The physics
A satellite on a circle falls all the time. The ground curves away just as fast. Gravity gives exactly the pull to the centre, mv²/r.
G M m / r² = m v² / r v = √(GM / r) G M = g R²
Here r is the distance from the planet's centre, r = R + h. A higher orbit is slower, and its lap is longer.
T = 2π √(r³ / GM) L = m v r = m √(GM r)
Too slow, and the path is an ellipse that dips inward. It can hit the ground. Too fast, and it swings out. At √2 times the circle's speed, it escapes.
On a circle, the energies follow a fixed pattern. The binding energy is −E. It frees the satellite.
K = G M m / 2r U = −G M m / r E = −G M m / 2r
A lap that takes one day keeps a satellite over one city. An astronaut in orbit still feels the pull. But she and the craft fall together, so her scale reads zero.