The mean distance of two planet a and b from the sun is 2 and 4 times the distance of earth from the sun respectively. Find the ratio of the time taken by the two planets to make one revolution around the sun.

Arun
25763 Points
3 years ago

As we know,
From kepler law,
T^2= k* r^3

Hence
(T1/T2)^2 = (r1/r2)^3
(T1/T2)^2  = (2r/4r)^3
T1/T2 = $\sqrt$(1/8)
T1/T2 = 1/2$\sqrt$2
Sayantan Garai
117 Points
3 years ago
From Kepler's law,
T²αR³
Hence,
(T1/T2)²=(R1/R2
=> T1/T2=√(1/2)³
=√(1/8)
=1 / 2√2
=√2 / 4
Hence answer is 1:2√2 or √2:4.