The space shuttle releases a satellite into a circular orbit 700 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?

Answer 1

700,000 = 7 * 10^5 meters above so
r = 7*10^5 + 6.38*10^6 = 70.8*10^5 = 7.08*10^6

m v^2/r = G m M/r^2

v^2 = G M/r

v^2 = 6.67*10-11 * 6*10^24 / 7.08*10^6

v^2 = 5.65 * 10^7 = 56.5*10^6

v = 7.5*10^3 = 7500 m/s