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# Re: Orbital Kinetic Energy

Brian Blais wrote:
I was wondering if anyone knew of a calculation showing that
the kinetic energy of an object in a circular orbit is equal
to half of the potential energy, where the calculation does
*not* use acceleration or force at all. Is there an argument
for this based purely on energy concepts? It occurred to me
that there should be, but I can't think of it.

It bothers me to write that the KE = 1/2 PE. Wouldn't it be better to
write that that KE = 1/2 |PE|, where PE is set to zero at infinite
separation?

That said, I think one can say that if KE = |PE| then the velocity would
be equal to the escape velocity and the object would be going too fast
to stay in orbit. Conversely, if KE=0 (and knowing that the PE
decreases as r decreases) the velocity would be zero and the object
would be going too slow to stay in orbit.

Can we figure out where (between KE=0 and KE=|PE|) the "right" KE is? I
don't know (without having to use derivatives or forces) but it is
tempting to think there must be a way...

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301