Re: NDSolve for Newtonian Orbits Question

• To: mathgroup at smc.vnet.net
• Subject: [mg47466] Re: NDSolve for Newtonian Orbits Question
• From: drbob at bigfoot.com (Bobby R. Treat)
• Date: Tue, 13 Apr 2004 06:26:18 -0400 (EDT)
• References: <c4jasf\$dpk\$1@smc.vnet.net> <c5di74\$nsv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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

Bobby

mathma18 at hotmail.com (Narasimham G.L.) wrote in message news:<c5di74\$nsv\$1 at smc.vnet.net>...
> "David Park" <djmp at earthlink.net> wrote in message news:<c4jasf\$dpk\$1 at smc.vnet.net>...
> > 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