Re: [Vo]:Anyone recognizes this astronomy integral?
I was referring to the first post in the thread Integral from -r0 to +r0 of (r0^2-r^2)/(R0-r)^2 dr It was the result of approximation and full precision gives 1/r^2 as in ordinary gravity. But of course any non point mass will have tidal effects so the center of mass issue remains. Are there any good sites on how this effect affects the stability of orbits. Maybe some other effect is balancing this effect to make orbits stable? Rotation of the elongation due to tidal effect also complicates things. I can imagine that only certain combinations of tidal elongation and rotation exists. Is the bulge of the elongation always between 0 to pi/2 radians from the direction to the other body? David David Jonsson, Sweden, phone callto:+46703000370 On Sat, Nov 27, 2010 at 7:39 PM, Mauro Lacy ma...@lacy.com.ar wrote: I'm not sure I understand what you mean. Are you saying that gravity behaves in the traditional (Newtonian) way inside solid bodies? Do you have links or papers to experiments that support this? As I said, there are reported anomalies inside boreholes. How do you or others explain them? Take into account that although gravity can be related to mass and density, that is, it can have a dependency on mass and density, that does not mean mass and density are the causes of gravity. Indeed, it makes a lot of sense to think just the opposite: that which causes mass (or the effects of mass) has to be massless in itself, to avoid a circular argument. The cause of gravity must be immune to the effects of gravity, by the very definition of cause. On 11/27/2010 08:45 AM, David Jonsson wrote: Sorry, if the integration is done with higher precision it turns out to be the traditional one. But it is still useful for determining the gravity from other geometries. I think it is bad that bodies are approximated with point sources in their center of gravity. David
Re: [Vo]:Anyone recognizes this astronomy integral?
Sorry, if the integration is done with higher precision it turns out to be the traditional one. But it is still useful for determining the gravity from other geometries. I think it is bad that bodies are approximated with point sources in their center of gravity. David
RE: [Vo]:Anyone recognizes this astronomy integral?
From David Johnson Sorry, if the integration is done with higher precision it turns out to be the traditional one. But it is still useful for determining the gravity from other geometries. I think it is bad that bodies are approximated with point sources in their center of gravity. To the best of my knowledge there is no practical way to map the positions of celestial bodies other than by exploiting brute force differentiation. It's a time-honored methodology, and it works. If you make the iterative slices sufficiently small the results appear to approximate what Nature seems to be doing. Besides, that's what computers are for! Granted, it is conceivable that an integral formula may actually exist, particularly for the simple one body elliptical model. However, to the best of my knowledge, no one has discovered it, or at least published their findings. To be honest, I can't conceive of how integrals could possibly be constructed to predict the characteristics of complicated models, particularly models consisting of two or more bodies. Differentiation alone has enough of a problem dealing with multi-body simulations. Meanwhile, I have been studying what one might consider the other end of the spectrum, where I deliberately allow the coarseness of the iterative feed-back loop to manifest in full bloom. I'm not attempting to suppress it. I often welcome their insane effects. With goals of abandon and destruction in mind I've been studying the interesting effects of various Celestial Mechanical computational permutations based on massive iterations of simple algorithms. Some of the results have astonished me. I've discovered the fact that the same simple algorithm can end up producing an astonishing variety of geometric shapes, all with just a simple infinitesimal tweak of a minor constant. The results are often chaotic - and yet surprisingly ordered. One quickly discovers an underlying order that seems to be mysteriously embedded within the chaos. Ordered chaos is in fact a curious characteristic of chaos that researchers are finally beginning to realize may hold practical value in possibly help explaining all sorts of subjects such as physics, health, sociology, macro economics - just to name a few. So far, and to the best of my knowledge, no one that I'm aware of seems to have shown much curiosity in analyzing the life spans along with the unique characteristics of these algorithms that have been deliberately infected with the virus of chaos. Because of what seems to have been as a lack of interest I've come to suspect many researchers may have missed valuable opportunities to analyze an astonishing number of shapes that can be produced from simple iterations of algorithms based on simple k*r, k/r, k/r^2, and k/r^3 - as well as various combinations. Needless to say, over the years I've acquired a much greater respect for the infinite shapes of CHAOS. IMHO, there is precious ore to be mined here. * * * PS: I've just completed a DVD course on Chaos theory. I also plan on taking another DVD course on discrete mathematics, just to make sure I cover as many bases as possible. The DVD courses I'm referring to are produced by an educational company called THE TEACHING COMPANY. See: http://www.teach12.com/greatcourses.aspx You can find a rich variety of course material available for immediate purchase. All the courses are taught by distinguished professors and teachers. The company often has special sales promotions, where certain courses are reduced from suggested prices of $250 - $300 price tag down to a mere $70. That's how I snapped up several mathematics courses, such as: CHAOS: ($254, marked down to $69) http://www.teach12.com/tgc/courses/course_detail.aspx?cid=1333 DISCRETE MATHEMATICS: ($254, marked down to $69) http://www.teach12.com/tgc/courses/course_detail.aspx?cid=1456 Bon appetite! Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
Re: [Vo]:Anyone recognizes this astronomy integral?
I'm not sure I understand what you mean. Are you saying that gravity behaves in the traditional (Newtonian) way inside solid bodies? Do you have links or papers to experiments that support this? As I said, there are reported anomalies inside boreholes. How do you or others explain them? Take into account that although gravity can be related to mass and density, that is, it can have a dependency on mass and density, that does not mean mass and density are the causes of gravity. Indeed, it makes a lot of sense to think just the opposite: that which causes mass (or the effects of mass) has to be massless in itself, to avoid a circular argument. The cause of gravity must be immune to the effects of gravity, by the very definition of cause. On 11/27/2010 08:45 AM, David Jonsson wrote: Sorry, if the integration is done with higher precision it turns out to be the traditional one. But it is still useful for determining the gravity from other geometries. I think it is bad that bodies are approximated with point sources in their center of gravity. David
Re: [Vo]:Anyone recognizes this astronomy integral?
