Two earth satellites, a and b, each of mass m, are to be launched into circular orbits about earth's center. satellite a is to orbit at an altitude of 5970 km. satellite b is to orbit at an altitude of 21200 km. the radius of earth reis 6370 km. (a) what is the ratio of the potential energy of satellite b to that of satellite a, in orbit? (b) what is the ratio of the kinetic energy of satellite b to that of satellite a, in orbit? (c) which satellite (answer a or b) has the greater total energy if each has a mass of 28.8 kg? (d) by how much?

(a) 0.448

The gravitational potential energy of a satellite in orbit is given by:

where

G is the gravitational constant

M is the Earth's mass

m is the satellite's mass

r is the distance of the satellite from the Earth's centre, which is sum of the Earth's radius (R) and the altitude of the satellite (h):

r = R + h

We can therefore write the ratio between the potentially energy of satellite B to that of satellite A as

and so, substituting:

We find

(b) 0.448

The kinetic energy of a satellite in orbit around the Earth is given by

So, the ratio between the two kinetic energies is

Which is exactly identical to the ratio of the potential energies. Therefore, this ratio is also equal to 0.448.

(c) B

The total energy of a satellite is given by the sum of the potential energy and the kinetic energy:

For satellite A, we have

For satellite B, we have

So, satellite B has the greater total energy (since the energy is negative).

(d)

The difference between the energy of the two satellites is: