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Perihelion Precession
of Mercury

The Short Version

I recently published a 32-page paper on this subject, a paper that many have found hard on their eyes and brains. In that paper I was very thorough and rigorous, including in my text a history of the problem and a full explanation of every new mathematical manipulation and axiom and correction. I believed this was necessary, and still do. But for PR purposes I have prepared this compression, hoping it will convince a few more people that I have indeed discovered several important corrections to Einstein. Here I will offer only the highlights of the longer paper, snipping all long explanations and most of the math.

The first highlight concerns my discovery that the historical procedure of solving this problem was logically flawed from the beginning. As is well-known, the equations of Newton failed to match the data, leaving a remainder in the data of about 43 arcsec/century. Einstein created a new set of equations which yielded this remainder, but he failed to recognize the flaw in his procedure. You cannot use one set of equations to produce a margin of failure, and then use a new set of equations to fill that margin. If Newton's equations fail, they fail in all places, not only in the margin. To be specific, data gives us 5600 arcsec of total precession and Newton predicts 5557. Well, in that case, Newton is wrong not only about the 43, he is wrong about the 5557. He cannot be wrong about one and right about the other. His equations are either correct or incorrect. If they are incorrect about the total, they must be incorrect about all subtotals.

This means that Einstein needed to use his new equations on all parts of the problem, including all perturbations. He did not do this. He simply found a number for additional curvature of Mercury's field caused by the Sun and added that to Newton's total. As both math and logic, that is a spectacular error.

The next highlight is my discovery that Einstein assigned the number .43 to the wrong time period. By studying his math very closely, I found that he gave no explanation of his time assignment. He simply assumed that once he found the number .43 [or .45, actually] he was finished. That was the number he needed, so he assigned it to one revolution of the Earth (1 year) and claimed victory. He was mistaken, and no one has noticed his mistake until now. What Einstein really found with his math was a number for field curvature at the distance of Mercury's orbit, not a number for precession. The field curvature is a constant, and can be applied to any given time period. To find precession due to this curvature, you have to assign the curvature to the right time period, and in this Einstein failed. Since the curvature is at the distance of Mercury's orbit, the time period must be the Mercury year, not the Earth year. Which means that Mercury must precess due to this curvature every 88 days, not every 365 days.

The third highlight is one final correction to Einstein's assumptions. It is a matter of history that Einstein's first solution to this problem gave him a number that was about half the number in his final solution. In his first GR paper he found .18 arcsec for the field curvature. I show that this was nearer correct than his final number of .43. The reason is because precession is a phenomenon that "uses" only half the field curvature. As I show with very simple math, the total field curvature at the distance of Mercury is indeed around .43 arcsec, but precession is influenced by only half this curvature. This is because the field curves both prograde and retrograde, but Mercury is not moving through the field in both directions. Mercury is moving through the field in one direction only. Precession is strictly an orbital event, and this event encounters only half the angle of curvature. For this reason and this reason alone, the equations of precession require only half the total field curvature. I show that the number for applicable curvature is .195 and that the precession period for this curvature is the Mercury year.

It may be that Einstein ignored all this for a very good reason. And it may be that history has allowed him to ignore it for the same reason. Neither he nor history has wanted to go back into the problem and make all the difficult corrections. It is much easier just to accept the number .43 and call it a day. Because once you discover that the curvature has to be applied to 88 days, it changes the number. You no longer have 43 arcsec/century. No, you now have 80 arcsec/century, which requires a correction to all the other numbers involved, including all perturbations and all the numbers of the Earth. Perhaps no one could see a way to do this, so it has all been swept under the rug.

Whether or not that is what happened, or whether it happened that no one noticed any of this, it is beyond question that Einstein did not fully solve the problem. I prove this by actually doing the perturbation correction, showing that 80 arcsec/century fits perfectly with the new corrected perturbation numbers. To find the corrected perturbation numbers, I assume that the percentage correction due to curvature will be about the same for all bodies in the solar system. Then I find the percentage correction for one body (the Earth perturbing Mercury) and change the total number by that percentage. This gives me the correct answer with a very small margin of error. Using some very simple and novel math, I find that the percentage change in perturbations due to Einstein's postulates must be about -4%. This takes the total perturbation number from 528 arcsec/century (the Newtonian prediction and currectly accepted number) down to 507 arcsec/century.

The necessity of this correction should have been seen long ago, and I have great difficulty believing no one has noticed the fact. How has it been possible to maintain a belief in the Newtonian perturbation number all these years, even after Einstein showed that Newtonian equations cannot be expected to give us the right numbers? How is it that no one in the 20th century thought to use Einstein's equations to correct the perturbation total? They did not do it, I think, because doing it would have immediately falsified the famous number .43.

At any rate, my new numbers, along with a new vector analysis, allowed me to solve the problem in a very convincing manner. I say vector analysis, since the standard model has also failed to add up all the numbers from data in the correct way. Since Einstein and the standard model were unaware of the precise mechanics involved, they have not recognized that some types of precession are in vector opposition to others. Precession can be either prograde or retrograde. Likewise, relative precession can be either prograde or retrograde. By precession, I mean precession relative to the solar field. By relative precession, I mean precession of one body relative to another body directly, without using the solar field. Einstein and the standard model have not been rigorous enough in differentiating between the two, often conflating one for the other. They have also not been rigorous enough in vector analysis of all these precessions. I do the full vector analysis, showing how and why some precessions are differentials rather than sums. This falsifies the current analysis, which is simply a naïve summation of all known numbers.

As a final highlight, I think I must point out that I am able to make all these corrections without once using the tensor calculus or any other difficult math. By a simple mathematical manipulation—given me by Einstein's own postulate of equivalence—I am able to do all field math with high-school algebra in a Euclidean field. This manipulation leads me quickly and transparently to Einstein's own numbers, but it also allows me to move beyond them. My math is so simple that it forces all the axioms and mechanics into high relief, making them obvious to all. The length of my original paper is caused by a thorough scrubbing of all the historical mistakes and subtleties, not by pages of complex equations.

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