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Debate:What is the exponent of r in Newtonian gravity? (view source)
Revision as of 04:20, March 12, 2010
, 04:20, March 12, 2010My simulation, with pictures. I can't see the pictures in the preview. Maybe they're OK, maybe not.
[[User:SamHB|SamHB]] 20:35, 26 February 2010 (EST)
[[User:SamHB|SamHB]] 20:35, 26 February 2010 (EST)
I have simulated the planetary orbits, with pictures. The orbital equations are not easy to simulate accurately. I used a "relaxation method" boundary-value solver, along the lines of chapter 17 of "Numerical Recipes" by Press, Teukolsky, Vetterling, and Flannery. Double precision (17 decimal place) arithmetic was used. The convergence criterion was 10^-10. The functions were interpolated with 2000 points.
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[[File:Sam_orbit_1.jpg|thumb|right|450px|Figure 00, exponent = 2.0]]
[[File:Sam_orbit_2.jpg|thumb|right|450px|Figure 03, exponent = 2.03]]
[[File:Sam_orbit_3.jpg|thumb|right|450px|Figure 2, exponent = 2.2]]
[[File:Sam_orbit_4.jpg|thumb|right|450px|Figure 4, exponent = 2.4]]
[[File:Sam_orbit_5.jpg|thumb|right|450px|Figure 436, exponent = 2.436]]
Figure 00 shows the familiar Kepler orbit with an exponent of exactly 2. It is an ellipse, of course. The parameters were set so that the eccentricity was about 2. (Way more than the planets in the solar system, by the way.)
Setting the exponent to 2.000000157, as Newcomb did, would give a graph visually indistinguishable from this.
Figure 03 shows the effect of setting the exponent to 2.03. The precession is clearly visible.
Figure 2 shows the effect of setting the exponent to 2.2. The precession has become so wild that it's not really following an ellipse.
Figure 4 shows the effect of setting the exponent to 2.4. The planet is looping around wildly, but still following a regular pattern.
Figure 436 shows the effect of setting the exponent to 2.436. At this value, the planet follows a double loop, sort of like the "figure 8" pattern referred to above. (For different values of angular momentum, the exponent required to get this shape would be different.)
In no case is the orbit not a regular repeating pattern, and in no case does the planet fall into the Sun. Simulations that show that are incorrect.
But this question is ill-formed as an aspect of "quantifying openmindedness". The question seems to be asking "Do you think is impossible that Simon Newcomb's 19<sup>th</sup> century formulation is superior to Isaac Newton's 17<sup>th</sup> century formulation? While Newcomb's formulation did finagle the exponent to get a correct precession value for ''one'' planet (Mercury), a 20<sup>th</sup> century formulation has superseded both. This gives extremely accurate explanations for all planetary precessions, as well as the correct (1.75 arc second) value for the bending of light beams close to the Sun, as well as the Shapiro effect, the Pund-Rebka experiment, the Hulse-Taylor pulsar orbit precession and decay, gravitational lensing, de-Sitter precession, Lense-Thirring frame-dragging precession, etc.
There is simply no reason to embrace Newcomb's formulation, except under a bizarre notion of what constitutes openmindedness. Asking whether one is openminded enough to accept the possibility that Newcomb's exponent fudging is correct is rather like asking:
*Are you openminded enough to admit the possibility that Ptolemy's geocentric formulation of the heavens, complete with epicycles, as opposed to the Copernicus/Kepler model, is correct?
*Are you openminded enough to admit the possibility that the phlogiston theory of combustion is correct?
*Are you openminded enough to admit the possibility that Trofim Lysenkos's genetic theories are correct?
*Are you openminded enough to admit the possibility that the cosmological theories of Immanuel Velikovsky, Erich von Daniken, L. Ron Hubbard, Gene "time cube" Ray, etc., are correct?
*Are you openminded enough to admit the possibility that the "Piltdown man" wasn't a hoax?
[[User:SamHB|SamHB]] 23:20, 11 March 2010 (EST)