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ABSTRACTINTRODUCTIONSUMMARYNOMINAL
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GENERAL
RELATIVITY or In this paper, theoretical tidal effects are derived, (similar to the earth-moon system), and then orbital precession comparisons are made with GR for twenty-two celestial bodies. TOP OF PAGE Six prior papers investigated the orbital precessions of the planet Mercury, the moon, the major satellites of Jupiter, Saturn, Uranus, and four binary stars. Special attention was given to the possibility that Newtonian tidal effects may account for excess precession, rather than resorting to general relativity for explanations. In this paper, theoretical tidal effects are derived, (similar to the earth-moon system), and then orbital precession comparisons are made with general relativity for twenty-two celestial bodies. TOP OF PAGE
1) Quite surprisingly, the derived nominal tidal effects model duplicates general relativity precessions for all celestial bodies in the solar system. However, for two binary stars, (DI Herculis and AS Camelopardalis), GR predicts double the measured orbital precessions, while the NTE model duplicates the measured values. The results of this investigation indicate that NTE provides better correlation with measured orbital precessions than does GR. 2) For the binary pulsar, (PSR1913+16), GR duplicates the measured orbital precession of 422 degrees per century, with a solar mass combination of 1.4/1.4 and assuming both bodies are neutron stars. With neutron stars the extreme density excludes NTE, which calculates to be only 189 degrees per century. However, a solar mass combination of 4.17/2.5 also duplicates the orbit of PSR1913+16, with NTE producing the measured 422 degrees per century. The 4.17 solar mass might be a neutron star, but the hidden component (2.5 solar mass) could be capable of producing the NTE precession. For this latter mass combination NTE excludes GR, which now calculates to be 727 degrees per century. 3) The orbital period decay of this pulsar has been attributed to energy being dissipated in the form of gravitational waves, which is a GR effect. However, this decay could also be attributed to a Newtonian propagation speed of gravity which is several million times the speed of light. With a speed of gravity several million times the speed of light, special relativity and general relativity appear to be violated, since nothing can presumedly travel faster than the speed of light. 4) From the results of this investigation, I believe that the reality of GR is subject to question. Newtonian tidal effects with a speed of gravity several million times the speed of light offers a reasonable alternative. Light bending around the sun has also been considered, and may be explained as a Newtonian refraction passing through the sun's corona, combined with the sun's gravitational pull on light photons as they pass by the sun. The implication is that the universe is ordinary three-dimensional space and time; that is, Euclidean, rather than conforming to GR. 5) A Euclidean universe that is just a few thousand years old would not have had time to collapse upon itself. Of course, with a very young universe we could not see light from stars that take billions of years to get here unless the transit speed of light were much higher. One possibility is that the average transit speed of light increment (above 186,000 miles per second) is proportional to its light source distance from the solar system divided by the age of the universe. This decaying super-light speed always arrives in the solar system at 186,000 miles per second regardless of its source distance. This possibility is referred to as the Hyperbolic Creation Model (HCM). 6) It is interesting to consider Supernova 1987 with its distance of 170,000 light-years, which was observed exploding in 1987. When did it actually explode? With light speed constant at 186,000 miles per second one would say 170,000 years earlier than 1987. However, using the HCM with a universe age of 6000 years, the explosion would have taken place 5783 years before 1987, just 204 years after creation. Further, the actual duration time of the explosion would have lasted only seven per cent of the time observed on earth. 7) What about a galaxy that is 12 billion light-years distance from the earth? Are we really seeing it as it was 12 billion years ago? Once again, using the HCM with a universe age of 6000 years, we would be seeing this galaxy as it was just 24 hours after creation, 6000 years ago. Further, its actual spin rate would have been a million times faster than the relatively slow spin rate that we now observe from earth. If it could have been seen on site it would have looked like a whirling fireworks display. TOP OF PAGE
