orbital velocity
How do you stay in orbit? The surprising answer is that you fall, but you also move sideways so fast that the ground curves away beneath you just as quickly as you drop toward it. You keep missing the Earth. Orbital velocity is the sideways speed that makes this balancing act work: fast enough to keep circling, not so fast that you fly off into space.
For a circular orbit the maths is clean. Gravity provides exactly the centripetal force needed to bend the path into a circle, so G M m / r^2 = m v^2 / r. The mass m of the orbiting object cancels, leaving v = sqrt(G M / r), where M is the mass being orbited and r is the orbit radius from its centre. Notice what this says: the closer you orbit, the faster you must go. Low satellites race around; distant ones dawdle.
For the International Space Station, just a few hundred kilometres up, v is about 7.8 km/s, roughly 28,000 km/h. That is why reaching orbit is mostly about gaining enormous horizontal speed, not just height. A common misunderstanding is that orbiting things have escaped gravity; in truth gravity is the very force holding them in their curved path, and they are in continual free fall around the planet.
For a low Earth orbit at r = 6.7 x 10^6 m, v = sqrt(G M / r) = sqrt(6.67 x 10^-11 x 5.97 x 10^24 / 6.7 x 10^6) = about 7.7 km/s. A satellite twice as far out would orbit at 1/sqrt(2) of that, around 5.5 km/s.
Orbital speed drops as the orbit widens; the mass of the satellite itself never enters the formula.
Counterintuitively, lower orbits are faster; and orbiting objects have not escaped gravity, they are in perpetual free fall held by it.