What is the period of moon B?Moon A is 1 J.D. from Jupiter and goes around in 1 day. Moon B is 5.1 J.D. from Jupiter. What is the period of Moon B? [0.00 decimal places]
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Tushar Chandra
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Kepler's third law of planetary motion gives us the relation between the orbital period and the distance that the body is revolving at as the square of the orbital period of the body being directly proportional to the cube of the distance from the body around which it is revolving. Or t^2 = k* r^3
Here, for Moon A, which is at a distance 1 J.D. from Jupiter, the period of completing 1 orbit is 1 day. So we have 1^2 = k * 1^3
=> k = 1
Now for Moon B, we have the distance of the orbit as 5.1 J.D.
=> t^2 = k* (5.1) ^3
=> t^2 = (5.1) ^3
=> t = (5.1) ^ (3/2)
=> t = 11.51
Therefore the period of the Moon B is 11.51 days.