A certain satellite has a kinetic energy of 7.5 billion joules at perigee (closest to Earth) and 3.5 billion joules at apogee (farthest from Earth). As the satellite travels from apogee to perigee, how much work does the gravitational force do on it?
Does its potential energy increase or decrease during this time, and by how much? (Enter a positive answer if the energy increases, and a negative answer if the energy decreases.)
To determine the work done by the gravitational force as the satellite travels from apogee to perigee, we can use the formula:
Work = Change in potential energy
The potential energy of an object in a gravitational field is given by the equation:
Potential energy = -GMm/r
where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the center of the Earth and the satellite.
Since we know the satellite has a kinetic energy of 3.5 billion joules at apogee and 7.5 billion joules at perigee, we can infer that the increase in kinetic energy is 7.5 - 3.5 = 4 billion joules.
The change in potential energy is equal to the negative of the change in kinetic energy, as the two are complementary. Therefore, the change in potential energy is -4 billion joules.
Since the question asks whether the potential energy increases or decreases during this time, we can see that the potential energy decreases. The change in potential energy, -4 billion joules, represents a decrease in potential energy.
Therefore, the answer is negative: The potential energy of the satellite decreases by 4 billion joules as it travels from apogee to perigee.