First slide

Motion of planets and satellites

Question

A satellite in equatorial plane is rotating in the direction of earth's rotation with time interval between its two consecutive appearances over head of an observer as time period of rotation of the earth , T_E. What is the time period of the satellite?

Moderate

A

$T_{E}$
B

$2 T_{E}$
C

$\frac{T_{E}}{2}$
D

$\frac{2 T_{E}}{3}$

Solution

For observer, $T^{'} = \frac{2 π}{ω_{S} - ω_{E}} = \frac{T_{S} T_{E}}{T_{E} - T_{S}}$
$= T_{E} (given) or T_{E}^{2} = 2 T_{S} T_{E} T_{S} = T_{E} / 2$

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