In reply to Mauro Lacy's message of Sat, 27 Nov 2010 15:39:30 -0300: Hi, [snip] Take into account that although gravity can be related to mass and density, that is, it can have a dependency on mass and density, that does not mean mass and density are the causes of gravity. Indeed, it makes a lot of sense to think just the opposite: that which causes mass (or the effects of mass) has to be massless in itself, to avoid a circular argument. The cause of gravity must be immune to the effects of gravity, by the very definition of cause. [snip] It's possible that cause and effect are indistinguishable, i.e. that the concept of cause and effect is not applicable. Regards, Robin van Spaandonk http://rvanspaa.freehostia.com/Project.html
Re: [Vo]:Anyone recognizes this astronomy integral?
On 11/27/2010 04:53 PM, mix...@bigpond.com wrote: In reply to Mauro Lacy's message of Sat, 27 Nov 2010 15:39:30 -0300: Hi, [snip] Take into account that although gravity can be related to mass and density, that is, it can have a dependency on mass and density, that does not mean mass and density are the causes of gravity. Indeed, it makes a lot of sense to think just the opposite: that which causes mass (or the effects of mass) has to be massless in itself, to avoid a circular argument. The cause of gravity must be immune to the effects of gravity, by the very definition of cause. [snip] It's possible that cause and effect are indistinguishable, i.e. that the concept of cause and effect is not applicable. I don't think that the concept of cause and effect is not applicable. Why would it be so? It could be that what we call gravity is the end result of a number of different factors, but in principle nothing prevents us from identifying those factors, and from determining their interaction, the resultant of which is what we ordinarily call gravity. But yes, it's possible that we are actually not able to separate causes from effects in the case of gravity. That seem to be the case at the moment. That will change in the future, I'm completely sure about it. And that change could even happen sooner than we expect. In a sense, it's happening right now, although it's not fully taking the form of a scientific or mathematical formulation. Maybe that's the most important point in all this: to understand gravity as what it really is, independently of attaining a mathemathical description of its workings. That, correctly understood, would produce a revolution far deeper than the frutis of a new gravitational formalism. And that understanding is happening right now, I can assure you. Best, Mauro
Re: [Vo]:Anyone recognizes this astronomy integral?
On 10/24/2010 10:33 PM, Mauro Lacy wrote: ... We'll probably never know for sure what forces are really exerted inside a solid mass, due to the simple fact that bodies don't move inside solids. Measurements of acceleration and velocity in the gaseous giants, or in Venus's atmosphere, can be very interesting to analyze. The problem would be drag, of course. Even if the density gradients can be adequately modeled, I assume drag would be very difficult to model. I was thinking that instead of in the gas giants or in Venus, experiments can also be done in Earth's oceans, in deep lakes, or even in abandoned drilling holes. If drag is difficult to model adequately, a static instead of kinematic approach can be attempted. Putting a sensitive gravimeter inside a containment chamber, and sinking it to the depths of the ocean, registering the intensity of the gravitational field at different depths, should yield very interesting results, which will probably be unexpected and anomalous based in current theory. Particularly, I predict that the intensity of the gravitational field under the surface will continue to take the form of an inverse square law; that is, will follow a non-linear variation, contrary to current theory. Take into account that, playing with different density models for the Earth's core and mantle, current theory can model the actual increase in gravity under the surface. See http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#Bodies_with_spatial_extent and particularly http://en.wikipedia.org/wiki/File:Earth-G-force.png What current theory will not be able to model, at least without resorting to exotic density models, is the form of the curve. That is, experiments should focus in the form of the curve more than in the increase of the field in itself, because the increases can be easily explained/modeled with adequate density gradient ratios for the core/mantle. The next step would be to see how exotic the density models must be to explain the results within standard theory, and particularly, if they agree with known density data for the crust and outer mantle, if that is available. I don't know much about gravimeters, by the way, but this seems to be an experiment that is not completely out of reach for the determined and resourceful amateur. Regards, Mauro
Re: [Vo]:Anyone recognizes this astronomy integral?
In reply to Mauro Lacy's message of Sun, 24 Oct 2010 22:33:48 -0300: Hi, [snip] On 10/24/2010 06:28 PM, OrionWorks - Steven Vincent Johnson wrote: From Mauro: ... It is interesting to continue reading the explanation, for the force exerted on points inside the sphere. Indeed, I bet it does get interesting! In my own computer simulations, this is where I've had to play god, so-to-speak, and change the algorithm used when the orbiting body presumably passes underneath the planetary surface of the main attractor body. At that point one has to jigger a different set of rules since, technically speaking, a point source no longer exists. It's like diving into a swimming pool. The water (the source of gravity) is all around you. AFAIK, that portion of the body that is at a greater radius than your own has no effect on you. IOW you can base your calculations on a that of a body with a radius equal to your own. It's effectively as though the planet shrinks with you. By the time you reach the center, there is no planet left, and the net effect is zero. Calculations would be simplified by assuming a constant fixed density for the planet. Regards, Robin van Spaandonk http://rvanspaa.freehostia.com/Project.html
Re: [Vo]:Anyone recognizes this astronomy integral?
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+drincParTime=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
Re: [Vo]:Anyone recognizes this astronomy integral?
Hi, Yesterday I was reading the wikipedia entry for Newton's law of universal gravitation http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation, and under Bodies with spatial extent it says: If the bodies of question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. In the limit, as the component point masses become infinitely small, this entails integrating the force (in vector form, see below) over the extents of the two bodies. In this way it can be shown that an object with a spherically-symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its centre.^[2] http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#cite_note-Newton1-1 (This is not generally true for non-spherically-symmetrical bodies.) It is interesting to continue reading the explanation, for the force exerted on points inside the sphere. Regards, Mauro On 10/24/2010 03:38 PM, David Jonsson wrote: 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+drincParTime=true http://www.wolframalpha.com/input/?i=Integral+from+-r0+to+%2br0+of+%28r0%5E2-r%5E2%29/%28R0-r%29%5E2+drincParTime=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 mailto: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
RE: [Vo]:Anyone recognizes this astronomy integral?
