really falling toward us, it would have crashed into Earth long ago.”Taken apart in step 2Thinking falling always means getting closer“The Moon stays up because gravity pulling it in is balanced by a force pushing it out, like a tug of war that ends in a draw.”Taken apart in step 3Thinking an outward force balances gravity“Something has to keep pushing the Moon forward, or it would slow down and drop.”Taken apart in step 3Thinking something must keep pushing the Moon along“The Earth sits still in the middle and the Moon goes round it.”Taken apart in step 4Thinking the Earth stands still while the Moon goes round“Things on Earth fall by gravity, but the Moon and planets are held up by some other, heavenly rule.”Taken apart in step 5Thinking the heavens follow different rules from Earth
Physics

More on physics

Why does kinetic energy grow with speed squared?26 min · freeWhy do mirrors flip left and right but not up and down?24 min · freeWhy use a database instead of just saving files?26 min · freeWhy is the Fourier transform so important?28 min · free
The short answerRather read it than work it out?Show it (it gives the steps away)

Earth's gravity reaches the Moon. It weakens with the square of the distance: at 60 Earth radii it is 1 part in 3,600 of its strength at the surface, about 0.0027 m/s². That is small but never zero, and with nothing else acting on the Moon it is enough.

Anything moving sideways while it falls follows a curve. Fire a ball sideways fast enough and the ground curves away as fast as the ball drops, so it falls for ever without landing: that is an orbit. The Moon falls about 1.4 mm toward Earth each second while moving about 1,020 m sideways, and its path bends by exactly that much.

At any height, one sideways speed gives a circular orbit: about 7.9 km/s just above the ground, about 1 km/s at the Moon. Slower and the path curves down into the ground; faster and it swings wide, and from the surface beyond about 11.2 km/s it escapes. All the while the pull is unbalanced, and it is what bends the path. There is no outward force holding the Moon up, and nothing needs to push it along.

The Moon pulls on Earth as hard as Earth pulls on the Moon. Earth is 81 times heavier, so it moves much less, and the pair circle a point about 4,670 km from Earth's centre, inside Earth, once a month. Earth wobbles round that point instead of standing still.

The pull that makes an apple fall also steers the Moon, and the Moon checks it. At 60 Earth radii the apple's 9.8 m/s² should shrink to 9.8 / 3,600 = 0.0027 m/s², and the Moon's measured acceleration, v squared over r with v = 1,022 m/s and r = 384,400 km, is 0.0027 m/s². One law explains falling apples, the Moon, tides and the planets.

Make it yours

Learn it with your own tutor.

Add it to your goals and Cognosc starts from what you already know, works through the rest with you, and keeps checking you still understand it.