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#31
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Einstein's biggest mistakes
Fatso cranked himself "Absolutely Vertical" when he wrote: Koobee Wublee wrote: Clemence was just using Le Verrier’s observation. So, nothing has changed per our discussion. shrug Fatso wrote: it doesn't matter what these things 'suggest to koobee wublee', since koobee wublee is an insane attention whore who has a serious detachment from reality. hanson wrote: but Fatso, your response looks like you are the "insane attention whore" who got aroused over KW's shrug ... [[[[ KW 1 -:- Fatso 0, zero, nil nada ]]]] Thanks for the laughs, though... ahahahahanson |
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Einstein's biggest mistakes
On 10.06.2013 05:30, Koobee Wublee wrote:
On Jun 9, 1:45 pm, "Paul B. Andersen" wrote: Koobee Wublee wrote: "Paul B. Andersen" wrote: According to: Myles Standish, Jet Propulsion Laboratory (1998) GR predicts 42.98 +/- 0.04 arc secs per century. According to: Clemence, G. M. (1947). "The Relativity Effect in Planetary Motions". Reviews of Modern Physics 19 (4): 361–364. The tug from other planets is 531.63 +/- 0.69 and the observed is 574.10 +/- 0.65 arc secs per century (both relative to 'stationary space') So the 'anomaly' is 42.45 +/- 1.13 arc secs per century GR's prediction is well inside the error bars. Has Paul ever examine the precession of the equinox more closely? shrug http://en.wikipedia.org/wiki/Axial_precession According to the above link, the exact period is 25,772 years (with no error bar given) which translates to 257.72 centuries. 360 * 60 * 60 / 257.72 = 5,028.7” As Paul has pointed out, Le Verrier had observed 5,600.0” (with no error bar given and with unknown digits of significance but at least 2). 5,600.0” – 5,028.7” – (531.63” +/- 0.69”) = 39.7” +/- 0.7” It is about 3” less than the fudged prediction of the Schwarzschild metric. So, it looks like the data is fudged as well as the prediction. shrug Never mind the number (38”) that Le Verrier had computed. What is important is the overall perihelion advance of Mercury which according to Le Verrier is 5,600” per century because we know how to compute for the anomaly from known effects of perihelion advance/retardation. shrug The 38” is considered as historical interest like what you said, but the 5,600” is of great importance to modern science. The accuracy of the latter number cannot be handwaved away since the accuracy of the said anomaly is thoroughly dependent on the accuracy of this 5,600”. shrug http://en.wikipedia.org/wiki/Axial_p...ion_(astronomy) To get to (42.45” +/- 1.13”) of accuracy calculated by Paul Andersen, the precision of the following three quantities must be called out to the second digit after the decimal. shrug ** Le Verrier’s observation = 5,600.00” +/- ? ** Precession of the equinox = 5,028.7” +/- ? Clemence was using the number 25,787 years as the period of the precession known at that time during Le Verrier’s time. However, modern astronomy has improved the accuracy to 25,772. That will affect the accuracy in the final anomaly value. shrug As far as I can understand, this paper from 2003 contains the values now commonly used: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf On the bottom of page 39, the following equation is given for the precession of the equinox: p_A = 5028".796195t + 1".1054348t + higher order terms where t is Julian centuries since J2000. The rate of the precession is the derivative: p = 5028".796195 + 2".2108696t + higher order terms. This will give the period 25,772 years at J2000. However, Clemence's measurments were done some 0.55 century before J2000, which will give the value: p = 5027".58.. per century I am not sure of the precision, it is considered in the paper, but it isn't easy to see what impact it will have on the final result. If we use this value together with Clemence's measurements, we get the anomaly 40".53 +/- ~1" With 38”, 39”, or 40” per 100 years, Le Verrier had weak justification to search for another planet. The anomaly is not as obvious as Uranus’s case. shrug So GR's prediction is some 1".4 outside of the error bar. I would question Clemence's measurements. How precise were they really? His measurements were done during only four years. I was very wrong about the four years. See below. Clemence did no measurement. His result was a recycle of Le Verrier’s observation about 8 decades prior. Not quite true. Here is Clemence's