You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part. A satellite of mass 4500 kg orbits the Earth in a circular orbit of radius of 9.3 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
1. What is the speed of the satellite? (m/s)
2. What is the minimum amount of energy required to move the satellite from this orbit to a location very far away from the Earth?

Answer

given,

Mass of satellite, m = 4500 kg

Mass of the earth, M = 6 x 10²⁴ Kg

Earth circular orbit radius, R = 9.3 x 10⁶ m

a) To find the speed of the satellite

   we need to equate the gravitation force between earth and satellite with the centripetal force.

   V = 6559.89 m/s

b) Minimum amount of energy of satellite

           E = 9.68 x 10¹⁰ J

Minimum amount of energy require to move satellite is equal to E = 9.68 x 10¹⁰ J

The minimum amount of energy that is required to move the satellite is 9.68 x 10¹⁰ J.

A) The speed of the satellite can be calculated by equating the gravitational force and centripetal force on the satellite,

Where,

= speed of satellite =?

- gravitational constant =

- mass of earth = 6 x 10²⁴ Kg

- radius of the circular orbit of satellite = 9.3 x 10⁶ m

Put the value in the formula, we get:

V = 6559.89 m/s

B) Minimum amount of energy of satellite to move

Put the values in the formula, we get:

E = 9.68 x 10¹⁰ J

Therefore, the minimum amount of energy that is required to move the satellite is 9.68 x 10¹⁰ J.

To know more about gravitational constant,