Question

late period of revolution of a Planet at a distance r from Star BT prove that if it was a distance of 2 hour from the star its period of revolution will be root 8T​

Answer 1

Late period of revolution of a Planet at a distance r from Star BT prove that if it was a distance of 2 hour from the star its period of revolution will be root 8t....

Answer:

According to Kepler's law ,

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,

Hence, time period will be √8T , when distance between planet and star will be 2R