From Mauro: ... It is interesting to continue reading the explanation, for the force exerted on points inside the sphere. Indeed, I bet it does get interesting! In my own computer simulations, this is where I've had to play god, so-to-speak, and change the algorithm used when the orbiting body presumably passes underneath the planetary surface of the main attractor body. At that point one has to jigger a different set of rules since, technically speaking, a point source no longer exists. It's like diving into a swimming pool. The water (the source of gravity) is all around you. I would also imagine the point source formula works best for perfect spherical bodies, and also where the volume of mass is assumed to be made of the same material and evenly distributed throughout. Obviously, in nature such uniformity never happens. Take the Earth for example. We have a nickel-iron core. The aggregate mass of the core of our planet is decidedly heaver than the collection of elements that make up the surrounding crust. This would imply that if one had a magic elevator shaft that could take a collection of geologists safely all the way to the center of the earth in order to measure one's weight what would systematically be recorded would not necessarily change in ways one might initially predict. For one thing I suspect one's weight would NOT necessarily become gradually less as one travelled through the Earth's crust. It is even conceivable to me that the geologist's weight might even increase slightly as they approached the boundary surface of where Earth's nickel-iron core begins. A significant portion of the planet's aggregate planetary mass is located there. Therefore, as the geologist approached this surface boundary the inverse square of the distance (1/R^2) formula might still, more or less, be in effect. I suspect only after our magic elevator has penetrated the surface of the nickel-iron core will our geologists begin to notice that their weight begins to gradually approach zero. Only when the elevator reaches the center of the planet will they feel weightless due to the fact that the collective mass of the entire planet is evenly distributed all around them. Regards, Steven Vincent Johnson www.Orionworks.com www.zazzle.com/orionworks
Re: [Vo]:Anyone recognizes this astronomy integral?
On 10/24/2010 06:28 PM, OrionWorks - Steven Vincent Johnson wrote: From Mauro: ... It is interesting to continue reading the explanation, for the force exerted on points inside the sphere. Indeed, I bet it does get interesting! In my own computer simulations, this is where I've had to play god, so-to-speak, and change the algorithm used when the orbiting body presumably passes underneath the planetary surface of the main attractor body. At that point one has to jigger a different set of rules since, technically speaking, a point source no longer exists. It's like diving into a swimming pool. The water (the source of gravity) is all around you. I would also imagine the point source formula works best for perfect spherical bodies, and also where the volume of mass is assumed to be made of the same material and evenly distributed throughout. Obviously, in nature such uniformity never happens. Take the Earth for example. We have a nickel-iron core. The aggregate mass of the core of our planet is decidedly heaver than the collection of elements that make up the surrounding crust. This would imply that if one had a magic elevator shaft that could take a collection of geologists safely all the way to the center of the earth in order to measure one's weight what would systematically be recorded would not necessarily change in ways one might initially predict. For one thing I suspect one's weight would NOT necessarily become gradually less as one travelled through the Earth's crust. It is even conceivable to me that the geologist's weight might even increase slightly as they approached the boundary surface of where Earth's nickel-iron core begins. A significant portion of the planet's aggregate planetary mass is located there. Therefore, as the geologist approached this surface boundary the inverse square of the distance (1/R^2) formula might still, more or less, be in effect. I suspect only after our magic elevator has penetrated the surface of the nickel-iron core will our geologists begin to notice that their weight begins to gradually approach zero. Only when the elevator reaches the center of the planet will they feel weightless due to the fact that the collective mass of the entire planet is evenly distributed all around them. And all this is highly speculative, of course. I must have said before: It is interesting to continue reading the explanation, for the *supposed* force exerted on points inside the sphere. We'll probably never know for sure what forces are really exerted inside a solid mass, due to the simple fact that bodies don't move inside solids. Measurements of acceleration and velocity in the gaseous giants, or in Venus's atmosphere, can be very interesting to analyze. The problem would be drag, of course. Even if the density gradients can be adequately modeled, I assume drag would be very difficult to model. Besides, the force exerted inside a hole in a solid body does not necessarily need to be the same force that is exerted inside the solid body itself. There are reported anomalies for the behavior of gravity inside bore holes. See this paper by Reginald Cahill, by example: http://arxiv.org/abs/physics/0512109 If gravity is not caused by mass, but by an in-flow of space, as Cahill suggests, the anomalies can be the result of channeling or tunneling of the flow inside or outside of the bore hole, by example. Gravity is such a curious mistress. A very curious mistress indeed, which is everywhere but is nevertheless extremely discreet and secretive.
Re: [Vo]:Anyone recognizes this astronomy integral?
Hi, I think that I must say a pair of additional things. First, I'm very grateful to Miles Mathis for his many insights, and for his clarity, freedom and generosity in openly sharing his ideas. He is a great source of inspiration and original ideas. Second, the only way to produce progress and novelty in a field, is by being wrong a good number of times. We have that right. The right of being wrong, if you excuse the pun. In the long term, we must only try that our hits surpass our misses, in number and particularly in importance. And talking about being wrong, it turns out that there is something wrong in the formulas below. And that that is interesting in itself. Let's see: I've made the intensity of the gravitational field directly proportional to the mass of the emitting body alone. This, one would presume, is the logical thing to do. But with a field like that, lighter objects fall faster than heavier objects. Due to inertia, and given the same field intensity, it's easier to accelerate a less massive object than a more massive one. Newton's second law. But(and here I'm indebted again to Miles Mathis), the gravitational field is a very particular field; a field so particular that the former does not happen. The gravitational field, in the centripetal direction, counteracts inertia, so to speak. It defies Newton's second law. That's why the gravitational force, in Newton's universal gravitational formula, is directly proportional to the *product* of the masses. If I multiply the numerator by the mass of the second body, that will later exactly cancel out the dividing mass in a=f/m, and we will have equal centripetal accelerations