paper: http://www.gethome.no/paulba/pdf/Clemence.pdf He says that he has used about 10,000 meridian observations of Mercury from 1762 to 1937, and 17 transit observations from 1799 to 1940. So Le Verrier's observations are included, but he also used just about all available observations at the time, which includes almost a century worth of observations after Le Verrier. This is interesting, because the question is what the rate of the precession of the equinoxes were at the time the measurements were done. If we use 1850 as the middle year, the equation from: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf p = 5028".796195 + 2".2108696t + .. yields: p = 5025".48 per century at J1850, which is pretty close to the number used by Clemence for the same year! So to sum it up: Observed precession of the perihelion of Mercury: 5599.74+/-0.5 Modern estimate of precession of equinoxes at J1850: 5025.48 Precession of the equinoxes relative to 'stationary space': 574.26+/-0.5 The tug from other planets is 531.63 +/- 0.69 Anomaly = 42.63 +/- ~1.2 Conclusion: GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. Le Verrier was not set out to measure the accuracy down to the last second, but his motivation was to find a sum of anomaly for him to justify whether if there is another planet further inside the orbit of Mercury. He did not find it. Thus, most of astronomers, and perhaps Le Verrier himself, at that time just attributed the lack of the extra planet to Le Verrier’s own observation accuracy. shrug Clemence realized without pinning down Le Verrier’s observation with better accuracy, the confirmation of GR cannot be definitively claimed. The question to ask is what Clemence’s justification is to claim such extreme accuracy on Le Verrier’s observation 8 decades prior. shrug But I am pretty sure the last word isn't said about the precession of the equinoxes. And there is a comment in the paper above which I find a bit puzzling: "The classical "general precession" which mixes the motion of the equator in the GCRS and the motion of the ecliptic in the ICRS (and moreover may not be defined in the framework of General Relativity without fundamental problems) should no longer be regarded as a primary precession quantity. It is considered here as a derived quantity,.." During glacial periods with more ice tapped in the polar regions, the precession of the equinox might be slightly more pronounced as it is today, but for the large part, the precession of the equinox should be very a constant given a span of several hundred years. With global warming in the past few decades where ice from the polar regions are melting at an unprecedented level, the precession value might be a little bit higher during Le Verrier’s time. However, Koobee Wublee does not have the authority to claim 25787 years as did by Le Verrier. shrug ** Tugs from other planets = 531.63” +/- 0.69” Among them, the precession of the equinox has been the most accurately measured besides the human history has only spanned a third of the period of the precession. The anomaly due to the processor of the equinox should be constant over time. shrug Thus, tugs from other solar objects have to be time dependent with dependencies on the locations (a function of time) of the planets throughout the course of measurement which is 100 years. This means the number you quoted (531.63” +/- 0.69”) would vary somewhat drastically depending for example if all planets are lined up. Intuitively, the net result should be zero if averaged out over time. In the next century, odds are against you to measure anything close to 532” from the gravitational effect of other planets. shrug I wonder if there isn't any newer measurements of the precession of the perihelion of Mercury. I have looked for it, but can't find any. With better computer simulation, the tugs from other planets should be a piece of cake to pin down, and measuring the overall Mercury’s perihelion since Le Verrier’s time should also be a piece of cake. The numbers would, of course, be drastically different from Le Verrier’s. Koobee Wublee thinks it had been done many timed before, but each time the net result showed great disappoint to the self- styled physicists. Le Verrier’s 140-year-old observation embarrassingly seems to be the best and only support to GR regarding Mercury’s orbital anomaly. Sad for self-styled physicists but very close to be true. Koobee Wublee would certainly like to know what the real value of this anomaly is. It does not look