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)

LM
Answered by Liam M. Physics tutor

5563 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is the Centripetal force, and how does it keep objects in circular motion?


Explain Rutherford's alpha particle scattering experiment and what it provided evidence for


How does a thermal nuclear reactor work?


Describe and explain the photoelectric effect (6 marks)


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning