1. The problem statement, all variables and given/known data A satellite is orbiting the Earth around an orbit of radius R=2.5R0, where R0 is Earth's radius. What additional velocity is needs to be directed along the radius of the orbit so that satellite escapes Earth's gravity? 2. Relevant equations Total Energy= K + U Conservation of Energy: K1 + U1 = K2 + U2 K=0.5mv2 U=-Gm1m2 / R1, 2 3. The attempt at a solution Hi guys! We worked some similar problems in school and I've been trying to follow that solving this problem. We've always used conservation of mechanical energy to do this. Our condition for when the satellite has just barely escaped Earth's gravitational field is: T2 = K2 + U2 = 0 U2 is effectively zero because R1, 2 (the distance between objects 1 and 2) is so great. K2 is zero because if the object has just barely escaped gravity, it wouldn't have any velocity. That all makes good sense to me! The initial energy is a little more confusing to me. There is definitely some gravitational potential energy: U=-Gm1m2 / R1, 2 I'll let mass, m, be the mass of the satellite and Mearth be the mass of the Earth. R1, 2 in this case would be 2.5R0. U1=-GmMearth/2.5R0 We've solved problems launching stuff on Earth into space, where the object initially has no kinetic energy. K1 - U1 would equal zero, so K1 = U1: 0.5mv2 = GmMearth/2.5R0 The mass of the satellite would cancel from each side, and I can plug in the known constants and get an answer (2.2 x 105 m/s is what I got). But.... I'm not sure if there's really no initial kinetic energy. The satellite is in space and is orbiting at some velocity, so wouldn't it have kinetic energy? If so, how would I go about finding it? Also, this seems "too simple." Is there something I'm overlooking?