independently of the masses of the second body. The right formula for the magnitude of the force is then: f=-star.mass*planet.mass/pow(r.length(), exponent); But the problem is now that this formula defies mechanics. This product in the numerator means that, if we stick to the idea of a force field, the emitting body must emit different intensities depending on the mass of the receiving body. And that does not make sense. This is probably also why GR speaks of space curvature. That way, it is dispensed with the need to explain this very particular behavior of the gravitational field. But there must be another explanation. An explanation that does not hide in geometry, and which also makes physical sense. The candidates I can come up are: 1) A given gravitational field is proportional to the mass of the emitting body, but is processed or felt differently by a receiving body, according to the body's mass, in a form that exactly cancels out the inertia of the body. That is, the intensity of a gravitational field felt by a body is directly proportional to its gravitational mass. So a=f/m no longer holds for the gravitational field. We instead have a=f, or better, a=f*mg/mi. mg in the numerator is the gravitational mass, and mi, the inertial mass. Normally, mg=mi. 2) A gravitational field is the result of an interaction of bodies, not an emission of any given body on its own. The intensity of this interaction is proportional to the product of the gravitational masses of the interacting bodies. The interaction itself works in ways that we don't understand yet. 1) looks more mechanically tractable, whereas 2) looks more wave like, or flow like. An approach like 2) can also probably explain dark matter, and gravitational anomalies. Notice also that 1) implies a kind of amplification effect. Particularly in the case of a greater body being influenced by a smaller one, the influence will depend on the mass of the second body. Which is strange, to say the least. Particularly in 1), to augment the gravitational interaction, we'll have to increase the body's gravitational mass(without increasing its inertial mass), to decrease its inertial mass(without decreasing its gravitational mass), or both. How to do it is left as an exercise for the reader at the moment :-) Mauro On 10/16/2010 09:28 PM, Mauro Lacy wrote: On 10/14/2010 08:06 AM, Mauro Lacy wrote: On 10/11/2010 01:50 PM, OrionWorks - Steven Vincent Johnson wrote: A question for you, Mauro: I would nevertheless love to computer simulate a so-called authentic elliptical orbit that is more accurately based on Miles' three-part gravity model, one that incorporates both the attractive 1/r^2 force and the repulsive E/M 1/r^4 forces. At present I'm at loss as to how I might do that -- that is without my computer simulations reverting back to nothing more than another mechanistic heuristic exercise. Maybe that's all one can really do in our so-called mechanistic world. You're right, and I'm doing exactly that at the moment. A celestial mechanics simulator based on first principles. I'll try to use the smallest number of principles. So far, I've identified four: - Newton's first law (uniform movement law, i.e. inertia) - Newton's second law (f=ma = a=f/m) - A spherically(circularly, in two dimensions)
Re: [Vo]:Anyone recognizes this astronomy integral?
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
Re: [Vo]:Anyone recognizes this astronomy integral?
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. Hi David, I'm sorry that your thread was hijacked. I suppose the answer to your initial question was No. :-) How big can this effect be? Not very big for d r, d being the distance between bodies and r the radius of the more massive body. It could be interesting to solve the integral, to precisely see the magnitude of the effects at different distances, but at first sight, the effects must follow an inverse square law also. So, for a given distance d, they will have a 1/d^2 importance. It may also be the case that the closer masses compensate the loss of the farther masses, and then, for the spherical case, the approximation to a point mass is perfectly valid; provided that the distance is greater than the radius of the body, and that the density of the body is homogeneous. Can anyone solve the integral? I haven't even tried, yet. Can Maxima solve it? David
Re: [Vo]:Anyone recognizes this astronomy integral?
On 10/14/2010 08:06 AM, Mauro Lacy wrote: On 10/11/2010 01:50 PM, OrionWorks - Steven Vincent Johnson wrote: A question for you, Mauro: I would nevertheless love to computer simulate a so-called authentic elliptical orbit that is more accurately based on Miles' three-part gravity model, one that incorporates both the attractive 1/r^2 force and the repulsive E/M 1/r^4 forces. At present I'm at loss as to how I might do that -- that is without my computer simulations reverting back to nothing more than another mechanistic heuristic exercise. Maybe that's all one can really do in our so-called mechanistic world. You're right, and I'm doing exactly that at the moment. A celestial mechanics simulator based on first principles. I'll try to use the smallest number of principles. So far, I've identified four: - Newton's first law (uniform movement law, i.e. inertia) - Newton's second law (f=ma = a=f/m) - A spherically(circularly, in two dimensions) radiating force field, with one (or more than one) transform(i.e. propagation) terms (1/r^0, 1/r^1, 1/r^2, ...) - Force fields act only in the centripetal direction, that is, they have no influence orthogonally. With that and a small enough interval, I think I can build an orbit simulator to test for laws using only first principles. More about this later, probably. Well, I've built a two-body, two-dimensional orbit simulator based in these four principles. It turns out it was very easy to program using vectorial arithmetics, so here's the method. It uses vector substraction, addition, invertion, normalization, and vector multiplying by an scalar. Let me know if you discover something that is incorrect. // inverse square law int exponent = 2; // vectors planet.pos and star.pos have the actual positions of the bodies. r=planet.pos-star.pos; // the radius vector is the vectorial substraction of the position of the bodies float f; // magnitude of the force f=-(star.mass/pow(r.length(), exponent)); // minus means attractive attractive force. r.length() gives us the // magnitude of the radius vector. planet.ac=r.normalized()*(f/planet.mass); // centripetal acceleration acts in the radius vector direction. r.normalized() gives us the unit vector. planet.velocity=planet.velocity + planet.ac; // vectorial addition of velocity and centripetal acceleration // now do the same for the star f=-(planet.mass/pow(r.length(), exponent)); // force of the planet on the star star.ac=-(r.normalized())*(f/star.mass); // centripetal acceleration produced on the star. In the opposite direction star.velocity=star.velocity + star.ac; // now calculate the new positions planet.pos=planet.pos + planet.velocity; star.pos=star.pos + star.velocity; That's it. Except for a=f/m and the force field transform, there are no other formulas. Suffice it to say that it produces elliptical orbits, which depend on the initial positions, velocities, masses and distance between the bodies. I've used Qt4 QVector2D implementation, but any vector class or library that implements basic vector operations will do. Regards, Mauro
Re: [Vo]:Anyone recognizes this astronomy integral?
