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 Gravitational Physics
Is gravitational physics and GR for totally real, for sure or not???
§ 24. Gravitation
Newton's gravity equation is represented as
F = (G m1 m2)/r2 .................................................. .................................................. ................................................67
Cavendish's experiment is used to justify Newton's gravity equation by measuring the value of Newton's constant G. Cavendish's experiment apparatus uses two lead spheres m1 = 158 kg and m2 = .73 kg separated by the distance of .23 m that forms a force of 1.74 x 10−7 N (≃ 2μg ) which is used to derive Newton's constant G,
G = F r2 / (m1 m2) = [(1.74 x 10−7 N) (.23 m)2 ] / [(158 kg )(.73 kg)] = 7.8×10−11 .................................................. ...68
Cavendish detected a gravitational force of 2 μg that is 1,000 times smaller than the weight uncertainty of 1 milligrams for a 1797 counter weight balance. To test Cavendish's experiment, a 73 kg lead sphere is suspended using a thin titanium wire and place .01 mm from a larger lead sphere (158 kg). A laser is used to detect the change in the angle of the wire that is suspending the 73 kg lead sphere (fig 18). As the 158 kg lead sphere is slowly rolled away from the smaller .73 kg suspended lead sphere no measurable change in the angle of the wire is observed which contradicts Cavendish's experiment. The earth's gravitational force is used to eliminate the horizontal lead ball gravitational force but the earth's vertical gravitational force is perpendicular to the lead spheres' horizontal gravitational force which depicts perpendicular gravitational forces that do not cancel. Newton's gravity equation is applied to an astronaut with a mass of 50 kg in the space station that is 249 miles (400,727 m) from the surface of the earth. The distance r which represents the distance from the center of the earth to the space station is,
r = (earth's radius) + (height) = (6.371 x 106 m) + (.4 x 106 m) = 6.771 x 106 m................................................. .............69
Using the distance for r (equ 70) in Newton's gravity equation forms,
F = (G m1 m2)/r2 = (6.7 × 1011) x (50kg) x (6 x 1024kg) / (6.771 x 106m)2 ≃ 438.4 N or 44.7 kg ....................................70
According to Newton's gravity equation, a 50 kg astronaut in the space station forms a 44.7 kg gravitational force pointed at the earth. The centripetal force CF is used to justify the weightlessness of an astronaut in the space station is calculated,
CF = mv2/r = (50 kg)(7672 m/s)2/ (6.771 x 106 m) = 437 N or 44.56 kg................................................ ..........................................71
The gravitational and centripetal forces form an equilibrium that produces the massless astronaut yet when a force is applied to an astronaut outside the space space and the astronaut propagates at a velocity of 50 mph in the direction opposite to the angular velocity, the described astronaut does not propagate towards the earth which proves the gravitational and centripetal forces do not function for a 50 kg astronaut propagating around the earth. Also, all of the space stations are orbiting the earth at approximately 250 miles above the surface of the earth. The 450 ton space station cannot orbit the earth at a height of 1000 miles above the surface of the earth which proves the gravitational and centripetal forces do not function for the space station at the height of 1000 miles. In addition, the centripetal force for a 50 kg mass on the surface of the earth propagating around the Sun is calculated,
CF = (50kg)(30,462m/s)2 / (695,700,000 m) = 67 N. or 6.8 kg................................................ .................................................. ........72
At 12:00 am (midnight), the centripetal force produced by the 50 kg mass on the surface of the earth propagating around the Sun is 6.8 kg pointed away from the earth which represents the decrease in the weight of the 50 kg mass yet at 12:00 am (noon) a 6.4 kg ( v = 29,648 m/s) the centripetal force would be pointing in the direction of the earth that would represent a 13.2 kg weight variation every 24 hours which are not experimentally observe and proves the centripetal force does not function for a 50 kg mass on the surface of the earth propagating around the Sun.
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In Einstein's paper, "The Foundation of the Generalised Theory of Relativity" (1916), Einstein represents gravity with Maxwell's equations.
dh/dt + rot e = 0...............................................73
div h = 0................................................. ..........74
rot h  de'/dt = i................................................7 5
div e' = p"................................................ ........76
(Einstein5, § 20). Einstein is representing gravity with Maxwell's equations that are derived using Faraday's induction effect but a small stone that is affected by gravity is unaffected by a magnet which proves gravity is not an electromagnetic phenomenon.
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Weber experimentally detected electromagnetic gravitational waves that have the frequency of sound (1662 Hz).
"Gravitational Waves........In 1916, Einstein (1) studied the weakfield solutions of the field equations" (Weber1, p. 87).
"A description is given of the gravitational radiation experiments involving detectors at opposite ends of a 1000 kilometer baseline, at Argonne National Laboratory and the University of Maryland. Sudden increases in detector output are observed roughly once in several days, coincident within the resolution time of 0.25 seconds. The statistics rule out an accidental origin and experiments rule out seismic and electromagnetic effects. It is reasonable to conclude that gravitational radiation is being observed." (Weber2, Abstract).
"EXPERIMENTS AT 1662 HERTZ" (Weber2, Intro).
Garwin and Douglas discredited Weber's experiment results.
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Gravitational physics is based an an electromagnetic analogy.
