Stable orbits

1. An object in a stable orbit stays at the same distance from the body it is orbiting, orbit after orbit.
2. The orbital radius is measured from the centre of the central body, so for a satellite it is the Earth's radius of about $6400km$ plus the satellite's height above the surface.
3. Gravity provides the inward force that keeps changing the direction of the orbiting object, bending its path into a circle.
4. For the orbit to be stable, the gravitational force must be exactly the size needed to bend the path into a circle of that radius at that speed.
5. A faster object needs a larger inward force to keep it on the same circle, because its direction has to change more quickly.

Gravity gets weaker with distance

1. The gravitational force between two objects becomes weaker as the distance between them increases.
2. A satellite in a small orbit, close to the Earth, therefore feels a much stronger pull than an identical satellite in a large orbit.
3. A strong pull can bend the path of a fast-moving object into a circle, so a satellite close to the Earth must travel fast to stay in a stable orbit.
4. A weak pull can only bend the path of a slower object into a circle, so a satellite far from the Earth must travel more slowly.
5. For stable orbits around the same body, a smaller orbital radius therefore goes with a higher orbital speed, and a larger orbital radius goes with a lower orbital speed.

Changing speed means changing radius

1. If an orbiting object's speed changes, its old radius no longer matches its new speed, so it cannot stay in the same orbit.
2. If the object is moving too fast for its radius, gravity is not strong enough to bend its path into that circle, so the object moves outwards to a larger radius.
3. If the object is moving too slowly for its radius, gravity pulls it inwards more than is needed, so it falls closer to the central body.
4. For the orbit to be stable at a new speed, the radius must change, with a higher stable speed needing a smaller radius and a lower stable speed needing a larger radius.
5. A satellite that is moved up to a higher stable orbit therefore ends up travelling more slowly than it did in its lower orbit.
6. The same pattern applies to the planets orbiting the Sun, so Mercury, the closest planet, moves fastest and Neptune, the furthest, moves slowest.
7. Low satellites such as the International Space Station feel a tiny drag from the thin upper atmosphere, so they slowly lose height and must be boosted back up by rocket engines.