Question

a satellite with a mass of 100kg fires it’s engines to increase velocity, thereby increasing the size of its orbit around the earth. as a result it moves from a circular orbit if radius 7.5x10^6 m to an orbit of radius 7.7x10^6 m. what is the approximate change in gravitational force from the earth as a result of this change in the satellites orbit?

Answer 1

The change in gravitational force from the earth on the satellite is approximately 2.6% as a result of the change in its orbit.

Step-by-step explanation:

The change in gravitational force from the earth can be calculated using the law of universal gravitation. The formula for gravitational force is F = G * (m1 * m2) / r², where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, the mass of the satellite is given as 100 kg and the change in the radius of the orbit is from 7.5x10⁶ m to 7.7x10⁶ m. The force is inversely proportional to the square of the radius, so the change in force can be calculated as:

F2 / F1 = (r1 / r2)²

F2 / F1 = (7.5x10⁶ / 7.7x10⁶)²

F2 / F1 = 0.974

This means that the gravitational force from the earth on the satellite decreased by approximately 2.6% as a result of the change in the satellite's orbit.