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A satellite is orbiting the earth of mas...

A satellite is orbiting the earth of mass `M` in equatorial plane in a circular orbit having radius `2R` and same sense of rotation as that of the Earth. Find duration of time for which a man standing on the equator will be able tosee the satellite continuously. Assume that the mans can see the satellite when it is above horizon. take Earth's angular velocity `omega`.

Text Solution

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The correct Answer is:
`(2pi)/(3[sqrt((GM)/(8R^(3))-omega_(e))])`
`m(2R)omega^(2)=(GM_(e))/((2R)^(2))`
`omega=sqrt((GM)/(8R^(3)))`
`omega_(rel)=omega-omega_("earth")impliesomega_(rel)=sqrt((GM)/(8R^(3)))-omega_(s)`
`t=theta/(omega_(rel))impliesT=((2pi//3))/(sqrt(GM)/(8R^(3))-omega_(e))`
`t=(2pi)/(3(sqrt((GM)/(8R^(3))-omega_(e))))`
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