BELIEVE   ME   NOT!    - -     A   SKEPTICs   GUIDE  

next up previous
Next: Tides Up: Orbital Mechanics Previous: Changing Orbits

Periods of Orbits

We can now explain (at least for circular orbits) Kepler's Third Law. The period  T  of an orbit is the circumference $2 \pi r$ divided by the speed of travel, v. Using the equation above for v in terms of r gives

\begin{displaymath}T = {2 \pi r \over \sqrt{GM_E \over {\textstyle r} }} \end{displaymath}


\begin{displaymath}\;\; = {2 \pi \over \sqrt{GM_E}} r^{\textstyle {3 \over 2}} \end{displaymath}


\begin{displaymath}\hbox{\rm or} \qquad T^2 \propto r^3 \end{displaymath}

as observed by Kepler. Newton explained why.



Jess H. Brewer
1998-10-08