Question

The orbital speed of a satellite revolving around planet in a circular orbit is $v_0$. if its speed is increased by 10%, then

• A. It will escape from its orbit
• B. It will start rotating in an elliptical orbit
• C. It will continue to move in the same orbit
• D. It will move in a circular orbit of radius 20% more than radius of initial orbit

Answer 1

The correct option is A It will escape from its orbit

Centripetal force = gravitational force

$\frac{{{mv}_0}^2}{r}=\frac{GmM}{r^2}$

From the above relations, we can conclude that:

The centripetal force balancing the gravitational force on the satellite is directly proportional to the velocity and inversely proportional to the radius of the orbit.

Thus;

$i.$ If the velocity increases, the centripetal force will also increase and to counter that, the radius of the orbit should decrease.

$ii.$ If we keep the radius unaltered in the equation, the centripetal force will increase more than the gravitational force and the satellite will escape.