The sun-tide produced by a planet may be understood if one imagines the sun being divided into two halves, connected by a powerful spring trying to hold the two halves together. From Newton's law of gravity, the half closest to the planet is pulled more strongly toward the planet than is the farthest half. This force differential causes the two halves to separate, limited by the powerful spring, but elongating the sun with a tidal bulge that has the closest half oriented in the direction of the planet. This orientation is maintained in spite of the fact that the sun rotates once a month on its own axis. If the planet's orbit were a perfect circle around the sun then this force differential would be constant, with no change in the radial distance due to tidal effects. However, with an elliptical orbit this force differential cycles with the planet's period. At aphelion, when the planet is farthest from the sun, the force differential between halves is at its lowest value, resulting in a positive incremental change (+KRF) in the orbital radius (R). Similarly, at perihelion, when the planet is closest to the sun, the force differential between halves is at its highest value, resulting in a negative incremental change (-KRF) in the orbital radius (R). The NTE sun-tide amplitude is proportional to a planet's orbital eccentricity, as given in equation (1). The constant (14,808) was derived from Mercury, which has an eccentricity of 0.20563, with a resulting sun-tide amplitude of 3045 feet (KRF). As will be shown later, this sun-tide amplitude (3045 feet) produces an incremental change in Mercury's orbital precession of 43 arc seconds per century, the same as that calculated from general relativity. TOP OF PAGE NOMINAL TIDAL EFFECTS EQUATIONS
The cyclical change in the orbital radius distance is in phase (resonant) with a planet's orbital period, as may be noted in the equations. It might have taken several years for this resonant tidal amplitude to be established. How can one say that this tidal effect is happening on the sun? Because the earth-moon tidal interaction is similar. We always see the same side of the moon because its orbital period (27.3217 days) is the same as its rotation rate. The tidal elongation of the moon is maintained and aligned with the earth, because the near side has a stronger force acting on it than does the far side, keeping it pointed toward the earth. The moon causes an oceanic bulge on the earth which is aligned with the moon. As the earth rotates, two tides a day result. A less well-known earth-tide also is aligned with the moon, which has an amplitude of about two to three feet due to the elasticity of the earth. Sun-tides would be expected to be much larger than earth-tides, because of the sun's lower density (1.4 compared to earth's 5.52), and the sun being primarily gaseous. Every atom of the sun-Mercury system would gravitationally interact with every other atom, according to Newton's law. In addition, complex elastic forces are involved. Therefore, any tidal effect analysis can only approximate the actual tidal amplitude. However, if one assumes that the orbital precession increment for Mercury (43 arc seconds per century) is due entirely to sun-tide effects, (rather than GR), then a tidal amplitude may be determined. This calculation involves use of a numerical integration simulation of Mercury and the sun, (plamd-2.bas), which is described in the Appendix of this paper. The calculation results in a sun-tide amplitude of about 0.6 miles (KRF = 3045 feet) due to Mercury's gravitational pull on the sun. This is less than one millionth of the sun's diameter (862,000 miles). Dividing 3045 by Mercury's eccentricity (0.20563) results in a sun-tide amplitude of 14,808 times a planet's eccentricity. (see NTE equations). TOP OF PAGE
PRECESSION CALCULATIONS FOR GR Calculated precessions for general relativity were accomplished using the equation below which was adapted from Tauber[5]. This equation results in the same predictions as Taylor[7,8] obtains for the binary pulsar PSR1913+16. GENERAL RELATIVITY PRECESSION EQUATION
For comparison purposes the nominal eccentricity of Mercury (0.20563) was varied, computing corresponding orbital precessions for both GR and NTE. The comparison indicated a remarkable similarity between GR and NTE, even as the eccentricity approached zero, (41.5 arc seconds per century for both GR and NTE). Of course, at zero eccentricity the orbit is circular with no definable perihelion longitude. With an eccentricity of 0.6, the orbital precession for NTE is 60 arc seconds per century as compared with 63 for GR. TOP OF PAGE
NTE does not include the mass contributions of the minor orbiting component, which is defined in this section for the five closest planets. First the spring rate for the sun is calculated to be 4.1133D+15 lb. per ft., based on the 3045 ft. amplitude for Mercury's sun-tide. The procedure for this calculation is outlined in the Appendix (tidal-2.bas). Using this derived spring rate for the sun the theoretical sun-tide amplitudes for Venus, Earth, Mars and Jupiter were calculated (tidal-2.bas). Next, the orbital precessions for TTE and NTE were calculated (plamd-2.bas). These results are compared with GR in the accompanying TABLE A. TOP OF PAGE TABLE
A
