Question

If satellite B is four time the distance of satellite A from the Earth, then the magnitude of the gravitational binding energy of satellite B is how many times that of satellite A

a. 1/16
b. 1/4
c. 1/2
d. 2 times
e. 4 times
f. 16 times

Answer 1

The magnitude of the gravitational binding energy of satellite B is 1/4 of that of satellite A because gravitational potential energy is inversely proportional to the distance from the center of the Earth, and satellite B is four times further away than satellite A.

Step-by-step explanation:

If satellite B is four times the distance of satellite A from the Earth, then we need to consider the formula for gravitational binding energy, which is given by the expression:

U = -G(Mm/r)

where U is the gravitational potential energy, G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance from the center of the Earth to the satellite. Since the question asks for the magnitude of the gravitational binding energy, we ignore the negative sign, which indicates that gravitational potential energy is always negative in a bound system.

Now, comparing the two satellites:

For satellite A, let's say the energy is UA = GMm/r

For satellite B, which is at four times the distance, the energy UB will be UB = GMm/(4r)

Hence, UB = UA/4

This means that the magnitude of the gravitational binding energy of satellite B is 1/4 that of satellite A.