A couple of satellites

Classical Mechanics Level 2

A satellite in a circular orbit of radius R has a period of 4 hours. Another satellite with orbital radius 3R around the same planet will have a period of (in hours):

16 16 4 27 4 \sqrt{27} 4 8 4 \sqrt{8} 4 4

Manish Mayank by Manish Mayank , 20, India

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2 solutions

Manish Mayank
Oct 30, 2014

Using Kepler's 3rd law of planetary motion we have, T 2 R 3 \frac{T^2}{R^3} = constant Thus, 4 2 R 3 \frac{4^2}{R^3} = T 2 ( 3 R ) 3 \frac{T^2}{(3R)^3} or, T = 4 27 \boxed{T=4 \sqrt{27}} .

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Are you truly 14 years old? If so, then you are a very learned teenager.

Om Dave - 6 years ago

Keplers 3rd law T^2 = kR^3

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