I gather that when you say 0 total energy the Kinetic energy exactly accounts for the potential energy at that point. Which implies that the velocity is sqrt(2*G*M/r), the escape velocity for that point. Is there any proof for this?
Thanks. I messed up the signs. As you say, If the potential is 0 at infinity as it moves closer and closer to the planet, the potential energy should become more negative. I should however have understood intuitively that kinetic energy increases as an object comes closer and closer to the...
I am trying to understand the existence of orbits apart from the elliptical one. I have used the following line of thought.
Consider an object moving from infinity towards a planet. The object has kinetic energy alone at infinity. But it develops a potential energy as it comes closer to the...