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,

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.