like it is anywhere close to +43” per 100 years from the lack of reports by the self- styled physicists. Koobee Wublee suspects it is more like null. shrug That 43” is just a myth conjured up by self-styled physicists to sell their garbage in SR and GR just because Paul Gerber was able to do it first. shrug The anomaly is less that 4% off the GR prediction, surely not enough to falsify GR. Clemence tried to justify the validity of GR by placing such precision on Le Verrier’s observation but instead shot himself in the foot where he fumbled with the precession of the equinox. The accuracy remains to be outside of GR’s prediction, and GR’s such prediction is very much “quantized” which leaves no room to negotiate with that extra 10% difference. Besides the Schwarzschild metric predicts only +20” to +30” (1 significant digit) per 100 years. The self-styled physicists are not interested to do anything for science but to prolong their elite status quo. Another example of fiasco is the GPS. Remember? shrug With that said, it is Adventure Time with Finn and Jake. Is Paul ready for more adventures in differential equations where Koobee Wublee has buried Paul every single time on simpler mathematics? :-) Is Paul beginning to wake up? shrug -- Paul http://www.gethome.no/paulba/ |
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Einstein's biggest mistakes
On 10.06.2013 20:40, Paul B. Andersen wrote:
Here is Clemence's paper: http://www.gethome.no/paulba/pdf/Clemence.pdf He says that he has used about 10,000 meridian observations of Mercury from 1762 to 1937, and 17 transit observations from 1799 to 1940. So Le Verrier's observations are included, but he also used just about all available observations at the time, which includes almost a century worth of observations after Le Verrier. This is interesting, because the question is what the rate of the precession of the equinoxes were at the time the measurements were done. If we use 1850 as the middle year, the equation from: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf p = 5028".796195 + 2".2108696t + .. yields: p = 5025".48 per century at J1850, which is pretty close to the number used by Clemence for the same year! So to sum it up: Observed precession of the perihelion of Mercury: 5599.74+/-0.5 Modern estimate of precession of equinoxes at J1850: 5025.48 Precession of the equinoxes relative to 'stationary space': 574.26+/-0.5 Should (obviously) be: Precession of the perihelion of Mercury relative to 'stationary space': 574.26+/-0.5 The tug from other planets is 531.63 +/- 0.69 Anomaly = 42.63 +/- ~1.2 Conclusion: GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. -- Paul http://www.gethome.no/paulba/ |
#34
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go, le Verrier!
that was expostulatory; no need to readmore.com
GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. The anomaly is less that 4% off the GR prediction, surely not enough to falsify GR. read more » |
#35
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Einstein's biggest mistakes
On 10.06.2013 05:30, Koobee Wublee wrote:
With that said, it is Adventure Time with Finn and Jake. Is Paul ready for more adventures in differential equations where Koobee Wublee has buried Paul every single time on simpler mathematics? :-) Is Paul beginning to wake up? shrug See Koobee Wublee bury Paul: http://www.gethome.no/paulba/pdf/Koobees_blunder.pdf -- Paul http://www.gethome.no/paulba/ |
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Einstein's biggest mistakes
On Jun 10, 11:40 am, "Paul B. Andersen" wrote:
Koobee Wublee wrote: "Paul B. Andersen" wrote: So the 'anomaly' is 42.45 +/- 1.13 arc secs per century GR's prediction is well inside the error bars. To get to (42.45” +/- 1.13”) of accuracy calculated by Paul, the precision of the following three quantities must be called out to the second digit after the decimal. shrug ** Le Verrier’s observation = 5,600.00” +/- ? ** Precession of the equinox = 5,028.7” +/- ? ** Tugs from other planets = 531.63” +/- 0.69” Clemence did no measurement. His result was a recycle of Le Verrier’s observation about 8 decades prior. Le Verrier was not set out to measure the accuracy down to the last second, but his motivation was to find a sum of anomaly for him to justify whether if there is another planet further inside the orbit of Mercury. He did not find it. Thus, most of astronomers, and perhaps Le Verrier himself, at that time just attributed the lack of the extra planet to Le