Question

let the period of revolution of a Planet at a distance R from the star be T prove that if it was a distance of 2R from the star it period of revolution will be root8T

Answer 1

According to Kepler's law , T²$\propto$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

Answer 2

According to Kepler's law , T²\propto∝ a³

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objects

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is T

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2R

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)Dividing equation (1) by (2)

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)Dividing equation (1) by (2)T²/T'² = kR³/k8R³ = 1/8

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)Dividing equation (1) by (2)T²/T'² = kR³/k8R³ = 1/8T'² = 8T²

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)Dividing equation (1) by (2)T²/T'² = kR³/k8R³ = 1/8T'² = 8T²square root both sides,

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)Dividing equation (1) by (2)T²/T'² = kR³/k8R³ = 1/8T'² = 8T²square root both sides,T' = \sqrt{8}8 T

According to Kepler's law , T²\propto∝ a³Here T denotes the time period and a denotes the distance between two objectsHere, when distance between planet and star is R then time period is Tmeans T² = kR³ [ here k is proportionality constant ]----(1)Again, Let the time period is T' when distance between planet and star is 2RT'² = k(2R)³ = k.8R³ -----(2)Dividing equation (1) by (2)T²/T'² = kR³/k8R³ = 1/8T'² = 8T²square root both sides,T' = \sqrt{8}8 THence, time period will be \sqrt{8}8 T , when distance between planet and star will be 2R

Explanation:

hope it helps you