Question

A spaceship moves from the Earth to the Moon and back. The greatest energy requires for the spaceship is to overcome the difficulty in
A) entering the Earth’s gravitational force
B) taking-off from the Earth’s field
C) taking-off from the Moon’s filed
D) entering the Moon’s lunar surface

Answer 1

The Earth and the Moon exert a gravitational pull on the spaceship as it takes-off from their respective surfaces. The spaceship then has to do some work against this gravitational pull to lift-off from each surface. The greater the work done more will be the energy required for the spaceship to take-off.

Complete step by step answer:
Step 1: Mention the forces in play as the spaceship travels from the Earth to the Moon and back to the Earth.
As the spaceship takes-off the surface of the Earth, the Earth will exert a gravitational pull on the spaceship. Similarly, the Moon also exerts a gravitational pull on the spaceship as it takes-off from the Moon’s surface.

The magnitude of the gravitational pull exerted by the Earth and the Moon will be directly proportional to the mass of the Earth and the mass of the Moon respectively.
We know that compared to the Earth the mass of the Moon is very small.
i.e., ${M_{moon}} \ll {M_{earth}}$ .
So the gravitational pull exerted by the Earth will be more than that exerted by the Moon.
So the work done against the Earth’s gravity will be more. This suggests that the greater energy is needed to take-off from the surface of the Earth.

Hence the correct option is B.

Note:
For the spaceship to take-off from the surface of the Earth or from the surface of the Moon, an upward thrust is necessary. This suggests that work has to be done against the gravitational field of the Earth or that of the Moon. As we have established that more work is done to take-off from the surface of the Earth than that from the surface of the Moon, more fuel will be consumed while taking-off from the Earth’s surface.