Question

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of the earth in new orbit is $2$ times than that of the earlier orbit. Find out the time period in the second orbit.

• A. $4.8$ hours
• B. $48\sqrt{2}$ hours
• C. $24$ hours
• D. $24\sqrt{2}$ hours

Answer 1

The correct option is B $48\sqrt{2}$ hours

Velocity of satellite $v_1=\sqrt{\frac{GM}{R}}$

For geostationary satellite Time period is 24 hours,so$T_1$ = 24 hour

so $T_1=\frac{2\pi R}{v_1}$

When radius is doubled $v_1=\sqrt{\frac{GM}{2R}}$

$T_2=\frac{2\pi 2R}{v_2}$

so $\frac{T_1}{T_2}=\frac{v_2}{v_1}$ ,also $T_1=24hour$

$T_2=48\sqrt{2}$