"Although in some sense the preceding arguments may be regarded as a derivation of Maxwell's equations, the limitations of this approach should be kept in mind. Clearly, we have had to make quite a few assumptions to reach Eq. [14]. The objective of our game with electrodynamics was to obtain a prescription for finding the field equations in the hope that an analogous prescription will lead us to the filed equation for gravitation." (Ohanian, p. 135).
"§35.11. CONPARISON OF AN EXACT ELECTROMAGNETIC PLANE WAVE WITH THE GRAVITATIONAL PLANE WAVE." (Misner, Thorne, Wheeler, p. 961).
"It represents an electromagnetic plane wave analogous to the gravitational plane wave of the last few sections." (Misner, Thorne, Wheeler, p. 961).
An analogy is a comparison yet gravitational wave have not been experimentally detected which begins into question if the electromagnetic analogy cannot be applied.
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Thorne, Gertsenshtein and Ohanian describes gravitational waves using an electromagnetic analogy.
"9.2 The physical and mathematical description of a gravitational wave" by Thorne. (Hawking, p. 338).
"General relativistic gravitational waves are ripples in the curvature of space time that propagates with the speed of light." by Thorne (Hawking, p. 338).
"Because gravitational and electromagnetic waves should propagate with the same speed, they can interact in a coherent way (Gertsenshtein, 1962)." by Thorne (Hawking, p. 361).
"Gravitational effects cannot propagate with infinite speed. This is obvious both from the lack of Lorentz invariance of infinite speed and from the causality violations that are associated with signal speeds in excess of the speed of light. Since the speed of light is the only Lorentzinvariant speed, we expect that gravitational effects propagate in the form of waves at the speed of light." (Ohanian, p. 241).
According to Thorne, Gertsenshtein, and Ohanian gravitational waves propagate at the velocity of light based on a electromagnetic analogy but gravitational waves have not been experimentally observed.
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Gravitational physics uses the gauge transformation of Maxwell's equations.
"The gauge transformation [3.49] for huv implies the gauge transformation" (Ohanian, p. 244).
"Associated with an electromagnetic disturbance is a mass, the gravitational attraction of which under appropriate circumstances is capable of holding the disturbance together for a time long in comparison with the characteristic periods of the system. Such gravitationalelectromagnetic entities, or "geons"; are analyzed via classical relativity theory." (Wheeler, Abstract).
"In electrodynamics, 21 the wave equation describing electromagnetic waves in vacuum is, in the Lorentz gauge....................Similarly, in general relativity, in the weak field limit, the wave equation describing gravitational waves in vacuum is equation (2.10.11)...........A similar analogy is valid for the gravitomagnetic field. 9 In electrodynamics, 21 from the Maxwell equations (2.8.43) and (2.8.44) and in particular from magnetic monopoles, ∇ · B = 0, one can write B = ∇ x A, where A is the vector potential. From Ampere's law for a stationary current distribution: ∇ x B = (4π/c)j, where j is the current density, one has then:" (Ciufolini and Wheeler, p. 317).
"TABLE 21.2 Gauge Transformations in Linearized Gravity and Electromagnetic
A > A + ∇Λ........................Φ > Φ  dΛ/dt".......................77a,b
(Hartle, p. 462). The gauge transformation is based on Maxwell's equations that are derived using Faraday's induction effect but gravitational waves have not been experimentally observed.
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"TABLE 5.1 FREQUENCY BANDS FOR GRAVITATIONAL WAVES
Designation....................................... .......Frequency...............................Typ ical sources
Extremely low frequency.......................107 to 104 Hz..........................Slow binaries, black hole (>108 Mo)
Very low frequency................................104 to 101 Hz.........................Fast binaries, black holes (<108 Mo), whitedwarf vibrations
Low frequency.......................................101 to 102 Hz..........................Binary pulsars, black holes (<105 Mo)
Medium frequency.................................102 to 105 Hz...........................Supernovas, pulsar vibrations
High frequency......................................105 to 108 Hz............................Manmade?
Very high frequency..............................108 to 1011 Hz..........................Blackbody, cosmological?" (Ohanian, p. 242).
"The most promising frequency band is that of medium frequency, from 102 to 105 Hz. There are several probable sources of gravitational waves in this band and, fortunately, detectors that respond to waves in this band can be built. There is little doubt that gravitational waves are incident on the Earth; the question is, can we build a detector sufficiently sensitive to feel them?" (Ohanian, p. 242).
Wheeler's gravity wave that has a frequency of 107 Hz forms a wavelength of 1015 meters that is more than a light year in length, and a gravity wave with a frequency of 104 Hz represents a wavelength of 104 m which represent a range of the gravity waves' wavelengths of 19 orders of magnitude.
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The Laser Interferometric GravitationalWave Observatory LIGO detected stellar gravitational waves that are formed by a pulsar (2009) using a laser interferometer.
"More usually, GWs distinguish themselves from electromagnetic waves by the fact that they are very weak." (LIGO, § 2).
"Figure 1 illustrates the basic concept of how a Michelson interferometer is used to measure a GW strain. The challenge is to make the instrument sufficiently sensitive: at the targeted strain sensitivity of 1021, the resulting arm length change is only ~1018 m, a thousand times smaller than the diameter of a proton." (LIGO, § 4).
The CaltechMIT Laser Interferometric GravitationalWave Observatory (LIGO) detected celestial gravitational waves produced by a pulsar using an interferometer that forms a strain of 1021 that represents the armature length contraction of 1018 which is less than the diameter of an electron.
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