Gravity and orbits: falling, and missing the ground
The Space Station is not beyond gravity. It is falling, constantly, and travelling sideways fast enough to miss.
Gravity is the weakest of the four fundamental forces by an enormous margin - a small magnet lifts a paperclip against the pull of the entire Earth. It dominates the universe anyway, because it is always attractive and never cancels, so at large scales it is the only force left standing.
The law
Newton: every mass attracts every other mass, with a force proportional to both masses and inversely proportional to the square of the distance between them.
The inverse square part is the interesting bit and it turns up everywhere - light, sound, radiation. The reason is geometric: spread something out from a point and it covers the surface of a sphere, whose area goes as radius squared. Twice as far, four times the area, a quarter of the intensity.
- Double the distance - a quarter of the force
- Triple it - a ninth
- Ten times - a hundredth
Weight is not mass
Mass is how much matter there is, in kilograms, and it does not change. Weight is the force gravity exerts on that mass, in newtons, and it changes with where you are.
On the Moon your mass is identical and your weight is about a sixth. Bathroom scales measure weight and are labelled in kilograms, which is a convenient lie that works because Earth's gravity is nearly constant everywhere on it.
Newton drew this in 1687 and it is still the clearest explanation there is. An orbit is not a balance of forces - there is nothing pushing outward. It is free fall with enough sideways speed to keep missing the ground.
So why do astronauts float
Not because there is no gravity. At the Space Station's altitude of about 400 km, gravity is roughly 90% as strong as at the surface. It is barely reduced at all.
They float because they are in free fall, and so is the station, and so is everything in it - all falling together at the same rate. You feel weight only when something pushes back on you: the floor, a chair, the ground. In free fall nothing pushes, so you feel nothing. The correct term is microgravity rather than zero gravity, and the same weightlessness happens briefly in a dropping lift or at the top of a rollercoaster.
Why the Moon does not fall on us. It is falling. It is also moving sideways at about a kilometre per second, so it keeps missing - exactly Newton's cannonball, on a larger scale. It has been doing this for four and a half billion years because there is nothing in the way to slow it down.
Einstein's correction
Newton's law is superbly accurate and describes gravity as a force. General relativity, in 1915, described it instead as curvature: mass bends spacetime, and objects follow the straightest available path through the bent geometry. No force is pulling; the shape of space is different.
The two agree almost everywhere. The difference shows near very large masses - Mercury's orbit shifts by a tiny amount Newton cannot account for and Einstein predicts exactly. GPS satellites need the correction too: their clocks run measurably faster than clocks on the ground, and without adjusting for it positions would drift by kilometres a day.
Which is a good illustration of how science handles being wrong. Newton was not discarded - he is still what you use to fly a spacecraft. He was shown to be an excellent approximation inside a wider theory.