Concept developed by November 1997 Simple Newtonian gravitation is sufficient to explain the entire behavior of Galaxy Spiral Arms. The wellknown Keplerian central force effect certainly dominates, but a Spiral Arm also has internal mutual gravitation, which has surprisingly strong local effects! The stability of galaxy spiral arms has long troubled the Astrophysics community. It has been ASSUMED that ONLY the Keplerian central force was acting, as suggested in the drawing at the right. The orange dot represents the current location of the Sun, within the blueoutlined Arm which we happen to be in. As noted here, we are currently fairly near the inner edge of an Arm called the Orion Arm. The rest of the Galaxy was left out of this drawing. If we make the usual assumption that the Sun is revolving in the Milky Way Galaxy with a tangential velocity of around 250 km/sec, and that the Sun is currently around 28,000 light years from the center of the Galaxy (the black arrow represents that radius vector), it is easy to calculate that a centripetal (Keplerian) acceleration must exist of a = v^{2}/r or 2.36 * 10^{10} meters/second^{2}. This acceleration must also equal G * M_{galaxy}/r^{2} which tells us that the effective Keplerian mass of the Galaxy must be around 125 billion solar masses. This is ONLY true GIVEN THE ASSUMPTION that ONLY a Keplerian central force is causing the Sun to have its revolution motion. However, Isaac Newton made very clear that such a basic assumption is absolutely WRONG! When Newton analyzed Kepler's Laws, he quickly realized that the Kepler Laws are all APPROXIMATE. Newton derived the EXACT formulations of Kepler's Laws. Kepler had assumed that only the Sun's mass applied, and the Gravitational attraction between the Sun and Earth would therefore be given by: Force = G * M_{Sun} * m_{Earth} / r^{2} Newton discovered that the SUM of the mass of both of the objects must be used, that is: Force = G * (M_{Sun} + m_{Earth}) * m_{Earth} / r^{2}. The fact that it was later determined that the Sun has a mass which is 330,000 times greater than the Earth, makes these two equations virtually identical. However, the first is APPROXIMATE and the second is far more precise. Newton also used the Calculus (Fluxions) which he invented, to discover another important fact. When a mass such as the Sun has its entire mass Integrated regarding gravitational effect (for any location OUTSIDE the Sun itself) the gravitational effect IS as though the entire mass of the Sun is gravitationally acting as though it is all at a point at the exact center of the Sun. This is ONLY true if the object is SYMMETRIC regarding density, and this is a basic problem given to beginning Physics students to solve as homework! In the case of the Solar System, this caused very minor differences, entirely because the Sun is so massive, that is, that virtually all of the mass in the Solar System resides in the Sun. The results of using Kepler's Laws, within the Solar System, therefore always gave wonderfully useful results. But Newton therefore knew that Kepler's Laws only (approximately) apply for a POINT SOURCE MASS such as the Sun. Our Milky Way Galaxy has DISTRIBUTED MASS, where hundreds of billions of individual stars all contribute to the total mass of the Galaxy. On a gross scale, that mass IS relatively symetrical, so for our gravitational effect on any other galaxy, yes, our entire Galaxy acts as though it is a point mass (as Kepler might have assumed). But for locations INSIDE our Galaxy, BOTH of these assumptions which are embedded in Kepler's Laws happen to be very wrong. Having overlooked this obvious fact, modern Astrophysics has felt it necessary to create countless unsupported speculations to try to explain how and why our Galaxy can rotate as it does and still not quickly fly apart! So they have come up with Dark Matter, Hidden Matter, Gravity Waves, massive numbers of Neutrinos and many other wild assumptions and speculations. If they had recognized, as Newton did, that Kepler's Laws only apply for pointsource masses like the Sun, and they certainly do NOT apply for distributed masses like a galaxy, they might have seen that standard Newtonian gravitation was the only explanation which is necessary! Specifically, the local irregularities regarding WHERE stars are, is extremely significant. If our Galaxy was a UNIFORM distribution of stars and other mass, the usage of Kepler's Laws would not be too terribly wrong. But our Sun and Earth happen to be near the (inner) edge of one of the Spiral Arms of our Galaxy. That is, radially inward from where we are, there are very few NEARBY stars (for several thousand Light Years distance). In contrast with that, radially outward from where we are, there are many millions of stars within that same several thousand Light Years distance. In other words, the UNIFORMITY of mass density upon which Kepler's Law must be based, is not remotely valid!


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