return to homepage Bending of Starlight A couple of years ago I published a call to astronomers, concerning the bending of starlight by Jupiter. I had developed a simple equation that gave me the same bending of starlight for the Sun as Einstein, and I applied this equation to Jupiter. I found that instead of .02 seconds of arc for Jupiter (Einstein’s prediction) my equation predicted 7 seconds of arc. Realizing that this was a huge difference, and that 7 seconds of arc should be visible even here under the Earth’s atmosphere, I sought experimental verification of it. If this paper was useful to you in any way, please consider donating a dollar (or more) to the SAVE THE ARTISTS FOUNDATION. This will allow me to continue writing these "unpublishable" things. Don't be confused by paying Melisa Smith--that is just one of my many noms de plume. If you are a Paypal user, there is no fee; so it might be worth your while to become one. Otherwise they will rob us 33 cents for each transaction.
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by the Planets
Experimental Proof of my Theory
by Miles Mathis
At first I thought this might interest some amateur astronomers, who could use their fancy equipment to do something constructive. But it soon became apparent that I was wrong. Everyone now has his own agenda and airtight schedule; and besides, testing General Relativity is not terribly sexy these days. If you agree with Einstein you are already on rock solid ground, it is thought: you don’t need to seek any more experimental proof. If you disagree, even in any minor way, then you are likely deep into your own esoteric theories, theories that include strings and donuts and hubcaps and pillbugs. If I wanted proof or disproof I was going to have to find it myself.
I lay in bed night after night, staring at the ceiling, trying to think of some way to run an experiment without spending a lot of money on telescopes and cameras and traveling about the globe like some modern-day Eddington. At last I had a revelation, and that is what this paper is about.
It finally occurred to me that I didn’t need a large telescope at all. What the telescope would do is make the planet very big, while the star stayed very small. But I didn’t need the planet to be very big. All I needed is the star anywhere near the planet. The planet’s relative size in the sky was immaterial to the observation. This is because, according to my theory, the bending of the starlight does not drop off with distance from the planet. All stars in the apparent vicinity of the planet would have equal bending, since the bending was an illusion to start with. As I showed in the previous paper, the appearance of bending—with the Sun and any planet—is caused not by the gravitational pull of the Sun or planet, but by the “gravity” of the Earth. It was caused by an increase in parallax due to the expansion of the Earth.
As a reminder, in the previous paper I showed that if you give the acceleration g to the Earth outward instead of to the gravitating body inward (by just flipping the vector g), you find that while the light from both the star and Jupiter are traveling to Earth from the vicinity of Jupiter, the Earth will have expanded a certain amount that is easily calculable. This sounds preposterous at first, but I remind you that it is a simple mathematical outcome of one of Einstein’s first postulates. Einstein used his elevator car in space to illustrate his postulate of equivalence. This postulate states that there is no experimental difference between gravity and acceleration. According to Einstein, the man in the elevator car cannot tell if he is accelerating up or gravitating down. No experiment he can do on the elevator will tell him the difference. Well, the Earth is our elevator car, and I have simply proposed reversing the vector. Make it an acceleration up instead of a pull down. You can change the math only or you can believe that the Earth is really expanding. It doesn’t matter. Just do the math, see where it takes you, and see if it answers any questions or allows you to make any interesting predictions. That is all I have done.
If you are at the central axis of the Earth, relative to the line from Jupiter, you won’t measure any parallax, standard or expansive, and won’t measure any bending of starlight. But if you are on any “edge” of the Earth, relative to Jupiter, you will see a much greater amount of parallax than current theory predicts, according to my theory. What this means experimentally is that if Jupiter is low in the sky, toward the horizon, my theory predicts at least 7 seconds of arc more parallax than current theory would provide.
That is to say, Jupiter should appear to be in the wrong place in the sky, for some positions on Earth. As I studied the diagram more closely, I saw that not every “edge” would expect to see the parallax increase, even when Jupiter was near the horizon. It would depend on Jupiter’s motion across the sky. From all points on the Earth, Jupiter’s parallax would increase vertically, that is, up or down the sky. If Jupiter were also moving mainly perpendicular to the horizon, then this would be “observable” only with a clock. For you see that Jupiter would arrive at a point on its path early or late, but would not deviate from its path. This would be very difficult to measure.
But from other points on the Earth, the deviation of Jupiter from the path would be a spatial deviation, not a time deviation. If Jupiter were moving mainly across the sky, then it might appear to be 7’’ too low. This was the observation I needed to seek.
The first question many readers will have is, “Too low with regard to what?” Too low relative to its predicted path. Astronomers can now tell you, with an accuracy of 1 second of arc or better, where all the planets will be at any given time. There are dozens of software programs available on the internet that can track all the planets into the distant past and future. They can tell you what constellation Jupiter was in when Christ was born and what star Saturn will be eclipsing in the year 4000. I have checked the math of one or two of these programs, and while I wouldn’t trust them to within 1’’ for the year 4000, they can’t be far wrong for current predictions. This is because they are normally extrapolations of data taken in the past decade, and planet/star conjunctions can’t get too far wrong in just a few years, unless the math is complete garbage.
