Why a satellite have greater speed when its radius of rotation is less ? By energy arguments please explain this.

Why a satellite has greater speed in elliptical orbit when its radius of rotation is less around a planet ?

Why a satellite have greater speed when its radius of rotation is less ? By energy arguments please explain this.

Here's a hint - think about what happens to a satellite's potential energy as the distance to the planet it orbits decreases - as it gets lower in the gravitational field its PE decreases, right? So what does that mean would happen to its kinetic energy?

At any moment during the orbit the total amount of energy is the same.

Lets consider a bullet fired upwards. First it has kinetic energy from it's speed. While climbing that energy is converted into potential energy. When the kinetic energy is nill, the potential energy is maximal. Now the bullet starts falling down again, and potential energy is converted into kinetic energy, while it's speed picks up again.

Now imagine that the bullet goes extremely fast, so fast that it gets into an eliptic orbit around earth. At the 'highest' point the speed away from earth is nill. But nearest to earth it's speed is maximum.

When the satellite is closer to the Earth, then it has smaller gravitational potential energy. Hence, larger kinetic energy and thereby larger speed.