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# As measured by an observer on earth, what would be the difference, if any, in the period of two satellite each in a circular orbit near the earth's equatorial plane, but one moving eastward and other moving westward.

a) time period of satellite moving towards west will be less than one moving towards east. b) the time period of one satellite moving towards east will be less than the one moving towards west.c) Both will be same d) cannot be determined

Let $'v'$ is actual speed of satellite.
$V$ velocity of earth on the equator.
Velocity of satellite moving towards east relative to earth will be $(V-v)$ while velocity of satellite moving towards west relative to earth will be $(V+v)$
Time Period 1$=T_{\large East}=\large\frac{2 \pi R}{V-v}$
Time Period 2$=T_{\large West}=\large\frac{2 \pi R}{V+v}$
Time period of satellite moving towards west will be less than one moving towards east.
Hence a is the correct answer.
edited Jul 2, 2014