Question

A 1 048-kg satellite orbits the Earth at a constant altitude of 101-km.

(a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 208 km?
MJ

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

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

Answer 1

To solve these problems, we need to determine velocity of satellite in a circular orbit which can be obtained from equation,

where G is gravitational constant and its value is , M is the mass of Earth which is and r is orbit distance which is radius of Earth + altitude of the satellite orbit.

Velocity of satellite at altitude 101 Km is,

Velocity of satellite at altitude 208 Km will be,

(a) Suppose energy E is required to move the satellite from altitude 101 Km to altitude 208 Km, then from conservation of energy,

        (1)

Here are gravitational potential and kinetic energy at altitude 101 Km and are gravitational potential and kinetic energy at altitude 208 Km.

Gravitational potential energy can be evaluated from equation below,

where m is mass of satellite i.e. 1048 Kg.

Gravitational potential energy at altitude 101 Km is,

Gravitational potential energy at altitude 208 Km is,

Kinetic energy at altitude 101 Km is,

Kinetic energy at altitude 208 Km is,

From equation (1),

(b) Change in system's kinetic energy is,

(c) Change in system's potential energy is,