I have a question about orbital speed. Imagine a shuttle moving in an orbit near the earth surface, its total energy is "-GMm/2r", so its total energy is directly proportional to -1/r In order to spiral into another orbit of smaller radius which mean it would have a larger angular speed, the shuttle should increase or decrease its orginal speeed so that it can get into a lower orbital ? 1) increase As orbital speed = (GM/r)^1/2, speed should increase in order to get a smaller r. 2) decrease As total energy directly proportional to -1/r, and total energy = PE + KE As r decrease, total energy is more negative and KE should decrease So the speed should decrease. Are there anything wrong in these two contradicting concept ? thank you!