Article: <6iclj8$2pn@sjx-ixn6.ix.netcom.com> Subject: Re: Challenge to Jim Scotti Date: 1 May 1998 14:18:16 GMT In article <3548AADD.74CF@my.signature>, Joshua Hewitt <look@my.signature> wrote: > Actually there is no analytical solution for Kepler's equation > (M=E-e*sinE) as it is trancendental in E (the eccentric anomaly) > apart from the trivial solutions E=j*pi when M=j*pi where j is > an integer, M=E when e=0. The most common ways of solving > it are using a series solution (diverges for e>.6627), Newton- > Ralphson iteration, modified Newton-Ralphson iteration, or a > Fourier sine series and Bessel functions or the Lagrange method. > > M=mean anomaly > E=eccentric anomaly > e=eccentricity In article <6ic2av$6ve@electra.saaf.se> Paul Schlyter > [ the parabolic case also has an explicit exact solution, however > Kepler's equation cannot be used in that case ] ... Here I > considered Kepler's equation (plus the corresponding parabolic > or hyperbolic equivalents -- or, alternatively those universal > forms which are valid for any eccentricity ) to be THE solution > (of course combined with various other formula which describes > the orbit), even though it's in closed form. Compare this to the > three-body problem, where one cannot even obtain any closed > formula, valid indefinitely, describing the motion. Even the > restricted 3-body problem (where the 3rd body is considered to > be of zero mass, i.e. the other two bodies are then moving in > unperturbed 2-body motion) cannot offer any analytical formula > describing the motion of that 3rd body at any time in the future. (Begin ZetaTalk[TM]) So you're saying that you DO NOT HAVE math to allow for the hypothetical orbit we described? You are boggled? (End ZetaTalk[TM]) Then what did Jim Scotti mean, when he stated: ....... 220 230896 <6ganqt$am2@dfw-ixnews7.ix.netcom.com> article Path: ix.netcom.com!news From: saquo@ix.netcom.com(Nancy) Newsgroups: sci.astro Subject: Re: Planet X/12th Planet Long Elliptical Orbit Date: 6 Apr 1998 14:11:41 GMT Organization: Netcom Lines: 41 Message-ID: <6ganqt$am2@dfw-ixnews7.ix.netcom.com> NNTP-Posting-Host: smx-ca16-01.ix.netcom.com X-NETCOM-Date: Mon Apr 06 9:11:41 AM CDT 1998 Xref: ix.netcom.com sci.astro:230896 In article <6g3109$qsc$1@news.ccit.arizona.edu> Jim Scotti writes: >> It's a fact that most suns are binaries, and some so close at >> to give : the appearance of barely keeping each other at arms >> length. Why should : it be astonishing that a planet would >> institute an orbit around BOTH? Are you saying it is impossible >> for a planet to orbit two suns? Impossible? > > A planet can orbit both suns in a binary star system. (Begin ZetaTalk[TM]) You went through an elaborate statement to say you base your theories on orbits upon what you have OBSERVED - inverse square on Gravity and momentum conservation of energy rules. Bearing in mind that you have not OBSERVED a planet orbiting two suns, both suns in a binary system, what would that orbit look like? For the sake of moving this argument forward, we will assume for the moment that your orbital mechanics are correct, and not under challenge. Just paint for us what that orbit would look like. Not the several pages of math, but just something simple, in the manner you are so very skilled at employing. A simple verbal description of what such an orbit would look like. You have a head start in that your astronomy computer programs already ASSUME a second foci in elliptical orbits. Just put that foci out there, WAY out there, some 18.724 times as far as Pluto is from your Sun. Assume the same factors published prior to the search for Planet X, Van Flandern's statement that the perterbations observed in the outer planets would require a planet or brown dwarf 2 to 5 times as large as Earth. We are requesting for this discussion that you assume a planet 4 times as large as Earth, as this is our statement. Grant us this assumption in return for our granting you that YOUR assumption on orbital mechanics is correct, tit for tat, one concession for another, and since both assumptions as based on human assumption, you should have no objections. This hypothetical discussion would be no different from any other occuring on sci.astro in that regard, applying known physics, as you say, to a hypothetical situation. What would such an orbit, where a planet orbited both suns in a binary system, look like? (End ZetaTalk[TM])