Hi No problem with hijacking. Your subjects are related and I read some of it but I realize it is too much to read for me right now. Maybe your programs can be adjusted with the force formula for spherical distributions.
Actually I just typed the ACSII version of the integral into Wolfram Alpha, a fantastic web resource, and after several seconds I got the answer http://www.wolframalpha.com/input/?i=Integral+from+-r0+to+%2br0+of+(r0^2-r^2)/(R0-r)^2+dr&incParTime=true A bit down it lists the indefinite integral as (R0^2-r0^2)/(r-R0)-2 R0 log(r-R0)-r+constant But the result dimensions do not fit... Something is wrong. For the spherical mass distribution I assume per particle F=GMm/R² and for a mass differential dM in the star (see attached picture) it becomes dF=G dM m / R² = G rho dV m / ( R0 + r ) ² = G rho pi (r0² - r²) dr m /(R0 - r)^2 Each dM is a vertical slice in the star. Each slice weighs dM = rho pi (r0² - r^2) dr. So I don't calculate to the highest precision. I just assume that the distance to all particles in the slice is R0-r and if I integrate to get the total it would become F = Integral from -r0 to r0 of G rho pi (r0² - r²) dr m /(R0 - r)^2 which is the integral I initially asked aboutand that Wolfram Alpha gave the indefinite form of. I can't see why using spherical distribution would make the computation much more complex? Computers can handle almost anything. Regards, David David Jonsson, Sweden, phone callto:+46703000370 On Mon, Oct 18, 2010 at 8:03 PM, OrionWorks - Steven V Johnson < svj.orionwo...@gmail.com> wrote: > From David > > > 12 replies to my question is not bad but the integral is actually about > what > > the gravity force is to a spherical mass distribution compared to a point > > mass. The so called center of gravity can not be used as a center of > gravity > > since matter closer to a body attracts more than what the remote parts > do. > > How big can this effect be? > > Can anyone solve the integral? I haven't even tried, yet. Can Maxima > solve > > it? > > David > > David, > > I must apologize as well. Guess you could say I intentionally > "hijacked" your thread. In your original question you brought up > interesting concepts that were related to a branch of mathematical > study that I've been exploring for years. I only hope the tangential > aspects of what has been discussed in your hijacked thread has been be > of some interest to the readers, including you. > > Following up on some of the tangential aspects, the physics text books > state that the force known as Gravity is considered to be several > orders of magnitude weaker than the strong and weak nuclear forces. > This is basic high school physics. > > In the meantime, David brings up an interesting concept that I > consider related to a similar discussion pertaining to whether it is > (legally) appropriate to computer model the effects of gravity using a > point mass, or whether one should model the effect as a spherical mass > distribution. From my own POV, and I'm speaking strictly from a > computer programmer's POV, it is FAR more convenient in the heuristic > sense to use a centralized point position in order model/generate > orbital simulations based on the so-called laws of Celestial > Mechanics. If one models one's algorithms using a point mass concept, > it is important to "play god" and summarily change the rules > so-to-speak where appropriate, particularly when the orbiting > satellite approaches too close to the main orbital body. To do so > introduces bizarre/chaotic orbital behavior. While it would probably > be more accurate (or realistic) to employ a spherical mass > distribution formula, to approach the problem as a computer > programming exercise, would increase the complexity of the algorithms > to the point that it would quickly become impossible to code. > > After reading just a sprinkle of Miles Mathis's papers, a novel > concept recently dawned on me pertaining to the fact that we could > speculate on the premise that the force of gravity may not necessarily > be as weak as the text books have always claimed the force to be. What > if we looked at the manifestation of gravity as emanating from the > "center" of each sub-atomic particle, what then? What if we were to > move the ground rules for "spherical mass distribution" away from the > surface of typical macro bodies, like stars, planets, or moons, and > scale it all the way down to the surface radius of protons and > neutrons... how strong would the "point mass" force of gravity > manifest at quantum-like distances? Obviously at that scale of > distance the effects of gravity would be several magnitudes stronger > that what is experienced within the familiar macro world! After all, > we are told neutron stars are held together by the crushing force of > the star's own gravity! A neutron star is essentially a gazillion > sub-atomic "point mass" neutron particles collectively behaving as if > they were all just one massive spherical mass distribution set as > perceived on the macro scale. I suspect that in some of Miles Mathis' > paper he is hinting at something akin to this. I suspect Miles is also > hinting at the premise that gravity, just like all the other forces, > are essentially one and the same "force" manifesting in different ways > and/or scales of distance. > > Regards, > Steven Vincent Johnson > www.Orionworks.com > www.zazzle.com/orionworks > >
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