## Comments about "Speed of gravity" in Wikipedia

This document contains comments about the article "Speed of gravity" in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
In classical theories of gravitation, the changes in a gravitational field propagate.

### 4. Laplace

The first attempt to combine a finite gravitational speed with Newton's theory was made by Laplace in 1805. Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or fluid.
And what is the difference between such a field or fluid as a particle field of gravitons?
This led Laplace to conclude that the speed of gravitational interactions is at least 7×106 times the speed of light.
At least Laplace concluded that gravitational interactions are not instantaneous. That is a hugh step forward. To calculate the speed based on actual observations is extremely difficult.
From a modern point of view, Laplace's analysis is incorrect. Not knowing about Lorentz' invariance of static fields,
Laplace anyway tried to find a more physical explanation.
This whole sentence is a sort of summary which does not belong here,
Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun had been if its position was retarded using the relative velocity
The retarded position is a function of the speed of the Sun, the speed of Gravity and the distance Earth-Sun
Immediate next we read:
Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth.
Why putting the Sun immobile?. It only makes sense to place the origin "at rest".
This whole discussion should start from the true or position (now) of all the objects involved.
The article should make a clear distinction between optical and retarded position and mention cg or vg for the speed of gravity.
The optical position is the delayed position of the true position based on the distance d between the object and the earth by an amount vd/c. The optical position is important to calculate the initial conditions of the true position of the objects.
The retarded position is the delayed position of the true position based on the distance d between two ojects by an amount of vd/cg. The retarded position is important as part of a simulation to calculate the future path of the objects. See also Reflection paragraph 4 "Laplace"
Next we read:
The pull of gravity would then be always displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position.
It is more accurate to write: retarded position or virtual position.
Next we read:
This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward.
And how much is a function of the speed of gravity.
Next we read:
Such an outspiral would be suppressed by an amount v/c compared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's c must be very large.
The beginning of this sentence is not clear. Again it is better to use v/cg. That number is an indication of the stability of the objects involved, how larger how more stable. The number should not be too large otherwise it can not be used to explain the trajectory of the planet Mercury.
As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence, it is instantaneous at distance, when seen by observers at constant transverse velocity. For orbits in which velocity changes slowly, it is almost infinite.
This sentence is not clear and requires a better explanation. The next sentence reads:
The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge.
Objects moving with a constant (steady) velocity in space do not exist. In reality all objects in space undergo accelerations. The concept "instantaneous position" does not exist. It is possible to define a true position, observed position and retarded position.
In a field equation consistent with special relativity (i.e., a Lorentz invariant equation), the attraction between static charges moving with constant relative velocity, is always toward the instantaneous position of the charge (in this case, the "gravitational charge" of the Sun), not the time-retarded position of the Sun.
Also in this sentence "instantaneous position" is used. I think they mean "real" or "true" position.
When an object is moving in orbit at a steady speed but changing velocity v, the effect on the orbit is order v^2/c^2, and the effect preserves energy and angular momentum, so that orbits do not decay.
The term v^2/c^2 comes from the Lorentz transformations. These transformations depend on c. The problem is that the trajectorys of the planets depend of the speed of gravity, which is physical completely different as the speed of light.

### 7.1 Background

This paragrph starts with the text:
General relativity predicts that gravitational radiation should exist and propagate as a wave at lightspeed: a slowly evolving and weak gravitational field will produce, according to general relativity, effects like those of Newtonian gravitation.
The second half of the sentence is not clear.
It should be understood that Newton's Law or Newtonian gravitation also produces a gravitational field except that the field propagates at infinite velocity.
Suddenly displacing one of two gravitoelectrically interacting particles would, after a delay corresponding to lightspeed, cause the other to feel the displaced particle's absence: accelerations due to the change in quadrupole moment of star systems, like the Hulse–Taylor binary have removed much energy (almost 2% of the energy of our own Sun's output) as gravitational waves, which would theoretically travel at the speed of light.
Sorry. This sentence is not clear.

### 7.4.1 Direct measurements of gravitational waves

The first direct observation of gravitational waves, from the merger of a pair of black holes, on 14 September 2015 allowed a more direct measurement of their speed.
It is a hugh challenge to detect gravitational waves. It is extremely difficult to measure the speed directly based on only what we observe now
The extent of any deviation of the speed of gravitational waves (vg) from the speed of light (c) can be parameterized in terms of the mass of the hypothetical graviton.
It should first be cleared if the photon has a mass. IMO it has a mass and is influenced by gravity.
The graviton is not influenced by other gravitons. The path of a graviton is straight.
If it was not massless, gravitational waves would propagate below lightspeed, with lower frequencies (ƒ) being slower than higher frequencies, leading to dispersion of the waves from the merger event.
Gravitational waves are disturbances of the gravitational fields continuous emitted by the two objects. The frequencies of the waves are a function of the rotating speeds of the two objects.

### 9. See also

Following is a list with "Comments in Wikipedia" about related subjects

### 10. External links

Following is a list of additional information:

### Reflection paragraph 4 "Laplace"

 ``` < x x o2 x m2 O m1 x o1 x x > Figure 1 ``` Consider two objects with the same mass m1 and m2 which are in a circular orbit with a speed v at a distance R from the center of gravity. This is a symmetrical situation. Figure 1 shows this the two masses m1 and m2 at the present position. The velocity of the two objects is counter clockwise. The point "O" is the center of gravity. The point o1 is the observed position of m1. That means it reflects a position in the past. The actual angle is a function of both the distance of the binary objects and the observer i.e. the earth. Secondly of the speed of light. Point o2 the observed position but for m2. When the speed of gravity is considered also the points o1 and o2 can be used, but now they are much closer to m1 and m2. The actual angle is a function first between the distance between m1 and m2 and secondly the speed of gravity.

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Created: 25 November 2016

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