Eight minutes, an ordinary topic

Jun 2016
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Logically the situation is the same,
however practically the differences in scale of the Earth and the Sun are so huge,
that almost anything the Earth does will produce little noticeable effect on the Sun.

P.S. I'm sorry to disappoint you with my lack of astronomical evidence,
but you are as likely to see it in your Scientific American magazine
as I am in my personal magazine of choice (New Scientist).

The gravity wave detectors will perhaps show evidence of this effect,
however, their data is probably too new (and too noisy) to really show it clearly (yet).
 
Oct 2017
577
297
Glasgow
Consider a small asteroid orbiting the Sun
The Sun burps out a huge mass ejection, at an angle to the orbit of the asteroid,
The change in the distribution of mass will alter the orbit of the asteroid.
However the orbit of the asteroid will not start to change until the "information" about the change in the distribution of mass reaches it."
............
Did any astronomical observation prove this?
Yes, but not by observing the system you describe. Instead, the speed of gravity is confirmed via different means.

From wikipedia article on "Speed of gravity":

Measurements[edit]
The speed of gravity (more correctly, the speed of gravitational waves) can be calculated from observations of the orbital decay rate of binary pulsars PSR 1913+16 (the Hulse–Taylor binary system noted above) and PSR B1534+12. The orbits of these binary pulsars are decaying due to loss of energy in the form of gravitational radiation. The rate of this energy loss ("gravitational damping") can be measured, and since it depends on the speed of gravity, comparing the measured values to theory shows that the speed of gravity is equal to the speed of light to within 1%.[20] However, according to PPN formalism setting, measuring the speed of gravity by comparing theoretical results with experimental results will depend on the theory; use of a theory other than that of general relativity could in principle show a different speed, although the existence of gravitational damping at all implies that the speed cannot be infinite.[citation needed]

In September 2002, Sergei Kopeikin and Edward Fomalont announced that they had measured the speed of gravity indirectly, using their data from VLBI measurement of the retarded position of Jupiter on its orbit during Jupiter's transit across the line-of-sight of the bright radio source quasar QSO J0842+1835. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.[21]

Several physicists, including Clifford M. Will and Steve Carlip, have criticized these claims on the grounds that they have allegedly misinterpreted the results of their measurements. Notably, prior to the actual transit, Hideki Asada in a paper to the Astrophysical Journal Letters theorized that the proposed experiment was essentially a roundabout confirmation of the speed of light instead of the speed of gravity.[22] However, Kopeikin and Fomalont continue to vigorously argue their case and the means of presenting their result at the press conference of the American Astronomical Society (AAS) that was offered after the results of the Jovian experiment had been peer-reviewed by the experts of the AAS scientific organizing committee. In a later publication by Kopeikin and Fomalont, which uses a bi-metric formalism that splits the space-time null cone in two — one for gravity and another one for light —, the authors claimed that Asada's claim was theoretically unsound.[23] The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded potentials, which was worked out by Kopeikin and co-authors[24][25] but was never properly employed by Asada and/or the other critics.

Stuart Samuel also suggested that the experiment did not actually measure the speed of gravity because the effects were too small to have been measured.[26] A response by Kopeikin and Fomalont challenges this opinion.[27]

It is important to understand that none of the participants in this controversy are claiming that general relativity is "wrong". Rather, the debate concerns whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions. A comprehensive review of the definition of the speed of gravity and its measurement with high-precision astrometric and other techniques appears in the textbook Relativistic Celestial Mechanics in the Solar System.[28]

The detection of the neutron star inspiral GW170817 in 2017, detected through both gravitational waves and gamma rays, currently provides by far the best limit on the difference between the speed of light and that of gravity. Photons were detected 1.7 seconds after peak gravitational wave emission; assuming a delay of zero to ten seconds, the difference between the speeds of gravitational and electromagnetic waves, vGW − vEM, is constrained to between −3×10−15 and +7×10−16 times the speed of light.[29]

This also excluded some alternatives to general relativity, including variants of scalar–tensor theory,[30][31][32][33] instances of Horndeski's theory,[34] and Hořava–Lifshitz gravity.[35][36][37]
 
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Mar 2019
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"The speed of gravity (more correctly, the speed of gravitational waves)..."
..............................................
What's the difference between gravity and gravitational wave?
I think the "information" Woody mentioned is gravitational wave?
 
Oct 2017
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297
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Gravity is the name for the phenomenon.
Gravity can be described/modelled in different ways.
Gravitational waves are a specific way of modelling gravity. Remember that Newton's treatment of gravity assumes it to be an instantaneous force (i.e. the force transmits at infinite speed).
 
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Mar 2019
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Woody's LEANING TOWER EXPERIMENT:
I imagine a vivid analogy for Woody's scinario. I don't know if it is appropriate. Sorry.
Assume Woody is standing on top of the Pisa leaning tower. He holds a string with an iron ball fixed on the other end. He shakes the string and a mechanic wave occurs on the string.
The tension of the string/or say the dragging force is the alternative of gravity;
The mechanic wave on the string is the alternative of gravitational wave;
The iron ball is the alternative of the asteroid;
The iron ball falls is the alternative of orbit changes of the asteroid.
Before the mechanic wave reaches the iron ball, Woody cuts the string on the end he holds, the iron ball will not fall immediately?
 

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Jun 2016
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Instead of a string, imagine a rubber "bungee" chord (or perhaps a spring).
Now as I let go of the end, the stretch of the chord will mean that the "information" due to me releasing the chord will take some time to reach the ball.
 
Oct 2017
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Before the mechanic wave reaches the iron ball, Woody cuts the string on the end he holds, the iron ball will not fall immediately?
Yes, but that's because the Earth, which is the source of the gravitational force, is continuously applying that force all of the time. So, the moment you cut the string, the object falls.

Let's imagine a thought experiment where you have the same setup, but with some magic switch that allows you to turn gravity on or off. Then, with the following steps:

1. Set-up Woody standing at the top of a tower dangling an iron ball from a string. The iron ball is stationary.
2. Turn gravity off. The iron ball would still be stationary because the tension in the wire would become 0 and the gravitational forces are 0.
3. Gently cut the cord. The ball would still not move because there's no gravity acting on it.
4. Turn gravity on and start a timer. Measure the trajectory of the ball as a function of time
5. Keep the experiment running until the ball hits the ground.

In Newton's theory of gravity, the ball would start moving immediately as soon as the timer is started. In other theories of gravity (GR or gravitational waves), there would instead be a very, very short delay between the ball moving and the timer being started because the gravitational force has to transmit at a finite speed (the speed of light).

This thought experiment can be made into a real experiment if you instead use the electric force and a man-made source of electric field, such as a capacitor or van der Graaf generator, but then you're making conclusions about the electric force instead...
 
Mar 2019
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"..Now as I let go of the end, the stretch of the chord will mean that the "information" due to me releasing the chord will take some time to reach the ball.."
@Woody:
The speed of the "information" in Woody's leaning tower case should be the propagation speed of the mechanic wave on the string/Bungee chord?
 
Jun 2016
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The speed of the "information" in Woody's leaning tower case should be the propagation speed of the mechanic wave on the string/Bungee chord?
That was the way I was thinking...
 
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Mar 2019
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Actually, this tramp in cosmos appreciates Woody's existence - interaction principle very much.
In Woody's scinario, we can consider the "jet" and the remaining part of the sun are difference existence. The existence of the remaining part of the sun and the existence of the asteroid are there in cosmos long long ago. So, the interaction between the remaining part of the sun and the asteroid are there in cosmos long long ago. It should be some kind of "information". As soon as the "jet" emitted, this interaction demonstrates itself immediately.