# Question #3ab6b

Aug 31, 2017

Because the comet has returned to its original position with the same speed.

#### Explanation:

As the comet circles the sun, its gravitational potential energy and kinetic energy are continually changing. However the sum of those 2 energies remains constant, ${E}_{\text{total}}$. Energy is transferred back and forth between the 2 types of energy.

When the comet is at its maximum distance from the sun, its speed is minimum. Therefore the kinetic energy is at its minimum value and its gravitational potential energy is at its maximum value. And the sum of the 2 is still at the constant value: ${E}_{\text{total}}$.

When the comet is at its minimum distance from the sun, its speed is maximum. Therefore the kinetic energy is at its maximum value and its gravitational potential energy is at its minimum value. And the sum of the 2 is still at the constant value: ${E}_{\text{total}}$.

The comet's ${E}_{\text{total}}$ does not change because the comet does not gain any total energy at any part of its path and does not loose from the total.

However, if you look at just a part of the comet's path, then there will have been work done by gravitational force. It might be positive work or negative work. It would be positive work if the comet's speed has increased, negative work if it has decreased. But for any complete cycle, there is no net work done.

Whatever point in its path the question might be referring to, the answer to the question is:
Because the comet has returned to its original position (gravitational potential energy is same as the previous time it was here) with the same speed (kinetic energy is same as the previous time it was here). And the total is still ${E}_{\text{total}}$.

I hope this helps,
Steve