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

5379 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

A wire has length l, cross-sectional area a, resistivity p and resistance R. It is compressed to a third of its original length but its volume and resistivity are constant. Show its new resistance is R/9.


How did rutherford's gold leaf experiment prove the existence of the nucleus?


Explain why a jet fighter pilot experiences "weightlessness" when at the top of a loop-the-loop manoeuvre.


Two pendulums consist of a massless rigid rod of equal length attached to a small sphere of equal radius, with one sphere hollow for one pendulum and the other solid. Each pendulum undergoes damped SHM. Which pendulum has the largest time period?


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