On 10/11/2010 01:50 PM, OrionWorks - Steven Vincent Johnson wrote: Hi again, Today is a state-wide furlough day for most state of Wisconsin employees, like me. ... How nice to have an extra holiday to explore some of Mile's concepts. I'll rake the lawn later... Regarding the distinction between using particles or waves to explain how the universe works, including the nature of gravity, I place far more faith in the proclivity of wave theory than I do in individual particles. Putting my faith in particles, to me, would seem to be nothing more than worshipping a static snap shot in time of what is actually happening in the universe on an infinitely dynamic scale. It might seem contradictory for me to say this, particularly since my own computer simulations could easily be perceived primarily as examples of the nature of particle theory. Not true! What I find far more interesting is the gradual build up of millions and trillions of individual point/particles as they gradually construct computer generated graphic patterns. These graphic patterns end up looking more like the influences of dynamic wave theory in action. It just takes time, and a lot of particle build up! ;-) As of Sunday evening I've managed to plow through Mile's Explaining the Ellipse paper - twice. Rather mind-bending at times. I also ordered his book through Amazon. It is obvious to me that my own CM computer simulations are completely mechanistic heuristic in nature. They don't necessarily explain how gravity truly works. While I'm willing to explore Miles' premise that tangential velocity shouldn't be confused with orbital velocity, the distinction Miles attempts to paint between the two concepts still eludes me to a large extent. Fortunately, Miles is aware of the fact that the distinction tends to baffle most of his readers. He attempts to compensate by giving additional examples. If I understand Mile's commentary, it seems obvious to me that my own CM computer simulations, which are obviously heuristic in nature, involve the feeding back of orbital velocities (not tangential) into the algorithm in order to get the next x,y coordinate position of the orbiting satellite. It's a simple algorithm to compute, and I've done this for years. Nevertheless, in my heuristic oriented computer programs there is no need to incorporate a third factor - a repulsive E/M (1/r^4) function. Granted I could easily incorporate the additional function of (1/r4) - and I HAVE incorporated similar exploratory repulsive functions in the past just to see what would happen, such as 1/r^3 in repulsive mode. As far as I can tell, however, there does not appear to be any practical/heuristic need to do so. Also the 1/r^4 force will QUICLY become negligible in most cases -- which I gather is precisely what Mathis is saying as well. It would only begin to possibly influence the position of an orbiting satellite as it approaches main attractor gravitational body. In fact, it would have to be VERY close indeed to the main attractor body for the repulsive forces to begin visibly manifesting. Well... maybe I need to rethink that! (I'm thinking out loud here.) I must confess that my own CM computer simulations based strictly on using 1/r^2 (with no additional algorithmic enhancements) have indicated to me a strong suspicion that all computed orbital ellipses are inherently unstable -- given enough time to let the simulation run its course. Err... Well... this gets even messier! I think it would be more accurate to state the fact that my orbits become unstable when the feed-back values become too large (or too coarse) between iterative feed-back steps, particularly as one approaches the central orbiting body and the individual vector values increase geometrically. This is where I've noticed that chaos will be entered into my computer simulations. The introduction of what is presumed to be unwanted chaos is also precisely what has fascinated me for years, even if the introduction of such chaotic behavior has absolutely nothing to do with accurately predicting true CM orbital behavior. Incorporating a repulsive 1/r^4 function into the original equation might help ameliorate the chaotic blow a bit, but I don't tend to think of it as the real solution, particularly since my algorithms are strictly heuristic in nature anyway and probably don't really explain the actual effects of gravity. A question for you, Mauro: I would nevertheless love to computer simulate a so-called authentic elliptical orbit that is more accurately based on Miles' three-part gravity model, one that incorporates both the attractive 1/r^2 force and the repulsive E/M 1/r^4 forces. At present I'm at loss as to how I might do that -- that is without my computer simulations reverting back to nothing more than another mechanistic heuristic exercise. Maybe that's all one can really do in our
RE: [Vo]:Anyone recognizes this astronomy integral?
The core of my heuristic-based CM simulations can be represented by the following algorithm. The code has been simplified for your viewing pleasure. The code/algorithm is represented in Visual Basic .NET (2008). I've also performed MC simulations using C#. But VisualBasic, in many ways is an easier language to use particularly since it automatically takes care of a lot of clerical details that can end up consuming much of a programmer's time. Using VB helps me focus on the primary task at hand. Using Microsoft's .NET architecture to generate graphics has also turned out to be a powerfully useful tool. ** ** ** '=== == 'Perform Basic Orbit Calculations: A FEED-BACK LOOP! '=== == For i = 1 To itterationCount Step 1 'Move current coordinates into previous vector settings 'in preparation to generate next itterative step in loop. prevXPos = currXPos prevYPos = currYPos prevXVec =.currXVec prevYVec = currYVec 'Determine current radius length/distance... based on distance starting at (0,0) origin. currAttractRadius = util.length(0.0, 0.0, currXPos, currYPos) 'Determine current attractive force, based on current determined distance, i.e. F = 1/r^2 etc... currAttractForce = util.force(currForceConstant, currAttractRadius, attractionPower) 'Generate current vector coordinates currXVec += (-1) * currAttractForce * (CurrXPos / currAttractRadius) currYVec += (-1) * currAttractForce * (CurrYPos / currAttractRadius) 'Feed current vectors back into x,y coordinates currXPos += CurrXVec currYPos += CurrYVec 'DO OTHER STUFF HERE...like plot the coordinate on an (x,y) graphic, generate statistics, etc... Next ** ** ** Again, the above code has been stripped to its core simplified. For example I don't explicitly show how I determine distance or the current Attractive Force. I placed the inner workings of that code in a utility class. Nevertheless, this is an accurate representation of what much of my research has been based on. I've been playing around with stuff like this for years. I've also experimented with oodles of interesting permutations and hybrid formulas, just to see what pops up. Occasionally I have been surprised, if not totally baffled. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks From: Mauro Lacy [mailto:ma...@lacy.com.ar] Sent: Thursday, October 14, 2010 6:06 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Anyone recognizes this astronomy integral? On 10/11/2010 01:50 PM, OrionWorks - Steven Vincent Johnson wrote: Hi again, Today is a state-wide furlough day for most state of Wisconsin employees, like me. ... How nice to have an extra holiday to explore some of Mile's concepts. I'll rake the lawn later... Regarding the distinction between using particles or waves to explain how the universe works, including the nature of gravity, I place far more faith in the proclivity of wave theory than I do in individual particles. Putting my faith in particles, to me, would seem to be nothing more than worshipping a static snap shot in time of what is actually happening in the universe on an infinitely dynamic scale. It might seem contradictory for me to say this, particularly since my own computer simulations could easily be perceived primarily as examples of the nature of particle theory. Not true! What I find far more interesting is the gradual build up of millions and trillions of individual point/particles as they gradually construct computer generated graphic patterns. These graphic patterns end up looking more like the influences of dynamic wave theory in action. It just takes time, and a lot of particle build up! ;-) As of Sunday evening I've managed to plow through Mile's Explaining the Ellipse paper - twice. Rather mind-bending at times. I also ordered his book through Amazon. It is obvious to me that my own CM computer simulations are completely mechanistic heuristic in nature. They don't necessarily explain how gravity truly works. While I'm willing to explore Miles' premise that tangential velocity shouldn't be confused with orbital velocity, the distinction Miles attempts to paint between the two concepts still eludes me to a large extent. Fortunately, Miles is aware of the fact that the distinction tends to baffle most of his readers. He
RE: [Vo]:Anyone recognizes this astronomy integral?