Verrier’s own observation accuracy. shrug Clemence realized without pinning down Le Verrier’s observation with better accuracy, the confirmation of GR cannot be definitively claimed. The question to ask is what Clemence’s justification is to claim such extreme accuracy on Le Verrier’s observation 8 decades prior. shrug Not quite true. Here is Clemence's paper: http://www.gethome.no/paulba/pdf/Clemence.pdf It only contains the final results. shrug He says that he has used about 10,000 meridian observations of Mercury from 1762 to 1937, and 17 transit observations from 1799 to 1940. So Le Verrier's observations are included, but he also used just about all available observations at the time, which includes almost a century worth of observations after Le Verrier. Le Verrier had 100 years of data. If Clemence did include Le Verrier’s data, how many years did Clemence use? It is not clear from the paragraph above. The overall number of 5,599.74 that Clemence came up with can only be Le Verrier’s data and nothing else. The paper does not justify the such great precision to Le Verrier’s observation. shrug This is interesting, because the question is what the rate of the precession of the equinoxes were at the time the measurements were done. If we use 1850 as the middle year, the equation from: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf p = 5028".796195 + 2".2108696t + .. yields: p = 5025".48 per century at J1850, which is pretty close to the number used by Clemence for the same year! Has Paul really read that paper? Koobee Wublee suspects not. Paul just made up bull****. According to this paper, the amount of precession measured in seconds can be calculated according to the following formula. shrug ** 5,208”79695 t – 1”11113 t^2 – 0”000006 t^3 Where ** t = (days – 2,000 Jan 1 noon) / 36525 Thus, on that day of January 1, 2,000, a tare (setting to null) on the precession angle is performed. A hundred years from now, you can add 1”1 to the rate which means the precession is getting worse (period getting longer). There is no qualification for you to extrapolate that backwards. In 1947, Clemence was merely using the same number as he knew then. shrug Besides with global warming if true, less ice will be trapped in the polar regions, and that would make the precession less severe (shorter period). shrug So to sum it up: Observed precession of the perihelion of Mercury: 5599.74+/-0.5 Modern estimate of precession of equinoxes at J1850: 5025.48 Precession of the equinoxes relative to 'stationary space': 574.26+/-0.5 The tug from other planets is 531.63 +/- 0.69 Anomaly = 42.63 +/- ~1.2 It is still inconclusive. The justification to why Le Verrier’s measurement of 5,600” is actually 5,599”74 +/- 0”5 remains not justified. According to Clemence’s paper, he said: “The contributions of the planets are directly proportional to their several masses, which are NOT ALL KNOWN WITH THE DESIRED ACCURACY. The quantities denoted by m^-1 are the reciprocals of the adopted masses, the sun’s mass being taken as unity, and the attached probable errors give rise to the probable errors associated with the theoretical contributions to the motions. In the case of Mercury each planetary contribution (except that of the Mercury itself) is the sum of three parts: the motion of the perihelion in the plane of the orbit, the contribution arising from the motion of the node, and the contribution from the motion of the ecliptic...” Clemence did not understand that the effect on Mercury’s orbit due to other planets would depend on where the planets were during the course of that 100 years. Clemence did not have any justification to place Le Verrier’s numbers within such accuracy. It is almost impossible to calculate, but it is easier (but still no trivial task) to simulate. shrug Conclusion: GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. Not quite. All these effects on Mercury’s orbit including GR one if indeed exists are not linearly additive. Any parameter will affect the final outcome depending on what other parameters are. You will realize this if you actually study the differential equations involved. Paul Gerber simplified the system as linear, and Koobee Wublee thinks he was wrong. The only way to address this is to do: ** The actual measurement which has more than 100 years of data ** Simulation on the entire system The difference should be the value reflected by the precession of the equinox. shrug |
#37
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Einstein's biggest mistakes
