gravitation question

[Wussok]

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TBR ex. 2.5b in Physics...Book doesn't give a solution to this one..but basically when a satellite is in orbit of a planet, when does it move fastest? There is acceleration that changes with respect to its position about the orbit so its speed cannot be constant..Is it

A (while it's farthest away from the planet)
B (approching the closest point to the planet in orbit)
C (the closest point in orbit)
D (constant speed --> ruled out)

My guess is the furthest point because logically, with little force acting on it here, it needs the momentum to pull it back towards the planet?

 

[phltz]

This is best understood as a conservation of energy question. The total energy of the satellite is a constant. When it's further away from the planet, it has more potential energy, and so it must have less kinetic energy. When it's closer to the planet, it has less potential energy, and so it must have more kinetic energy. When the satellite is closest to the planet, the kinetic energy and therefore the speed are at a maximum.