Question

If a satellite orbits as close to the Earths surface as possible then which of the following statement(s) is/are incorrect?

• A. Its speed is maximum
• B. Time period of its rotation is minimum
• C. The total energy of the earth plus satellite system is minimum
• D. The total energy of the earth plus satellite system is maximum

Answer 1

Answer: (A), (B), (C)

The correct options are
A The total energy of the earth plus satellite system is minimum
B Time period of its rotation is minimum
C Its speed is maximum

Speed is given by:

$v=\sqrt{\frac{GM}{r}}$ i.e. $v\propto \sqrt{\frac{1}{r}}$

So, speed will be maximum as $r$ is lowest. Hence option A is correct.

Time period is given by

$T=\left(\frac{2\pi }{\sqrt{GM}}\right)r^{\frac{3}{2}}$

$T\propto r^{\frac{3}{2}}$

So, when $r$ is minimum, time period is also minimum.

Total energy $E=-\frac{GMm}{2r}$

$E\propto -\frac{1}{r}$ So, total energy is also minimum when $r$ is minimum.