On 11.06.2013 00:44, Koobee Wublee wrote:
On Jun 10, 11:40 am, "Paul B. Andersen" wrote: This is interesting, because the question is what the rate of the precession of the equinoxes were at the time the measurements were done. If we use 1850 as the middle year, the equation from: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf p = 5028".796195 + 2".2108696t + .. yields: p = 5025".48 per century at J1850, which is pretty close to the number used by Clemence for the same year! Has Paul really read that paper? Koobee Wublee suspects not. Paul just made up bull****. According to this paper, the amount of precession measured in seconds can be calculated according to the following formula. shrug ** 5,208”79695 t – 1”11113 t^2 – 0”000006 t^3 Where ** t = (days – 2,000 Jan 1 noon) / 36525 Thus, on that day of January 1, 2,000, a tare (setting to null) on the precession angle is performed. A hundred years from now, you can add 1”1 to the rate which means the precession is getting worse (period getting longer). There is no qualification for you to extrapolate that backwards. Did someone mention bull****? :-) According to this paper: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf The _accumulated_ precession, that is the angle of the equinoxes with the angle at J2000 as the reference is: p_A = 5028".796195 t + 1".1054348 t^2 + 0".00007964 t^3 + .. (up to t^5) Where t is in Julian centuries since J2000. This is a phase. But the _chance_ of the angle of precession per century is: p = dp_A/dt = 5028".796195 + 2".2108696 t + 0".0001302 t^2 + .. This is an angular frequency. The rate of change of the precession of the equinoxes at J2000 is 5028".796195 per century, or 50".28796195 per year. So the period of the precession is at J2000: (T = 2pi/w) (360*60*60)"/(50".28796195 per year) ~= 25772 years. This is the period you claimed to be the "correct one". It is - at J2000. But no dramatic change happened in the solar system at J2000, so there is no reason to claim that the equation above can't be used for the centuries prior to J2000. So the 'most modern' estimate of the rate of precession of the equinoxes at J1850 is: p(1850) = 5028".796195 - 2".2108696 1.5 ~= 5025".48 per century (second order terms and higher ignored) So to sum it up: The observed precession of the perihelion of Mercury is found in Clemence's paper: http://www.gethome.no/paulba/pdf/Clemence.pdf Observed precession of the perihelion of Mercury: 5599.74+/-0.5 Modern estimate of precession of equinoxes at J1850: 5025.48 Precession of the perihelion relative to 'stationary space': 574.26+/-0.5 The tug from other planets is 531.63 ± 0.69 Anomaly = 42.63 ± ~1.2 Conclusion: GR's prediction for the 'anomaly': 42.98 ± 0.04 is well inside the error bar. -- Paul http://www.gethome.no/paulba/ |
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Einstein's biggest mistakes
On Jun 11, 6:19 am, "Paul B. Andersen" wrote:
Koobee Wublee wrote: "Paul B. Andersen" wrote: So the 'anomaly' is 42.45 +/- 1.13 arc secs per century GR's prediction is well inside the error bars. To get to (42.45” +/- 1.13”) of accuracy calculated by Paul, the precision of the following three quantities must be called out to the second digit after the decimal. shrug ** Le Verrier’s observation = 5,600.00” +/- ? ** Precession of the equinox = 5,028.7” +/- ? ** Tugs from other planets = 531.63” +/- 0.69” Clemence did no measurement. His result was a recycle of Le Verrier’s observation about 8 decades prior. Le Verrier was not set out to measure the accuracy down to the last second, but his motivation was to find a sum of anomaly for him to justify whether if there is another planet further inside the orbit of Mercury. He did not find it. Thus, most of astronomers, and perhaps Le Verrier himself, at that time just attributed the lack of the extra planet to Le Verrier’s own observation accuracy. shrug Clemence realized without pinning down Le Verrier’s observation with better accuracy, the confirmation of GR cannot be definitively claimed. The question to ask is what Clemence’s justification is to claim such extreme accuracy on Le Verrier’s observation 8 decades prior. shrug Did someone mention bull****? :-) From Paul, yes. :-) According to this paper: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf The _accumulated_ precession, that is the angle of the equinoxes with the angle at J2000 as the reference is: p_A = 5028".796195 t + 1".1054348 t^2 + 0".00007964 t^3 + .. (up to t^5) Where t is