A satellite needs a specific velocity to revolve in a specific orbit.

Question

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

A satellite needs a specific velocity to revolve in a specific orbit.

Answer 1

True.

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

∴ \(v^2_c=\frac{GM}{R+h}\)

∴ v_c = \(\sqrt{\frac{GM}{R+h}}\)

Thus, if the value of h changes, the value of υc 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.