As a satellite in orbit moves from a distance of 300 kilometers to a distance of 160 kilometeres above the?

Question

Earth, the kinetic energy of the satellite

a. decreases
b. increases
c. remains the same

Answer 1

Assuming no friction - the satellite's potential energy has reduced from 300mg to 160mg, so its kinetic energy must have increased by 140mg. This is not strictly accurate since the value of g will have increased by about 4.3% as the satellite approaches the earth, but the net effect is a significant increase in kinetic energy.

Answer 2

Increases.

You need mathematics to show this, but most good books will explain it.

This is why satellites in orbit losing total energy (friction with upper atmosphere maybe) will drop to a lower orbit, but will be moving faster in its orbit.

It's got to do with Bode's Law that periodic time T of a planetary body, and the radius of the orbit R, is linked by the equation

T^2 = k R^3 where k is a constant.

When R decreases from 300 km to 160 km, T would decrease.

This means it does one orbit in a shorter time.
Hence, this means it goes faster.