in Julian centuries since J2000. This formula looks better since with the melting of the polar ice caps the precession period ought to get longer. shrug This is a phase. This is only valid after 2000 and after for a few centuries. shrug But the _chance_ of the angle of precession per century is: p = dp_A/dt = 5028".796195 + 2".2108696 t + 0".0001302 t^2 + .. This is an angular frequency. So, according to Paul, 230k years ago, the precession was null. shrug Let’s see if that equation agree with you. Say t is indeed -1.5 (150 years ago when Le Verrier made his final measurement on Mercury’s orbit) and -2.5 (250 years ago when Le Verrier’s data started). pA at -1 .5 = 5028”8 (-1.5) + 1.1 (-1.5)^2 = -7544”5 pA at -2 .5 = 5028”8 (-2.5) + 1.1 (-2.5)^2 = -12578”9 The rate ought to be (12578”9 – 7544”5 = 5034”4) which is not probable. Paul is a joker. Paul is a mathemagician. shrug So to sum it up: Observed precession of the perihelion of Mercury: 5599.74+/-0.5 Modern estimate of precession of equinoxes at J1850: 5025.48 Precession of the equinoxes relative to 'stationary space': 574.26+/-0.5 The tug from other planets is 531.63 +/- 0.69 Anomaly = 42.63 +/- ~1.2 It is still inconclusive. The justification to why Le Verrier’s measurement of 5,600” is actually 5,599”74 +/- 0”5 remains not justified. According to Clemence’s paper, he said: “The contributions of the planets are directly proportional to their several masses, which are NOT ALL KNOWN WITH THE DESIRED ACCURACY. The quantities denoted by m^-1 are the reciprocals of the adopted masses, the sun’s mass being taken as unity, and the attached probable errors give rise to the probable errors associated with the theoretical contributions to the motions. In the case of Mercury each planetary contribution (except that of the Mercury itself) is the sum of three parts: the motion of the perihelion in the plane of the orbit, the contribution arising from the motion of the node, and the contribution from the motion of the ecliptic...” Clemence did not understand that the effect on Mercury’s orbit due to other planets would depend on where the planets were during the course of that 100 years. Clemence did not have any justification to place Le Verrier’s numbers within such accuracy. It is almost impossible to calculate, but it is easier (but still no trivial task) to simulate. shrug Conclusion: GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. Not quite. All these effects on Mercury’s orbit including GR one if indeed exists are not linearly additive. Any parameter will affect the final outcome depending on what other parameters are. You will realize this if you actually study the differential equations involved. Paul Gerber simplified the system as linear, and Koobee Wublee thinks he was wrong. The only way to address this is to do: ** The actual measurement which has more than 100 years of data ** Simulation on the entire system The difference should be the value reflected by the precession of the equinox. shrug |
#39
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there ain't no pascals, thereatsville
Kepler discovered the curvature of space,
with his three orbital constraints; Gauss measured it with a theodolite of his own construction in Allsace-Lorraine -- it is not perfectly convex. GR is "just" a manifestation of gravity, what ever it really is. what it is definitely not, though, is any perfect "pascalian" vacuum (with no pascals .-) GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. Not quite. *All these effects on Mercury’s orbit including GR one if indeed exists are not linearly additive. |
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Einstein's biggest mistakes
On 11.06.2013 18:44, Koobee Wublee wrote:
On Jun 11, 6:19 am, "Paul B. Andersen" wrote: According to this paper: http://syrte.obspm.fr/iau2006/aa03_412_P03.pdf The _accumulated_ precession, that is the angle of the equinoxes with the angle at J2000 as the reference is: p_A = 5028".796195 t + 1".1054348 t^2 + 0".00007964 t^3 + .. (up to t^5) Where t is in Julian centuries since J2000. This formula looks better since with the melting of the polar ice caps the precession period ought to get longer. shrug This is a phase. This is only valid after 2000 and after for a few centuries. shrug Not at all. The J000 is but a - not entirely arbitrary - chosen reference point. As you possibly know, the equatorial coordinate system is used by astronomers to give the position of stars and other objects. This is a spherical coordinate