First slide

Motion of planets and satellites

Question

Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is 2:1.If one of them is at a height of 100km, the height of the other satellite is(in km)

Easy

A

19600
B

24600
C

29600
D

14600

Solution

$V_{0} = \sqrt{\frac{G M}{R + h}} \Rightarrow V_{0} α \frac{1}{\sqrt{R + h}} \frac{V_{1}}{V_{2}} = \sqrt{\frac{R + h_{2}}{R + h_{1}}} \Rightarrow \frac{2}{1} = \sqrt{\frac{6400 + h_{2}}{6400 + 100}} \Rightarrow \frac{4}{1} = \frac{6400 + h_{2}}{6500} \Rightarrow h_{2} = 26000 - 6400 = 19600 k m$

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