Question

The gravitational force exerted by the Sun on the Moon is about twice as great as the gravitational force exerted by the Earth on the Moon, but still the Moon is not escaping from the gravitational influence of the Earth. Mark the option which correctly explains the above system.
(A). Escape speed is independent of the direction in which it is projected.
(B). The rotational effect of the Earth plays a role in computation of escape speed, however small it may be.
(C). A body thrown in the eastward direction has a less escape speed.
(D). None of the above.

Answer 1

- Hint: The Earth-Moon system is a bound system. A body will escape from Earth’s gravitational influence when it gains enough positive energy so that total energy of the system is greater than or equal to zero.

Complete step-by-step solution -
The Earth exerts gravitational force on the Moon and Earth-Moon system is a bound system. So the total energy of this system is negative. In order to escape from the Earth’s gravitational field we need to provide an additional positive energy so that the total energy of the system is greater than or equal to zero. Even though gravitational force exerted by the Sun on the Moon is two times greater than the gravitational force exerted by Earth, the Sun does not provide any energy to the Moon. Therefore, the Moon is not escaping from the gravitational influence of the Earth.
The statements in option A, B, and C are correct but they are not the correct explanation for the system given in the question.

Hence, the correct answer is option (D).

Note: The escape velocity depends on many factors. But the body will not escape unless and until the total energy of the system is greater than or equal to zero. Satellites are bound to their planets by the strong gravitational force exerted by planets. The Sun also exerts gravitational force on these satellites but it does not add any energy to satellites, therefore, satellites don’t escape from the plant’s gravitational influence.