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 > running thread in sci.math about < Differential equations of periodic > functions > in: http://groups.google.co.in/groups?dq=&hl=en&lr=&ie=UTF-8&th=63b9b64ea13f1c82 > ; Thomas Nordhaus, Peter Montgomery and Roger Bagula have made > interesting comments. Best Regards, Narasimham