This means that all I had to do is download some of these programs, look at planet/star conjunctions, and see if the data matched my observations. The first thing I did was see which software was giving the best predictions for my latitude and longitude, looking only at conjunctions high in the sky. I tried several, but found that an astrology program called ZET was the most accurate predictor. There may be many reasons for this, but I suspect that among the main ones are that astrologers are more interested in planet/star conjunctions than astronomers, and so they pay more attention to the algorithm in question. Or maybe they just do more conjunction observations and therefore have more data. More data equals a better extrapolation. Finally, ZET corrects for standard parallax, even on the distant planets. I believe that some other programs may correct for parallax only regarding the Moon, or not at all. This parallax is caused by the Earth’s radius relative to the distance to the planet, so in the case of Jupiter it would not be appreciable (1.7’’). But all errors are multiplied together, so that being fastidious even with small numbers may help a lot in the end.
In the beginning, I wanted data on Jupiter, but I soon realized that my observations would be much more efficient if I just took what the sky offered me. If Saturn was in the sky, I took down data for Saturn. If Uranus was in the sky, I took it. I also took data for Mars in the beginning. But I had to take data for a planet that was moving as I needed it to. If the planet was moving relative to me so that the only parallax I could measure would be a time parallax, I didn’t bother. That was just too difficult to confirm. Only if the planet were moving so that I might possibly see a spatial shift did I bother to take data. What this means is that if the planet were moving mainly parallel to the horizon, or across the sky, I took it. If it was moving mainly up the sky or down the sky, I ignored it. To understand why this is, you must study the diagram above. According to my theory, the Earth is expanding in all directions (or, at least, we must treat the kinematics as if it is). This means that if I am standing on the Earth, looking toward the horizon, my motion is up the sky. I am moving up. If the planet is moving in that same line, up or down, then it is in the line of the parallax, and any change will only be a time change. If there is any parallax increase, the planet will arrive at conjunction late or early. What I needed, however, is for the increase in parallax to push the planet noticeably out of its predicted path when it is near the horizon. This could only happen if the planet were moving mostly across my line of sight.
Another thing to look for was a planet near the horizon at dawn or dusk—specifically, rising at dawn or setting at dusk. This would mean, of course, that the viewer was as far as possible away from the planet as he could be, and still see it at night. If the viewer got any farther away in the relative orbits, the planet would only be up during the day, when it is not visible. I showed in the previous paper that using this logic, and my math, Jupiter’s expected parallax could be increased to 8.7 seconds of arc or more, in certain situations.
I soon saw that Saturn, Uranus, and Neptune would also be good candidates; better than Jupiter in many ways. The increase in distance to these outer planets gave me an increase in the expected parallax, and they were plenty bright enough for my purposes. In fact, since they were smaller they were more pointlike, making the separation measurement between them and the conjoining star that much easier to see. With Jupiter, the size of the planet (particularly through binoculars or a small telescope) brought its radius into the measurement. Whereas with Uranus and Neptune I could just measure from point to point.
For instance, Saturn’s maximum increase in parallax near the horizon, rising at dawn, and moving as much as possible across the sky, would be 16 seconds of arc. For Uranus it would 32.3’’. For Neptune it would be 50.5’’. For Mars it would be 2.56’’. For this reason I soon stopped collecting data on Mars. In most instances my observations of Mars would have yielded an expected increase in parallax well below 2’’, which was beneath my margin of error. I simply couldn’t measure at that precision. Even if the predictions from my software were correct to below 1’’, my ability to measure separation was nowhere near that accurate. The margin of error of any such measurement here on Earth is estimated to be around 2’’, even with optimum viewing conditions and the best equipment. This is due to atmospheric turbulence and many other possible factors. With my tools, the margin or error was closer to 4’’ or more, which, as you will see, soon led me to abandon Jupiter as well as Mars.
The reason for this is that the planets are almost never moving parallel to the horizon. There is always some angle that makes the calculations one step more difficult. You have to take a horizontal component of the motion, since only that component will show the change, even if it exists. As an example, if Jupiter is moving at a 45o angle to the horizon, then you have to take the sine of 45o, which means you multiply the expected change in parallax by 71/100. This would give me a potential increase in parallax of under 5’’, which is dangerously close to my margin of error. I soon saw that it was just too difficult to work with Jupiter, given my limitations. I needed the outer planets, which would offer me those “huge” deviations near the horizon.
Finally, I want to make clear what I mean by “moving across the sky”. I am not talking about apparent motion caused by the Earth spinning on its axis. I am not talking about the quick motion that we see every night as the stars and planets race across the sky. I am talking about the long term motion of the planet relative to the star in question. This motion is caused by the motion of both the planet and the Earth around the Sun. It is the apparent motion of the planets through the zodiac. It is this motion that needs to be as nearly flat to the horizon as possible. And this is the first of several reasons I needed to be as near 66N as possible (see below).