Thanks Harry, Unfortunately, I get no sound that accompanies the you tube demonstration. Regarding Celestial Mechanics and the orbital pattern that makes up the classic ellipse shape - the two foci, especially the ghost/empty foci has been a mystery and enigma that has haunted many prominent individuals for hundreds of years. Years ago I started investigating the problem as well, initially thinking I was breaking new ground. Silly me! Nevertheless, my probing continues, on and off. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks -Original Message- From: Harry Veeder [mailto:hlvee...@yahoo.com] Sent: Monday, October 11, 2010 6:41 PM To: vortex-l@eskimo.com Subject: Re: [Vo]:Anyone recognizes this astronomy integral? Steven and Mauro, I think you'd like how Ellipitical orbits are explained in these links. They are based on Feynman's so called lost lectures, where he showed how to use geometry without calculus to derive elliptic orbits. paper: http://journal.geometryexpressions.com/pdf/kep.pdf video tutorial in several parts: http://www.youtube.com/user/nymathteacher#p/u/17/ObVDk7WPm9Y harry
RE: [Vo]:Anyone recognizes this astronomy integral?
planet solar systems and the orbital perturbations that were generated. I gather you're an old hand at performing these kinds of computer simulations. No? Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks From: Mauro Lacy [mailto:ma...@lacy.com.ar] Sent: Sunday, October 10, 2010 9:03 PM To: vortex-l@eskimo.com Subject: Re: [Vo]:Anyone recognizes this astronomy integral? Hi, It's in fact thanks to you that I discovered Mathis's work, when researching your precession question. So I thank you, too. He seems to be a kind of contemporary Newton, yes. I suppose he'll perdure. Time will tell. I don't like his mechanistic ideas, although I agree that it's convenient to have a mechanistic approach first, and only when that shows its limitations move on to other models and ideas. Always make things as simple as possible, but not simpler. I agree also with Physics being a fundamentally mechanical science, not mathematical delusions, diversions, or perversions. I don't like his expansion model for gravity, at all. I understand that his model can probably be made to work if you add a repulsive electromagnetic component, which keeps bodies apart against the gravitational apparent attraction, but I find expansion ideas an unnecessary (and unbelievable, frankly) burden. Gravitation can probably be understood in terms of wave interactions. I think than we can imagine a normally repulsive (due to emission) field, that when encountering another similar field, manifests attraction(coalescence and accretion, actually) due to the appearance of a kind of interference pattern between the fields. That interference pattern would model a force field, and that force field will cause gravitational acceleration. In my theory, gravity is then always the result of an interaction, never the result of a single field. But of course you need something like waves, not particles, to make it work. My model explain the repulsive-attractive (i.e. elastic) nature of the field at solar system levels as deviations in the interference pattern, which in one direction cause attraction, and in the other, repulsion. To see what I mean, take by example a function like the square root, and apply it to a distance between bodies, normalized in the form that 1 is the equilibrium distance. The square root of 1 is 1, and you'll have stable equilibrium. The square root of any number greater than 1 tends to 1, that is, to equilibrium. And the same happens with any number smaller than 1. So you have an effect that(and between a certain range, of course), independently of the initial distance being greater or smaller than the equilibrium distance, tends to the equilibrium distance. Temporary divergences from equilibrium will be due to the inertia of the bodies, and to perturbations. That means that, given enough time, and provided that the interacting fields are mantained, all orbits would decay into circular orbits. That is gravity working at the celestial level. At the planetary levels, bodies fall to the center of the planet because they are completely overwhelmed by the local field on the Planet, which is again the result of the interacting fields at the celestial level. That means that Earth's gravity, by example, is not a consequence of the mass of the Earth, but conversely, the (accreted) mass of the Earth is a consequence of Earth's gravity. The field was first, and the accretion came later, provided that the field entered or directly formed in a zone with matter to accrete. By the way, so called dark matter is no more that a consequence of insufficient accretion, that is, fields that are devoid of matter at the moment. All very nice, but what is missing are the fields themselves! what are those fields? from where they originate? are they internal to the solar system or external? are they the result of space pressure? are they a result or manifestation of the turbulence of a dark fluid? what is then that dark fluid? and how exactly it interacts with normal matter? what are the formulas to describe those interactions? etc etc. On 10/09/2010 10:51 PM, OrionWorks - Steven Vincent Johnson wrote: Mauro, Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
Re: [Vo]:Anyone recognizes this astronomy integral?
From: OrionWorks - Steven Vincent Johnson orionwo...@charter.net To: vortex-l@eskimo.com Sent: Mon, October 11, 2010 12:50:28 PM Subject: RE: [Vo]:Anyone recognizes this astronomy integral? While I'm willing to explore Miles' premise that tangential velocity shouldn't be confused with orbital velocity, the distinction Miles attempts to paint between the two concepts still eludes me to a large extent. Fortunately, Miles is aware of the fact that the distinction tends to baffle most of his readers. He attempts to compensate by giving additional examples. If I understand Mile's commentary, it seems obvious to me that my own CM computer simulations, which are obviously heuristic in nature, involve the feeding back of orbital velocities (not tangential) into the algorithm in order to get the next x,y coordinate position of the orbiting satellite. Maybe he means speed (a scalar quantity) when he says orbital velocity, and he means velocity (a vector quantity) when he says tangential velocity. Harry
Re: [Vo]:Anyone recognizes this astronomy integral?