The comparison indicates that NTE precessions duplicate the GR precessions for these five planets. The theoretical tidal precession for the earth also agrees with GR precession (3.89 and 3.54 arc seconds per century). For Venus, the TTE precession is 17.09 compared to 8.78 for NTE. The orbit of Venus is nearly circular, (eccentricity = 0.00678), which makes its perihelion longitude difficult to determine from observations. For example, Mercury's eccentricity is thirty times greater than for Venus. Added to this is the complexity of extracting the excess precession from observed precessions, which include the gravitational interactions of the other planets. The theoretical sun-tide amplitude for Mars is just 39 feet, as compared to the NTE value of 1383 feet. This results in an orbital precession of 0.04 for TTE as compared to 1.37 for NTE. Jupiter has 0.06 for NTE and 0.12 for TTE. All of these differences are expected to be within the accuracy of observed measurements. NTE calculations were also made for the moon, an asteroid Toutatis, Jupiter's four Galilean moons, Saturn's Titan, and the five major moons of Uranus. These calculations duplicate GR precessions. One might think that NTE is just another way of describing GR, until it is realized that GR fails the test for two binary stars, DI Herculis and AS Camelopardalis[4]. NTE duplicates the measured orbital precessions of these two binary stars, as will be shown in the next section. TOP OF PAGE
The measured orbital precessions for the binary stars DI Herculis and AS Camelopardalis are respectively 1.05 and 15.0 degrees per century. These observations cover a time span of about 18 years by Dr. Edward Guinan[4]. Using NTE the precessions are respectively 1.19 and 15.4, close to the measured values. GR predicts precessions of 2.35 and 26.8 degrees per century, about double the measured precessions. It should be noted that the article[4] quotes GR's contribution for AS Camelopardalis as 8.5 rather than 26.8 degrees per century calculated in this paper using the GR equation above. I believe that the latter 26.8 degrees per century is the correct value. The eccentricities for the two binaries are respectively 0.489 and 0.150, as personally reported by Guinan. TABLE B presents comparative data for three binary stars and a nominal and optional mass combination for PSR1913+16. TOP OF PAGE TABLE
B Binary Stars
Binary Pulsar PSR1913+16
The same article states, "MIT physicist Sean Carroll, who has worked with Guinan on DI Her, has tried without success to modify general relativity so it is consistent with DI Her and the many situations in which general relativity works."[4]. Another physicist, John Moffat of the University of Toronto, is reported to have come up with a modified version of GR[4]. However, it does not appear to be practical to change GR as defined by Einstein. Joseph Taylor and Russell Hulse, having studied the binary pulsar PSR1913+16, have determined that the pulsar's apsidal motion (423 degrees per century) "...fits in beautifully with general relativity."[4] They have interpreted the pulsar's orbit in terms of GR, excluding tidal effects by assuming that it is made up of two neutron stars, having extremely high densities, so great that Newtonian tidal effects are not possible, which would "muddle" the apsidal motion. For this reason Taylor considers the binary pulsar to be a much stronger test of general relativity than DI Her; saying, "My suspicion is that for reasons none of us have thought of, something else is causing this discrepancy. It would be very hard for me to conclude on the basis of DI Her alone that the place you should be looking for fault is in the fundamental gravity itself."[4] Of course, for Taylor, GR is an integral part of "fundamental gravity". It may be noted from TABLE B that for PSR1913+16 there is a nominal interpretation (conforming to GR), and an optional interpretation (conforming to NTE). For nominal solar masses of 1.4/1.4 the 422 degrees per century orbital precession is matched with GR, (408 is approximately equal to 422). Using GR the 408 number increases to 422 using an eccentricity of 0.6171308 reported by Kleppner[10], rather than 0.6 used in this paper. NTE calculates a precession of 189 degrees per century. For solar masses of 4.17/2.5 the 422 degrees per century is matched with NTE, while GR now calculates 727 degrees per century. The two pulsar component orbits are identical in size for either mass combination. However, the mean orbital radius for the 4.17/2.5 combination is 1.335 times the 1.4/1.4 combination, which when squared in the GR equation results in the increased GR precession calculation from 408 to 727 degrees per century. The nominal tidal amplitude is increased from 12,438 feet to 37,050 feet, resulting in an orbital precession increase from 189 to 422 degrees per century. With mean specific densities of 11.34 or higher for either mass combination, physical contact at periastron is avoided. Lead has a specific density of 11.34. Periastron is the closest approach of the two orbiting bodies to each other. Higher densities provide greater clearance at periastron. The pulsar signal (16.94 beeps per second) may be the spin