My next problem was actually measuring the separation. Even when looking at Neptune, I couldn’t expect to accurately measure separations of less than 1’ of arc with the naked eye. One minute of arc is about .18mm at an arm’s length, so I was looking for a naked eye difference of about a tenth of millimeter, even for Neptune. With binoculars this would become one or two millimeters. Still not enough for comfort, especially with Saturn. I needed a small telescope. A 4.5” Dobsonian would give me about 135x magnification, which would make Neptune’s difference up to 2cm and Saturn’s difference up to 6.3mm. More than enough to settle the question without any doubt.
Fortunately a friend had a cute little Orion telescope he had bought for his daughter, and she wasn’t much interested in it. He loaned it to me and I got to work. I soon discovered that one thing was working for me and one thing was working against. The against was that I was in Bruges, Belgium, where it is cloudy all the time. Finding clear nights and open horizons was not easy. The country is flat, but lines of tall trees crisscross the fields, following the canals. I found that I had to go to the beach every time I wanted data. On the beach there was light pollution and air pollution, but these didn’t matter much since I wasn’t trying to peer into deep space or resolve dim objects or see tiny variations. I was basically looking for a hidden elephant in the sky, and all I needed was an unobstructed view. The thing that was for me was that I was at a good latitude. According to my calculations I needed to be at 66oN or above, which, with the tilt of the Earth of 23.5o, would put me at the “top” of the Earth relative to the planets at a certain time of the night. This would work to maximize my findings. Bruges is only at 51o, but this is considerably better than my previous locations: Austin, Texas, at 30o and Amherst, Massachusetts, at 43o. In the summer of 2006 I took a long train ride to Rorvik, in Norway, to make some observations, but this was mostly just for fun. By then I was already getting big confirmations in Belgium. Being 15o too far south was not hurting me that much, since it translated into almost 97% optimal (cos15o).
But I had to be careful, since that 97% applied only at one time during the night. Twelve hours later at that same location I could expect only 46% (sin27.5o). The same thing was true at 66oN: at one time during the day or night, I would expect 100%, but 12 hours later I would expect 67% (sin42o).1
As would be expected, my best confirmations were on Uranus and Neptune. I would recommend anyone trying to find similar data to concentrate on those two planets. They must also use the math and logic spelled out above, in order to calculate the best hour of the night to observe, and in order to predict what increase in parallax they should expect.
When I say increase in parallax, I must be a bit more rigorous. If you are using a program like ZET that already gives you numbers that include normal parallax, then you are looking for a straight deviation from that given number. In other words, you don’t have to add the expected normal parallax to the expected increase in parallax due to my theory, since it is already included in the given number.
This paper is a presentation of my findings, not my raw data. Since I did not have a camera on my telescope, I have no pictures to publish. My data consists of just math and numbers, and I have already published the math (above and in the previous papers). My experimental numbers matched my predictions on all planets to within a margin of error of about 10’’. Many numbers were exact matches, given my equipment, but other matches were only rough confirmations. If I throw out Mars and Jupiter, due to this margin of error, then I have only three planets that confirm. For me, Uranus and Neptune were the easiest to use, but those with better equipment should get very accurate confirmation from Saturn, and possibly even Jupiter.
Once my results are verified with better equipment, I know that astronomers are not going to be satisfied with my theory. They may accept my math, but they will not like my kinematics at all. They will try to find other explanations for the increase in parallax. The first thing they will try to do is give the bending of the light to the gravitational field of the earth, using current gravitational theory (gravity as a pull) and the math of General Relativity. I hope you can see that this will immediately fail, since GR predicts a bending of starlight of 1.7” for the Sun and .02’’ for Jupiter. This would make the bending of light by the Earth about .00006”. And the Earth will not be able to bend light from Neptune more than light from Jupiter. So General Relativity cannot explain my data at all.
The next thing that astronomers will try to do is pass off the increase in parallax as due to some atmospheric phenomenon—scattering or refraction or turbulence or some combination of all of them. But this won’t work for the same reason. It is possible that light from planets is affected by the atmosphere in slightly different ways than light from stars2, but even if this is true, it doesn’t explain the huge difference in my data between various planets. My numbers show a direct dependence on distance, not on brightness. And, besides, if refraction of planet light varied so greatly on the horizon, it would be expected to vary at the zenith as well. It might not vary as much, since there is less atmosphere overhead. But the zenith variance would be expected to be a large fraction of the horizonal variance, since there is still a lot of atmosphere at the zenith. And yet we see no variance at the zenith.
Atmospheric turbulence would also tend to create wavering, as the current theory of twinkling shows. This means we would expect to see a displacement both up and down. But my theory and numbers show only a displacement down. It is a kinematic effect of parallax, not an effect of the medium due to heat or atmosphere. In the end, it would be supremely difficult to argue that planets are not affected by the atmosphere, in order to explain twinkling, and to argue that planets are affected by the atmosphere, in order to explain the variance in parallax.
I take the confirmation of my mathematical predictions as confirmation that gravity is in fact a proportional acceleration outward of all bodies, of all sizes. I have found the elephant in the sky.
1This is another reason I decided to go to Norway, since I could basically ditch all my time-of-night calculations, go out whenever I wanted, and still expect almost 70% optimal conditions.
2In my paper on twinkling, I refute this theory of turbulence.