Kepler’s 3rd Law Formula
Statement: “The square of its revolution around the sun is directly proportional to cube of the distance of planet from sun”.
From fig, S = Sun
P = Planet
F = Force
If r is the arrange distance of the planet from the sun and T is period of revolution, then from the above statement.
T2 ∝ r3
T2 = Kr3
K is const of proportionality
I.e. T2/r3 = constant = K
So, T2 = Kr3 —- (1)
This is required equation.
Numericals on Kepler’s 3rd Law:
The time period at Jupiter 11.86 years to complete the one revolution around sun. What is its distance from sun? Distance of the earth from the sun is 1.5×1011 m.
Given: TJ = 11.86 years
re = 1.5×1011m
Te = 1 year
RJ =?
We know the Kepler’s third law
T2 ∝ R3
Te2 ∝ r3e —– (i)
TJ2 ∝ rJ3 —— (ii)
(Te/TJ)2 = (re/rJ)3
(Te/TJ)2/3 = re/rJ
rJ = re (TJ/Te)2/3
= 1.5×1011 (11.86/1)2/3
RJ = 7.90 × 1011 m