[Physics] Physics Digest, Vol 8, Issue 9

[cj at mb-soft.com]

I said "often" because Newton made a logicl requirement for that calculation, that the object under study must be symmmetric for all the Integration to perfectly cancel out.  When an object is not symmetric, such as some asteroids, the Shell Theorems cannot apply.

We  are discussing Newton's Theorems XXX and XXXI.

You don't consider "Kepler's Laws" to be mathematical calculations???  A hundred years after those CALCULATIONS of Kepler, where he ignored the mass of the planets, Newton and his Fluxions corrected them with the more accurate versions.  Kepler had incorrectly assumed that ONLY the Sun's mass counted for the math.  Newton (with his Theorems XXX and XXXI and others) corrected those errors and he even explained and showed why.  

Newton waas not aware that the Milky Way Galaxy was an entity, or he would have made sure that no one should use Kepler's Laws for a "distributed mass which was not symmetric".

YOU claim to know the MASS of the Galaxy, but that is likely to be incorrect as it is based on Kepler's Law regarding the position and  velocity of the Sun and Earth and its distsance to the Core.

But I guess it is foolish to try to explain this to  someone who believes he is the smartest person who ever lived.

For anyone else, the process of trying to calculate the parameters of the Galaxy are far more obscure than most people realize.  In the 1920s, star velocities were found for thousands of nearby stars.  The stars which are OPPOSITE the Core were found to appear to "Drift" in a relatively common direction, and the ones that are TOWARD the Core appeared to "Drift" very slightly faster.  This isi essentially the entirety of the available data.  The DIRECTION of those Drifts was the reason why we feel we are "orbiting" the Core, in a specific direction, called the Apex of the Sun's  Way.  The DIFFERENCE of the two Drifts are the entire source of information regarding how FAST we believe the Sun is orbitting in the Galaxy.  These VERY approximate estimates were then used in Kepler's Law to calculate the mass of the Galaxy.

We don't actually even know WHERE the Core of the Galaxy is.  Yes, it is in the DIRECTION of sagittarius, but no one knows how far away the Core is.  The ONLY real evidence is based on the fact that we know where a couple hundred Globular Clusters are, and it was assumed that they are in a spherical pattern around the Core.  We can never SEE the core due to too much intervening material and gases, but most astronomers THINK it is around 29,000 light years away from where we are.  If you look, you will see some experts who think it is much greater or less than that.  And when the above-mentioned "tangential velocity" and "radial distance" are put in Kepler's Law, a value for the mass of the Galaxy is found.  But experts vary tremendously on that.  Some of my associates think it is triple that mass, while others think it is half.  The accuracy of the minnimal data is terrible.

Around twenty years ago, I published an article which discussed all this and more at http://mb-soft.com/public/galaxy.html

A large graphic sky map is included which shows the Apex of the Sun's Way, the Core, the tangential distance for us in the Galaxy, andn they are quite far apart.  The Apex of the Sun's Way is angled INWARD from the alleged direction we are orbiting, and it is also UPWARD.  Others than me had done those calculations, which decently match up with my figures.  Given the THICKNESS of the Galaxy in our region, the UPWARD velocity indicates that we will likely LEAVE THE GALAXY in only around nine million years, which is totally illogical.  THAT information was the basis for my hypothesis that we are "cycling" up and down in our Arm, with a fairly brief cycle time.  Similar information regardingn the Apex of the Sun's Way showed me that we are also currently moving "coreward" at a minimal velocity, where we will soon (a couple million years) stop and begin to accelerate toward the mass of the stasrs in our Arm.  Rather than using Kepler's Law for such calculations, I had to INDIVIDUALLY calculate the gravitational attraction of each star for the Sun, and then numerically Integrate that net Force, which resulted in my math saying that we cycle radially in our Arm with a period of around 52 million years and we are currently around 13 million years from having passed theough the Arm centerline.

In 1997, relatively few observational astronomers used powerful computers.  I KNOW because I ASKED a number of my associates about needing more powerful computers than the four PCs which I had running nearly constantly in doing all the Newton gravitational Force calculations and summing them, and then repeating all that for various locations along the "cross-Arm cycle path".  I had to do all that to arrive at the 52 million year cycle period.  At the time, few of them were using even their University computers for very significant math.  I hope that has changed now.  Since I was in regular communication with those Astronomy Departments at the time, I suppose I should not be surprised that YOU KNOW that they had results that they then kept secret from me.  Several of them ENCOURAGED my efforts and even awaited my results at the time.  Obviously, they informed YOU of the "more accurate results" that I was then struggling to calculate.
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