Steven and Mauro, I think you'd like how Ellipitical orbits are explained in these links. They are based on Feynman's so called lost lectures, where he showed how to use geometry without calculus to derive elliptic orbits. paper: http://journal.geometryexpressions.com/pdf/kep.pdf video tutorial in several parts: http://www.youtube.com/user/nymathteacher#p/u/17/ObVDk7WPm9Y harry
Re: [Vo]:Anyone recognizes this astronomy integral?
Hi, It's in fact thanks to you that I discovered Mathis's work, when researching your precession question. So I thank you, too. He seems to be a kind of contemporary Newton, yes. I suppose he'll perdure. Time will tell. I don't like his mechanistic ideas, although I agree that it's convenient to have a mechanistic approach first, and only when that shows its limitations move on to other models and ideas. Always make things /as simple as possible/, /but not simpler/. I agree also with Physics being a fundamentally mechanical science, not mathematical delusions, diversions, or perversions. I don't like his expansion model for gravity, at all. I understand that his model can probably be made to work if you add a repulsive electromagnetic component, which keeps bodies apart against the gravitational apparent attraction, but I find expansion ideas an unnecessary (and unbelievable, frankly) burden. Gravitation can probably be understood in terms of wave interactions. I think than we can imagine a normally repulsive (due to emission) field, that when encountering another similar field, manifests attraction(coalescence and accretion, actually) due to the appearance of a kind of interference pattern between the fields. That interference pattern would model a force field, and that force field will cause gravitational acceleration. In my theory, gravity is then always the result of an interaction, never the result of a single field. But of course you need something like waves, not particles, to make it work. My model explain the repulsive-attractive (i.e. elastic) nature of the field at solar system levels as deviations in the interference pattern, which in one direction cause attraction, and in the other, repulsion. To see what I mean, take by example a function like the square root, and apply it to a distance between bodies, normalized in the form that 1 is the equilibrium distance. The square root of 1 is 1, and you'll have stable equilibrium. The square root of any number greater than 1 tends to 1, that is, to equilibrium. And the same happens with any number smaller than 1. So you have an effect that(and between a certain range, of course), independently of the initial distance being greater or smaller than the equilibrium distance, tends to the equilibrium distance. Temporary divergences from equilibrium will be due to the inertia of the bodies, and to perturbations. That means that, given enough time, and provided that the interacting fields are mantained, all orbits would decay into circular orbits. That is gravity working at the celestial level. At the planetary levels, bodies fall to the center of the planet because they are completely overwhelmed by the local field on the Planet, which is again the result of the interacting fields at the celestial level. That means that Earth's gravity, by example, is not a consequence of the mass of the Earth, but conversely, the (accreted) mass of the Earth is a consequence of Earth's gravity. The field was first, and the accretion came later, provided that the field entered or directly formed in a zone with matter to accrete. By the way, so called dark matter is no more that a consequence of insufficient accretion, that is, fields that are devoid of matter at the moment. All very nice, but what is missing are the fields themselves! what are those fields? from where they originate? are they internal to the solar system or external? are they the result of space pressure? are they a result or manifestation of the turbulence of a dark fluid? what is then that dark fluid? and how exactly it interacts with normal matter? what are the formulas to describe those interactions? etc etc. On 10/09/2010 10:51 PM, OrionWorks - Steven Vincent Johnson wrote: Mauro, I have to thank you again for bringing Mathis's work to my attention. I'm pretty sure I need to purchase his book. It's the least I can do to support Mathis's continuing research. I want to do more than fork over a tiny PayPal donation. Actually, I just want his book! ;-) I'm currently plowing through EXPLAINING the ELLIPSE. It's conceivable the article might end up helping me out in my own CM computer simulation research. Hopefully I'll enjoy the challenge of trying to comprehend Miles's perception on these matters, particularly the mathematical aspects. His mathematical prowess is far more developed than my own mathematical abilities. Hopefully, I'll still be able to make some headway. OK... and now for the weird part. I fully confess the fact that the following two comments are totally unscientific in nature. They are in fact totally subjective in nature, and quite personal. But what the hey! I'll blurt them out anyway! COMMENT 1: Several years ago while disengaging my mind in the midst of jogging I found myself speculating about the link between gravity, acceleration, and the curvature of space. It was during one of these jogging sessions when I suddenly
Re: [Vo]:Anyone recognizes this astronomy integral?
On 10/08/2010 03:00 PM, OrionWorks - Steven Vincent Johnson wrote: BTW, Mauro Lacy suggest googling Miles Mathis, for an entertaining read on certain formulas used in regards to Celestial Mechanics. I've waded through Mathis' article on Mercury's Precision. Lots of interesting stuff there. Hi, You probably meant precession. Or precessional precision, properly. I have been reading Mathis's physics papers during these weeks. You can start from any point, but I recommend reading his analysis of Celestial Mechanics and the Nebular Hypothesis, and from then into his own theories. He sheds light into many issues, from relativity to quantum mechanics. He's very good at deconstructing and criticizing (demolishing in some cases), and also at correcting or extending existing physical dogma, with a depth, clarity and simplicity that's amazing, and much welcomed. A refreshing back to the basics approach, which reveals big holes in current physical theories. Not so good, in my opinion, developing his own theories. He seems to be in a rush to do that, and that's not good. He's also probably very wrong in some main ideas. His idea of gravitation based on expansion is untenable, to say the least. But I feel that he adopted it because it's relatively economical, and simple. In my opinion, gravity is not separated from electromagnetics(by example by the adoption of a expansion model for gravity) but gravitational attraction and electromagnetic repulsion are both aspects of a unique form of interaction, mediated by an extended form of electromagnetism. Thinking that gravity and electromagnetism are completely different physical effects, which have completely different physical causes, is probably Mathis's biggest blunder. A kind of late mechanistic, a 18th or 19th century genius in the 21th century. He thinks, by example, that by fixing Celestial Mechanics, the indeterminacies will disappear; i.e. he thinks that the indeterminacies are the result of wrong math and models, not essential limitations of mathematics itself. He noticed that time is a derived(not intrinsic) quantity in physics. By the way, his article a revaluation of time is a good starting point also. variar Probably the best I've read at the moment is: - His article on Celestial Mechanics, where he shows that a 1/r² spherically varying force alone cannot produce elliptical orbits(it will produce spirally decaying orbits in the capture scenario). He also shows that Newton's derivation of the universal gravitational law from Kepler's equations is physically unsound, and that CM is then an heuristic science, due to Newton's use of the centripetal acceleration equation (a=v/r²) without physical justification. - His analysis and subsequent demonstration of charge being dimensionally equivalent to mass. - The article where he shows that Newton's equation already contains the electromagnetic part of the interaction. He modifies the Calculus. I'm not convinced yet of his reformulation of the a=v²/r equation. But I find very plausible that that equation(or a similar one) is hiding the attractive-repulsive (i.e. elastic) character of the compound gravitational-electromagnetic interaction. In short: it's very interesting and stimulating to read the work of a real genius on the internet, for a change. Regards, Mauro
RE: [Vo]:Anyone recognizes this astronomy integral?
