Originally posted by Nereid
Jim/NEOclassic: you may be making things more complicated than they need to be.
Try this: assume there's only the Earth and the Moon (a 2-body problem) and ignore GR for the moment. Assume a circular orbit. Assume the Earth's mass is very, very much greater than the Moon's, perhaps the Moon is just a 'test mass'. Where's the centre of the circle? Where's the Earth?
Now assume the Earth and Moon have equal masses, and are not in elliptical orbits. How do the two bodies orbit each other? in a circle? where's the centre of the circle? what's at the centre?
Now if the Earth:Moon mass ratio is something between 0 and 1, still assuming circular orbits ... where's the centre of the circle(s)?
Finally, if the circles are just very slightly elliptical, more elliptical, ... ?
Hello Nereid,
You have posted five statements that appear to be so ordered that logic alone infers some kind of reality that the truth of your premise is in the final statement. I err! These are not statements but rather questions that imply that the reader has only one of two choices in order to agree or disagree with the ultimate conclusion; if agreement does not happen, then non sequitur's occur and logic is denied. However, I will try to answer your 5 questions (the question hidden in the first statement is revealed if it were to read: "Aren't you making things - - -?"
1. Complication is in the eyes of the beholder - your model is equally complicated to me as my model is to you.
2. It would be clarifying if you were to reveal what effect would exist if GR (I assume you mean General Relativity) had not been ignored. Concentric circular orbits (one for each body) do exist and that singularity is positioned somewhere between the two bodies; when that position is determined by the static balance-beam model an arbitrary position that I call a "fulcrum" can be calculated - there is a caveat that obtains with the static modeling; considering that the system is really dynamic. Assuming that the Earth's mass be very very much greater than that of the moon's obfuscates the reality that most of the solar orbits' fulcrums are at radii from the sun's center less than the radius of the sphere of incandescence contrasted with the earth-moon fulcrum that is away from the Earth's surface as manifest by the Lunar influence on the Earth's oceanic tides. An even more nearly perfect explanation of the position of the true fulcrum is shown by the SOHO space telescopic camera that is adjusted toward that virtual point in an effort to overcome optical aberrations that are evident when eclipses are observed from the face of the earth. The short answer is: [My fulcrum is the center. Viewed from the center of the lunar surface, the Earth is viewed as being constantly at high noon.
3. The quick answer: [For equal body masses, the fulcrum is midway between the diameter of the shared orbit.]
4. I repeat as answered above: [the center of concentric circles is at the fulcrum.]
5. Without a dynamic counter-force to gravitation, a stable orbit would be impossible: If gravity is removed the planet goes off on a tangent and if the planet's motion ceases, it crashes into the sun.
A point I made earlier needs clarification concerning the paradox of the place in a planet's orbital, of minimum velocity. It can be argued that because of conservation of momentum (m*v*r), the smaller "r" is, the larger is the velocity; it follows that the radius is smallest at the position of the minor axis. The paradox becomes evident when the equal-area-sweeps are contrasted at the ends of the major axis - at the perihelion end the apparent orbital velocity is maximum contrasted with a minimum velocity at aphelion. I propose that consideration be given to the notion that the point of reference be moved to the center of the actual ellipse rather than from the focus position. From that reference point the swept areas become congruent as will as equal and total elliptic symmetry obtains. It should be recalled that an invalid assumption that the orbital velocity is maximum at perihelion, suggests that the minor axis has been shifted to the position of the latus-rectum of a parabolic orbit.
I thank you for your audience if you are still here; I have often reminded potential readers who doubt my models to simply treat them as science fiction. To those whose logic, like mine, is constantly tempered by communication with peers, can only find consensus in small degrees because of that human trait: "a mind convinced against its will is of the same opinion still." Cheers.