rate of the inner core of the pulsating component, rather than demanding that the entire component be a neutron star spinning at 16.94 cycles per second. However, if the pulsating component with the solar mass of 4.17 is a very high density neutron star (diameter 13.6 miles), then the 2.5 solar mass hidden component could have a calculated diameter of 1.3 million miles. The mean specific density for the hidden component would be just 1.073, being primarily gas. At periastron, with the pulsar traveling at 726 miles per second relative to the hidden component, its spin rate of 16.94 revolutions per second would be maintained as it makes gentle contact with the hidden companion's surface. According to the Cambridge Atlas of Astronomy[12], a photograph obtained by J. A. Tyson at Kitt Peak has been suggested by some researchers as possibly being the companion of PSR1913+16. For either mass combination the hidden component would not block the pulsating signal, because the orbital plane is tilted 45 degrees as viewed from the earth[8]. The decrease in the pulsar's orbital period is reported to be 0.076 seconds per year[12]. However, the decrease is probably closer to 0.4 seconds per year, based on a linear slope of data presented by Weisberg[8]. This decrease has been explained as due to energy being carried away by gravitational waves, a by-product of Einstein's general theory of relativity[8]. However, either decrease in period may also be calculated due to a speed of gravity which is respectively 17 and 3 million times the speed of light. This calculation utilizes the numerical integration simulation in the Appendix (plamd-2.bas). The simulation is analogous to connecting the two orbiting bodies with a hydraulic strut (linear damping), which tends to circularize the orbit with a decreasing period, mean radius, eccentricity, and a loss of orbital energy. Energy would be radiated in the form of heat. TOP OF PAGE
Sir Arthur Eddington[6] in keeping with general relativity states, "...gravitation is propagated with the speed of light, and there is no discordance with observation". His argument is valid for circular orbits but makes no allowance for a changing radius with an eccentric orbit. For a speed of gravity equal to the speed of light there can be a very significant lag in the R distance in Newton's equation. Using the earth-sun as an example, with a speed of gravity equal to the speed of light, the decrease in the earth's orbital period would be 15 seconds per year, with a corresponding decrease in its mean distance from the sun of 30 miles per year. These large changes are not supported by observations. Again using the earth-sun simulation, with a speed of gravity three million times the speed of light, the earth's distance from the sun would decrease about 0.6 inches per year, which is about 1.6 centimeters per year. It is interesting to note that laser measurements from reflectors on the moon, (placed there by astronauts), result in an increase in the moon's distance from the earth of about four centimeters per year. Perhaps the earth's orbit is shrinking, pulling away from the moon, rather than the moon's orbit expanding. The increasing separation may be due to a speed of gravity several million times the speed of light. The earth's primary attractor is the sun and the moon's primary attractor is the much closer earth. TOP OF PAGE
The HCM cosmogony mentioned in the Summary is defined below. Although the rate of decay of the assumed transit super-speed light is not defined, it always arrives in the solar system at 186,000 miles per second, which is the same as one light-year per year. HYPERBOLIC CREATION MODEL EQUATIONS
Interesting Newtonian time dilation effects due to this decaying super-speed light were noted in the Summary with regard to Supernova 1987 and a galaxy 12 billion light-years distance from earth. The time dilation equations are presented below. TIME DILATION USING HCM EQUATIONS
HCM time dilation effects may also be involved with PSR1913+16. With the pulsar's distance of 15,000 light-years, the time interval between observed pulses on earth may be greater than the actual interval at the pulsar. This would result in computing an orbit for PSR1913+16 which is not the same as the actual orbit[14]. For example, using the HCM with a universe age of 6000 years and the 4.17/2.5 mass combination, the beep rate would actually be 34.67 beeps per second, rather than the measured 16.94. On site orbital precession would be 866 rather than 423 degrees per century. NTE would match the 866 value, but GR would now compute 1488 rather than 727 degrees per century, still the same discrepancy ratio. TOP OF PAGE
The results of this investigation indicate that NTE provides a better overall correlation with measured orbital precession than does GR. More measured data is desirable. Io (one of Jupiter's satellites) with its excess precession of about 270 arc seconds per century would appear to be a likely candidate. However, its gravitational interaction precession resulting from the other three major satellites is about 200 degrees per century[2]. This is 2700 times the NTE or GR precession increment, making this extraction unreliable. RW Tauri (a well-known binary star) might be another candidate for measurement with its predicted precession of 7 to 9 degrees per century, which is about ten times that of DI Herculis. TOP OF PAGE
