Question

When a satellite going round the earth in a circular orbit of radius $r$ and speed $v$, loses some of its potential energy, then :

• A. both $r$ and $v$ will increase
• B. both $r$ and $v$ will decrease
• C. $r$ will decrease and $v$ will increase
• D. $r$ will increase and $v$ will decrease

Answer 1

The correct option is C $r$ will decrease and $v$ will increase

This problem is based on the topic of Binding Energy of Satellite

$\bullet$ The Universal Constant of Gravitation is denoted by $G,$ the mass of earth by $M$ and the mass of the satellite by $m.$

$\bullet$ The potential energy P.E. of a satellite is given by the formula $P.E.=-\frac{GMm}{r}$

Here the negative sign indicates that the satellite is bound to earth due to the force of attraction of gravity.

$\bullet$ The speed of the satellite is given by $v=\sqrt{\frac{GM}{r}}$

Now look at the formula for P.E. carefully.

$m$ cannot change unless something goes wrong with the satellite.

$r$ is the only quantity which can change.

P.E. is decreasing means the denominator $r$ should increase. However, due to the minus sign, vice-versa will happen.

So $r$ will decrease.

Now look at the formula for $v.$

The $r$ is decreasing means $v$ will increase.