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  4. The orbital velocity of earths satellite near surface is 7 km/s. When the radius of orbit is 4 times than that of earths radius. Then orbital velocity in that orbit will be :

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Q. The orbital velocity of earths satellite near surface is 7 km/s. When the radius of orbit is 4 times than that of earths radius. Then orbital velocity in that orbit will be :

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Solution:

From the formula, the orbital velocity is $ {{\upsilon }_{0}}=\frac{\sqrt{GM}}{R}=7km/\sec $ ?..(1) If the radius of the orbit is four times that of the earth, then we have $ \upsilon _{0}^{}=\frac{\sqrt{GM}}{4R} $ ...(2) Now from equation (1) and (2) we get $ \frac{7}{\upsilon _{0}^{}}=\frac{\sqrt{GM/R}}{\sqrt{GM/4R}}=\frac{2}{1} $ So, $ \upsilon _{0}^{}=\frac{7}{2}=3.5km/s $