General relativity can hardly be relied upon to predict the characteristics of the entire universe, if it can only predict orbital precession increments in the solar system, and then fails the test for binary stars. The proofs for general relativity have always been subject to controversy, searching for proof in the noise level of data. It appears that we should go back to square one with Newton; that is, Euclidean space and time for the entire universe. Nominal Tidal Effects (NTE) combined with the Hyperbolic Creation Model (HCM) described in this paper offer a reasonable alternative to a universe cosmogony which is explained using general relativity (GR). The HCM cosmogony is heliocentric (sun-centered), as also is the well-known background Red Shift. The cause of the Red Shift frequencies could be a decaying transit super-speed of light. Finally, the possibility that the age of the universe is just a few thousand years has been demonstrated. TOP OF PAGE
QUICKBASIC PROGRAMS TIDAL-3.bas Calculates earth tidal amplitude (ft.) resulting from the moon's gravitational pull, using a specified elastic spring rate of the solid earth (lb./ft.), diameter of the earth (ft.), mass of the earth (lb.), mass of the moon (lb.), mean separation distance (AU), and the moon's orbital eccentricity around the earth. Assumes that the earth is divided into two equal halves, separated by D/2, and held together by a powerful spring. The force differential between halves (lb.) is calculated first at apogee radius (greatest earth-moon separation, ft.), and then at perigee (closest earth-moon separation, ft.). The difference between these two differential forces is then divided by two times the elastic spring rate to get the earth tidal amplitude (ft.). Varying the specified spring rate to satisfy the desired earth tidal amplitude (0.3 ft.) was accomplished to calculate an earth spring rate of -2.024D+17 (lb./ft.). Decimal point is 17 places to the right. TIDAL-2.bas Calculates sun-tide amplitude resulting from a planet's gravitational pull on the sun, in the same way as TIDAL-3.bas was done for the earth (above). The spring rate for the sun is -4.1133D+15 (lb./ft.) for all planets. A sun-tide amplitude of 3045 ft. results from Mercury's gravitational pull on the sun, (using this spring rate), and causes an incremental change in Mercury's orbital precession of 43 arc seconds per century, calculated using the PLAMD-2.bas program. The theoretical sun-tide amplitudes for five planets are presented in TABLE A. Based on these tidal amplitudes, the orbital precessions were then calculated using PLAMD-2.bas program, which are also presented in TABLE A. PLAMD-2.bas This program is a two-body numerical integration simulation using double precision for calculating longitudinal orbital precession of the periapse, (the closest approach of the two orbiting bodies). Specified constants are the major component mass (WE, lb.), the minor component mass (WM, lb.), the orbital eccentricity, the orbital period (DAYORBM), and the tidal amplitude (KRF, ft.). The initial conditions for the simulation are established at apoapse, balancing the two components to orbit about their common center of mass, using Kepler's area law (equal areas swept out in equal times). An incremental adjustment is made in the initial tangential velocity to ascertain that the orbital period and eccentricity are closely matched to nine decimal places during the integration process, with the tidal amplitude (KRF) set equal to zero. A time increment about 0.0001 (or less) times the orbital period is recommended. A baseline run of 100 orbits is made (KRF = 0), with periapse longitudes calculated for each orbit cycle. This determination is accomplished by reducing the time increment to 1000th of its nominal value as periapse is approached and crossed for the reading. Then the time increment is returned to its nominal value. Averages for 20 orbits are printed out for day, periapse longitude, and eccentricity. Five blocks are printed for a total of 100 orbits. After completing the baseline run, the baseline orbital precession is determined by taking the difference in the perihelion longitude from block one and five, then dividing by the day difference from block one and five. A second run of 100 orbits is made after changing (KRF = 0) to the desired tidal effect amplitude (KRF). The orbital precession for the second run may then be determined in the same way as was for the baseline run. Subtracting the baseline precession from the second run precession gives the actual precession. The orbital precession is very linear with KRF, so that any other precession (for the same initial conditions) may be determined by the KRF ratio times the calculated precession. TOP OF PAGE
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