Question

State with reasons whether the following sentences are true or false
a. If a spacecraft has to be sent away from the influence of earth’s gravitational field, its velocity must be less than the escape velocity.
b. The escape velocity on the moon is less than that on the earth.
c. A satellite needs a specific velocity to revolve in a specific orbit.
d. If the height of the orbit of a satellite increases, its velocity must also increase.

Answer 1

a. The statement is false. This is because the minimum velocity with which the spacecraft must be projected so that it escapes the Earth's gravitational pull is known as escape velocity. So, the initial velocity of the spacecraft must be greater than or equal to escape velocity of Earth.

b. Escape velocity on a planet is given as:
$v_{\mathrm{esc}}=\sqrt{\frac{2GM}{R}}=\sqrt{2gR}$
Since, acceleration due to gravity on Moon is one-sixth of that on Earth, thus the escape velocity on the Moon is less than that on the Earth. Hence, the statement is true.

c. The specific velocity with which the satellite revolves around a planet is known as critical velocity. It is given as
$v_{\mathrm{c}}=\sqrt{\frac{GM}{R+h}}$
So, it can be observed that the critical velocity of a satellite changes depending on the height of the orbit from the surface of a planet. Thus, to revolve in a specific orbit, a satellite would require specific velocity. Hence, the statement is true.

d. The specific velocity with which the satellite revolves around a planet is known as critical velocity. It is given as
$v_{\mathrm{c}}=\sqrt{\frac{GM}{R+h}}$
So, we see that as the height (h) of the orbit of a satellite increases, it velocity must decrease. Hence, the statement is false.