system with the coordinates declination (Dec) and Right ascension (RA). The Dec is the angle from the equatorial plane, and the RA is the 'horizontal' angle from the vernal equinox. Since the vernal equinox is moving, and it would be very impractical to continuously rework the star charts, it must be specified which year (epoch) a set of coordinates is valid for. Standard years are chosen, usually every 50 years or so. The currently used epoch is J2000. This is the reason why J2000 is used in the Equation for pA above. So when you find the coordinates of the star in a EPOCH2000 star chart, the angle pA for the current year is what you have to add to the charted RA to find its real position. The equation is valid several centuries in both direction. But the _chance_ of the angle of precession per century is: p = dp_A/dt = 5028".796195 + 2".2108696 t + 0".0001302 t^2 + .. This is an angular frequency. So, according to Paul, 230k years ago, the precession was null. shrug No, because then the higher order terms would come into play. The result would be ridiculous, though. It would be equally ridiculous for 230k years in the future. Let’s see if that equation agree with you. Say t is indeed -1.5 (150 years ago when Le Verrier made his final measurement on Mercury’s orbit) and -2.5 (250 years ago when Le Verrier’s data started). pA at -1 .5 = 5028”8 (-1.5) + 1.1 (-1.5)^2 = -7544”5 pA at -2 .5 = 5028”8 (-2.5) + 1.1 (-2.5)^2 = -12578”9 Correct numbers: pA(J1850) = -7540.7074534702 arcsecs pA(J1750) = -12565.0836925488 arcsecs The rate ought to be (12578”9 – 7544”5 = 5034”4) which is not probable. Paul is a joker. Paul is a mathemagician. shrug Correct numbers: pA(J1850)-pA(J1750) = 5024.3762390786 arcsecs per century p(J1800) = 5024.3761718400 arcsecs per century (the two are not exactly equal because the curve isn't linear) What's your problem with this? However, Clemence estimate is based on observations from 1765 to 1940, so 1850 is a more reasonable middle year. http://www.gethome.no/paulba/pdf/Clemence.pdf p(1850) = 5025.4807492700 arcsecs per century And if you wonder if your way of calculating agrees with this: pA(J1900) = -5027.6908636587 arcsecs pA(J1800) = -10053.1716684064 arcsecs pA(1900)- pA(1800) = 5025.4808047477 arcsecs per century So to sum it up: Observed precession of the perihelion of Mercury: 5599.74+/-0.5 Modern estimate of precession of equinoxes at J1850: 5025.48 Precession of the equinoxes relative to 'stationary space': 574.26+/-0.5 The tug from other planets is 531.63 +/- 0.69 Anomaly = 42.63 +/- ~1.2 It is still inconclusive. The justification to why Le Verrier’s measurement of 5,600” is actually 5,599”74 +/- 0”5 remains not justified. According to Clemence’s paper, he said: “The contributions of the planets are directly proportional to their several masses, which are NOT ALL KNOWN WITH THE DESIRED ACCURACY. The quantities denoted by m^-1 are the reciprocals of the adopted masses, the sun’s mass being taken as unity, and the attached probable errors give rise to the probable errors associated with the theoretical contributions to the motions. In the case of Mercury each planetary contribution (except that of the Mercury itself) is the sum of three parts: the motion of the perihelion in the plane of the orbit, the contribution arising from the motion of the node, and the contribution from the motion of the ecliptic...” Clemence did not understand that the effect on Mercury’s orbit due to other planets would depend on where the planets were during the course of that 100 years. Clemence did not have any justification to place Le Verrier’s numbers within such accuracy. It is almost impossible to calculate, but it is easier (but still no trivial task) to simulate. shrug Conclusion: GR's prediction for the 'anomaly': 42.98 +/- 0.04 is well inside the error bar. Not quite. All these effects on Mercury’s orbit including GR one if indeed exists are not linearly additive. Any parameter will affect the final outcome depending on what other parameters are. You will realize this if you actually study the differential equations involved. Paul Gerber simplified the system as linear, and Koobee Wublee thinks he was wrong. The only way to address this is to do: ** The actual measurement which has more than 100 years of data ** Simulation on the entire system The difference should be the value reflected by the precession of the equinox. shrug -- Paul http://www.gethome.no/paulba/ |
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