Transcription of The Two-Body Problem
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The Two-Body Problem
The Two-Body ProblemIn the previous lecture, we discussed a variety of conclusions we could makeabout the motion of an arbitrary collection of particles, subject only to a fewrestrictions. Today, we will consider a much simpler, very well-known problemin physics - an isolated system of two particles which interact through a centralpotential. This model is often referred to simply as thetwo- body the case of only two particles, our equations of motion reduce simply tom1 r1=F21;m2 r2=F12(1)A famous example of such a system is of course given by Newton s Law ofGravitation, where the two particles interact through a potential energy givenbyU12(|r1 r2|) =U21(|r2 r1|) =Gm1m2|r1 r2|2,(2)whereGis Newton s constant,G= 10 11N m2/kg2.
simply de nes the position of the smaller mass with respect to the position of the larger mass, which is the center of mass itself. Thus, to a good approximation,
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