Show that the radius of an orbit may be expressed as follows: R^3=((GM)/4*pi^2)T^2

Start with Newton's Law of Gravitation: F=(GMm)/R^2 (1) Since orbits are assumed to be circular recall the equation for centripetal force: F=(mv^2)/R (2) We can now equate these 2 forces due to them being action-reaction pairs (Newton's 3rd Law) (GMm)/R^2= (mv^2)/R We notice that small m on both sides cancel and 1/R^2 may be reduced to 1/R on the LHS giving an equation for v^2: v^2=GM/R (3) Since we have a circular orbit we can use the radial velocity equation: v=Rw (4) We then sub (4) into (3) R^2w^2=GM/R (5) Remember w=2pi/T (6) this can be substituted in and the R terms may be collected to give R^3 (4pi^2/T^2)R^3=GM (7) Finally divide by 4pi^2/T^2 to give the correct equation R^3=((GM)/4*pi^2)T^2 (8)

Answered by Liam M. Physics tutor

4942 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Is a photon a wave or a particle??


Why does current split between branches of a parallel circuit, but voltage remains the same for each branch?


What is the difference between accuracy and precision?


Draw and describe the major points of a typical stress-strain graph for a metal.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences