If the height of the orbit of a satellite increases, its velocity must also increase.

Question

State with reasons whether the following statement are true or false.

If the height of the orbit of a satellite increases, its velocity must also increase.

Answer 1

False.

Explanation:

Centripetal force on the satellite \(\frac{mv^2_c}{R+h}\) = gravitational force exerted by the earth on the satellite \(\frac{GMm}{(R+h)^2}\)where,

m : mass of the satellite

v_c : critical velocity of the satellite

h : height of the satellite from the surface of the earth

M : mass of the earth 

R : radius of the earth 

G : gravitational constant

Thus, if the value of h changes, the value of v also changes. It means a satellite needs to be given a specific velocity (in the tangential direction) to keep it revolving in a specific orbit.

As per the formula v_c = \(\sqrt{\frac{GM}{R+h}}\), if the value of h increases, the value of v_c decreases. 

Hence, if the height of the satellite from the surface of the earth increases, its velocity decreases.