Let the period of revolution of a Planet at a distance R from a star be T prove that if it if it was at a distance of 2R
from the star its period of revolution will be out of rrt of 8 T
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Answered by
9
Hi.....
According to Kepler's law , T² is directly proportional to a³
Here T denotes the time period and a denotes the distance between two objects
Here, when distance between planet and star is R then time period is T
means T² = kR³ [ here k is proportionality constant ]----(1)
Again, Let the time period is T' when distance between planet and star is 2R
T'² = k(2R)³ = k.8R³ -----(2)
Dividing equation (1) by (2)
T²/T'² = kR³/k8R³ = 1/8
T'² = 8T²
square root both sides,
T' = sqrt{8}T
Hence, time period will be sqrt{8}T , when distance between planet and star will be 2R...
Hope this helps u!!
According to Kepler's law , T² is directly proportional to a³
Here T denotes the time period and a denotes the distance between two objects
Here, when distance between planet and star is R then time period is T
means T² = kR³ [ here k is proportionality constant ]----(1)
Again, Let the time period is T' when distance between planet and star is 2R
T'² = k(2R)³ = k.8R³ -----(2)
Dividing equation (1) by (2)
T²/T'² = kR³/k8R³ = 1/8
T'² = 8T²
square root both sides,
T' = sqrt{8}T
Hence, time period will be sqrt{8}T , when distance between planet and star will be 2R...
Hope this helps u!!
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