Mauro, I have to thank you again for bringing Mathis's work to my attention. I'm pretty sure I need to purchase his book. It's the least I can do to support Mathis's continuing research. I want to do more than fork over a tiny PayPal donation. Actually, I just want his book! ;-) I'm currently plowing through EXPLAINING the ELLIPSE. It's conceivable the article might end up helping me out in my own CM computer simulation research. Hopefully I'll enjoy the challenge of trying to comprehend Miles's perception on these matters, particularly the mathematical aspects. His mathematical prowess is far more developed than my own mathematical abilities. Hopefully, I'll still be able to make some headway. OK... and now for the weird part. I fully confess the fact that the following two comments are totally unscientific in nature. They are in fact totally subjective in nature, and quite personal. But what the hey! I'll blurt them out anyway! COMMENT 1: Several years ago while disengaging my mind in the midst of jogging I found myself speculating about the link between gravity, acceleration, and the curvature of space. It was during one of these jogging sessions when I suddenly found myself free floating or speculating about a version of an expansion model (aka curved space), where I wondered: What if all matter is expanding/accelerating outwards. I then realized: If all matter is expanding/accelerating relative to each other, would the observer (who is also made of the same accelerated matter) notice anything different, except for the manifestation of gravity. I was truly astonished to find that some of Mile's mathematical articles, such as the one about the precession of Mercury's orbit, where he touched on the expansion model mathematically explored the very concepts I had tried to visualize geometrically in my head while in the midst of jogging. I hasten to add that I don't mean to imply that I fully understand a significant portion of Mile's mathematical analysis concerning his interpretation of the expansion model. I'm still totally baffled by Miles's use of the trig function, the tangent (tan0) formula. I realize the function is used to calculate the curvature (angle) of space at specified distances in relation to accelerating bodies, but I don't know why we use the TAN trig function. Still doesn't make any sense to me. Nevertheless, I'm still plugging away, trying to comprehend as much as my brain can absorb. COMMENT 2: (Warning: the following commentary is totally metaphysical in nature.) Earlier today something within me moved me to make a visual comparison of Miles Mathis and that of Isaac Newton. When I made side-by-side comparisons the two individuals feel strikingly similar to me. Even more striking to me is the fact that Miles appears to be continuing the work of Newton (and Kepler), including fixing mathematical errors Isaac might have made in his most famous previous life. Miles also appears to be clarifying a slew of mathematical mistakes and/or misconceptions that he claims contemporary professionals in the sciences continue to make in regards to Newton's original math. I've found myself wondering if Miles might possibly be a new revised edition of Newton. If so, it would appear that the revised Newton is rounding out his already well developed mathematical prowess with enthusiastic academic pursuits in the arts and humanities. Looks to me as if the revised Newton is having a hoot of a time, too. I bet the ladies like him! ;-) He's probably a little bit relieved that he's NOT the old Newton this time around! Probably doesn't even want to speculate on such a bizarre possibility either! Why have such an albatross hanging around one's neck - specifically being metaphysically linked to a world renown mathematical genius, a glory from some past century, particularly when there's so much stuff to explore in today's world! I could see how such a distinction could constantly get in the way of one's current life's pursuits. Perhaps Mile's is also pursuing alchemical interests as well, though perhaps somewhat revised. For additional info on Miles Mathis' check out his web site: http://mileswmathis.com/ Miles recently published a book on his mathematical research, See Amazon out at http://tinyurl.com/35ba7zr Titled: The UN-DEFINED FIELD and other problems . the greatest standing errors in physics and mathematics ** Final comment. Regardless of my blatantly metaphysical mumbo-jumbo rant, it is obvious to me that Miles has some interesting things to say. As Mauro has already pointed out, I also suspect Miles will make significant contributions, even if his most noted contributions may not immediately be recognized for the significance that they truly are within our lifetime. We should also keep in mind that Miles is still a very young lad, probably still in his 30s. Give him some time and space to
RE: [Vo]:Anyone recognizes this astronomy integral?
From: David Jonsson Integral from -r0 to +r0 of (r0^2-r^2)/(R0-r)^2 dr r0 is radius of star. R0 is distance to star center from a satellite of the star. The integral is most often approxiamted with something proportional to 1/R0² which is the case when r0 - 0. I think the approximation is too course for modern precision demands. David Im still wading through a weeks worth of email, having been on vacation. So I dont yet know if someone has already responded to this query. But yes, I do recognize 1/r^2. Ive been using this simple formula in my own Celestial Mechanics research for several years now. Ive also been experimenting with hybrid formulas as well. Ive been researching not so much what might be called the Macro Celestial Mechanics aspects but more the theoretical/mathematical chaotic aspects, particularly when ones feed-back approximations are too coarse. Im fascinated with what Im uncovering. BTW, Mauro Lacy suggest googling Miles Mathis, for an entertaining read on certain formulas used in regards to Celestial Mechanics. Ive waded through Mathis article on Mercurys Precision. Lots of interesting stuff there. Hope this is helpful. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
