Maharashtra Class 10 Answered
Let the period of revolution of a planet at a distance of 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 √8T
Asked by yuvrajbhosale96 | 27 Mar, 2019, 12:42: PM
Expert Answer
According to Kepler's law ,
T² is directly propotional to a³
Here T denotes the time period and a denotes the radius of revolution
Here when the radius of revolution is R then time period is T means
Here when the radius of revolution is R then time period is T means
T² = kR³ [ here k is proportionality constant ]----(1)
Again,
Let the time period is T' when the radius of revolution is 2R
T'² = k(2R)³ = k.8R³ -----(2)
Dividing equation (1) by (2)
Dividing equation (1) by (2)
T²/T'² = kR³/k8R³ = 1/8
T'² = 8T²square root both sides, we get
T' = √8 T
Hence, proved.
Answered by Ankit K | 27 Mar, 2019, 07:49: PM
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