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MathGroup Archive 2004

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Re: NDSolve for Newtonian Orbits Question

  • To: mathgroup at
  • Subject: [mg47466] Re: NDSolve for Newtonian Orbits Question
  • From: drbob at (Bobby R. Treat)
  • Date: Tue, 13 Apr 2004 06:26:18 -0400 (EDT)
  • References: <c4jasf$dpk$> <c5di74$nsv$>
  • Sender: owner-wri-mathgroup at

It's probably not new to most of you, but I have a notebook on the
Mathematica page at that proves (via ODE's) the
equivalence of Kepler's Laws and Newton's gravitation law.


mathma18 at (Narasimham G.L.) wrote in message news:<c5di74$nsv$1 at>...
> "David Park" <djmp at> wrote in message news:<c4jasf$dpk$1 at>...
> > I am trying to obtain a numerical solution for Newtonian orbits... For a start I just want to solve for the radius r as a function of time.
> You are the frequent solution provider ...This may not give a proper
> answer.I was earlier told some non-linear equations like y y''=
> constant are not so easy to solve on Mathematica, but you may find it
> is not so ..
> I tried to get the the earliest Newton's differential equation
> involving radius solved with respect to time. [(r-th) ellipse solution
> is well known.]. Wonder how Newton obtained radius as a time function,
> or whether it is mentioned  in Principia. I eliminated h (angular
> momentum) to get a decoupled (r-time) non-linear ODE. FWIW, please see
> running thread in sci.math about < Differential equations of periodic
> functions > in:
> ; Thomas Nordhaus, Peter Montgomery and Roger Bagula have made
> interesting comments.  Best Regards, Narasimham

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