Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, it's period of revolution will be product of root of 8 and T
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According to Kepler's Law of planetary motion, the square of time period of a satellite is directly proportional to the cube of the radius of its orbit.
T^2 = K (R^3) ...(i)
When radius of orbit becomes 2R,
T1^2 = K (2R)^3 = K (8R^3) ...(ii)
Dividing equation 1 by 2, we get ratio between initial time period and final time period.
(T/T1)^2 = 1/8
T1^2 = 8 T^2
T1 = (8)^0.5 T
Hence the above statement is proved.
T^2 = K (R^3) ...(i)
When radius of orbit becomes 2R,
T1^2 = K (2R)^3 = K (8R^3) ...(ii)
Dividing equation 1 by 2, we get ratio between initial time period and final time period.
(T/T1)^2 = 1/8
T1^2 = 8 T^2
T1 = (8)^0.5 T
Hence the above statement is proved.
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