Final answer:
The change in energy of a payload taken from Earth to the Moon is negative, and from the Moon to Earth is positive. Calculating the energy needed to move a payload assumes recoverable energy, but may not be accurate in real-life scenarios.
Step-by-step explanation:
The change in energy of a 1000-kg payload taken from rest at the surface of Earth and placed at rest on the surface of the Moon is negative. When the payload is lifted from Earth to the Moon, it gains gravitational potential energy. However, it also loses an equal amount of kinetic energy due to the decrease in its speed as it moves away from Earth. Therefore, the overall change in energy is negative.
If the payload were taken from the Moon's surface to Earth, the change in energy would be positive. The payload gains kinetic energy as it falls towards Earth and loses an equal amount of potential energy. Therefore, the overall change in energy is positive.
Calculating the energy needed to move a payload back and forth assumes that all the energy is recoverable. However, in reality, there would be energy losses due to friction, air resistance, and other factors. So this calculation may not accurately represent the actual energy needed to move a payload between Earth and the Moon.