Question

A 993-kg satellite orbits the Earth at a constant altitude of 98-km.

(a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 199 km?

(b) What is the change in the system's kinetic energy?

(c) What is the change in the system's potential energy?

Answer 1

(a) Given mass of the satellite m = 993kg, At first it is at a radius r1 = 98km = 98000m. Now its radius is extended to 199km. So the second radius, r2 = 199000m.

Total energy of the satelitte when its radius is r1 is

where G = universal gravitational constant = 6.67 x 10-11Nm2kg-2 and M is the mass of the earth. M = 5.97 x 1024kg.

Similarly total energy of the satelitte when its radius is r2 is

Now the change in total energy when the satellite move from r1 to r2 is

Positive sign shows that the TE increased. The amount of energy that must be added to the system to move the satellite from r1 to r2 is 1.02 x 1012 J.

(b) Kinetic energy of the satelitte when its radius is r1 is

Similarly kinetic energy of the satelitte when its radius is r2 is

Now the change in kinetic energy when the satellite move from r1 to r2 is

Negative sign shows that the kinetic energy decreased. So the change in kinetic energy of the system is 1.02 x 1012 J.

(c) Potential energy of the satelitte when its radius is r1 is

Similarly potential energy of the satelitte when its radius is r2 is

Now the change in potential energy when the satellite move from r1 to r2 is

Positive sign shows that the potential energy increased. So the change in potential energy of the system is 2.04 x 1012 J.

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