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The radius of a spiral galaxy is usually 5☓104 light years. The stars, planets and other mass are orbiting around the center of the galaxy. If the speed of gravity was equal to the speed of light, the star at the distance of 5☓104 light years from the center only could orbit the center at the time of 5☓104 years ago. It should result in that a galaxy is not in the form of a disc. Usually, a galaxy is older than 1☓1010 years. In this time, a galaxy should become a strip longer than 5☓106 light years. It is contradicted with observation.

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... Because all stars/stellar are orbiting around the center of the galaxy [10,17], just as the planets are orbiting around the Sun. And, only the Newtonian theory of orbit perturbation is valid to understand the celestial orbit [10,16]. Therefore, the orbit of a star around the center in a galaxy only can be described with the Newtonian theory of orbit perturbation: ...

The new observations, including both the fastest star and the circular velocity curve of the Milky Way, should imply that the mass of the center of the Milky Way is almost 1011 times the mass of the Sun.

... It is noted that, in the Newtonian theory of gravity, besides the center of the galaxy, other stars also have actions on the orbit. Because all stars are orbiting around the center of the galaxy, [21,28] just as the planets are orbiting around the Sun, and, only the Newtonian theory of orbit perturbation is valid to understand the celestial orbit, [21,29] the orbit of a star around the center in a galaxy only can be described with the Newtonian theory of orbit perturbation: ...

The new observations, including the fastest star, the circular velocity curve of the Milky Way and the fast galaxy bar, should imply that the mass of the center of the Milky Way is almost 10 11 ⨀.

... Third, it was observed that the speed of gravity is much larger than the speed of light. [24][25][26] And, the negative speed of light and the fast light are measured. ...

In any region of a space, the gravitational field cannot be eliminated. The speed of light in a vacuum has never been observed and cannot be observed with current technology. Till now, only the speed of light in a gravitational field has been observed. Here, it is presented that light could be dispersion in a gravitational field analogous to the dispersion of light in the Newtonian prism experiment. The relativistic mass density on the surface of a neutron star is on the level of 10 17 kg −3 while on the surface of the Earth is only 6.63 × 10 −7 kg −3 , the speed of light acted by the gravitational field of the neutron star is much larger than that by the Earth. Therefore, light dispersion in strong gravitational field could be observed from the picture of a star and it may be observed through the double gravitational lens and the spectroscopic binary system.

... [3][4][5] But, the conclusion is questioned. 6 Here, the difference of the gravitational forces of the Sun acting on a geosynchronous satellite between present and retarded positions of the Sun is observed. It is shown that the force perturbing the orbit of this satellite is from the present position of the Sun. ...

This is the second version. Here, the speed of gravitational force is defined. And, the speed of gravity related the gravitational wave detected by LIGO is discussed.

We present a determination of the cosmic microwave background dipole
amplitude and direction from the COBE Differential Microwave Radiometers
(DMR) first year of data. Data from the six DMR channels are consistent
with a Doppler-shifted Planck function of dipole amplitude ΔT =
3.365±0.027 mK toward direction (lII, bII)
= (264°.4±0°.3, 48°.4±0°.5). The implied
velocity of the Local Group with respect to the CMB rest frame is
υLG = 627±22 km s-1 toward
(lII, bII) = (276°±3°,
30°±3°). DMR has also mapped the dipole anisotropy
resulting from the Earth's orbital motion about the Solar system
barycenter, yielding a measurement of the monopole CMB temperature
T0 at 31.5, 53, and 90 GHz, T0 = 2.75±0.05
K.

We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.

The book contains almost 500 problems and solutions in the fields of
special relativity, general relativity, gravitation, relativistic
astrophysics, and cosmology. Emphasis is placed on computable results,
predictions, and models for material phenomena in the real universe. The
problems deal with special-relativistic kinematics, dynamics, coordinate
transformations, invariants, and tensors; relativistic electromagnetic
theory; basic concepts of relativistic thermodynamics and hydrodynamics;
metric geometry; covariant differentiation and geodesic curves; and the
study of curvature on the basis of the Riemann tensor. Other topics
investigated include Killing vectors and symmetries; angular momentum in
general relativity; physical consequences of gravitational interactions;
the Einstein field equations; physical processes in curved spacetime;
the Schwarzschild geometry; spherical symmetry and relativistic stellar
structure; black holes; gravitational radiation; cosmological models;
and experimental tests of general relativity.

The observed absence of gravitational aberration requires that `Newtonian' gravity propagate at a speed cg>2×1010c. By evaluating the gravitational effect of an accelerating mass, I show that aberration in general relativity is almost exactly canceled by velocity-dependent interactions, permitting cg=c. This cancellation is dictated by conservation laws and the quadrupole nature of gravitational radiation.

I present the theory and analysis behind the experiment by Fomalont and Kopeikin involving Jupiter and quasar J0842+1845 that purported to measure the speed of gravity. The computation of the v_J/c correction to the gravitational time delay difference relevant to the experiment is derived, where v_J is the speed of Jupiter as measured from Earth. Since the v_J/c corrections are too small to have been measured in the Jupiter/quasar experiment, it is impossible that the speed of gravity was extracted from the data, and I explain what when wrong with the data analysis. Finally, mistakes are shown in papers by Fomalont and Kopeikin intended to rebut my work and the work of others. Comment: LaTeX (or Latex, etc), two figures, which are also available at http://www-theory.lbl.gov/~samuel/figure1.pdf and http://www-theory.lbl.gov/~samuel/figure2.pdf

On the Speed of Gravity and the Jupiter/Quasar Measurement

- S Samuuel

Samuuel S., On the Speed of Gravity and the Jupiter/Quasar Measurement, Int. J. Mod. Phys. D 13, 1753
(2004)