Kepler’s 3rd Law Formula and Numericals on it

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:  T_J = 11.86 years

re = 1.5×10¹¹m

Te = 1 year

R_J =?

We know the Kepler’s third law

T² ∝ R³

Te² ∝ r³e —– (i)

T_J² ∝ r_J³ —— (ii)

(Te/T_J)² = (re/r_J)³

(Te/T_J)^2/3 = re/r_J

r_J = re (T_J/T_e)^2/3

= 1.5×10¹¹ (11.86/1)^2/3

R_J = 7.90 × 10¹¹ m