Question

find the ratio of time periods of revolution of two planets around the sun whose distance 20 AU and 40 AU respectively from the sun.

Answer 1

let linear velocity of both planets are same then

$t = \frac{2\pi}{w} .......w \: is \: angular \: velocity \\ \\ t = \frac{2r\pi}{v} \\ t \: is \: directly \: proportional \: to \: r$
let R1=20
R2=40

so
T1:T2=R1:R2=20:40=1:2

T1:T2=1:2