Derive Keplers 3rd law

Equate gravitational force (GMm/r^2) to centripetal force (mv^2/r). Rearrange to get v^2=GM/r. Due to the approximated circular orbit v=2pir/T so v^2=4pi^2r^2/T^2. Therefore GM/r=4pi^2r^2/T^2. Rearranging gives GM=4pi^2r^3/T^2. Rearranging futher gets T^2=(4pi^2/GM)r^3. Hence T^2 is proportional to r^3.

MS
Answered by Michael S. Physics tutor

3697 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

How would you calculate the vertical and horizontal components of the velocity of an object with an initial velocity of 15m/s which is travelling upwards at an angle of 30 degrees to the horizontal?


In the photoelectric effect, what happens as you increase the frequency of light keeping the same intensity constant?


What does a negative velocity mean?


A ball is released from stationary at a great height. Explain how the forces acting on it change before it hits the ground and how these forces affect the velocity of the ball.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences