Will this work? As we know, the speed of gravity is known to be equal to the speed of light. The following experiment could provide a reasonably accurate result.
Let’s say we place a satellite at the Lagrangian point L4 at t=0, see diagram. The satellite’s on-board clock is synchronised to the Earth’s clock. At t=0 the satellite would, in a gravitational sense, “see” the Earth at point P0, as gravity would take a finite time (approx 500 seconds) to reach the satellite. At t=0 the Earth would, in fact, be at point P1, or approximately 450.5 light seconds from the satellite, since the Earth would have moved to P1 500 seconds ago. If we launched a time-stamped radio signal from the satellite at t=0 towards Earth, it would take approximately 401 seconds (99 second difference) for this signal to reach Earth, since the Earth has now moved from point P1 to point P2.
The above calculations assumes the speed of gravity is equal to the speed of light. If the speed of gravity was different, there would be a different delta in the time that the pulse reaches the Earth. In the scenario where the speed of gravity is infinite, we would only measure approximately a 45 second difference, as the satellite would experience an “instant” gravitational effect (t=0 is now at P0) from the Earth and we would be measuring just the finite speed of light.
Does relativity effect the calculations? I feel it would be insignificant. Have I made some gross assumptions? Are the calculations correct? Appreciate your comments.
I was typing this up late last night. Perhaps I should have given short intro and brief explaination to why I think this setup/experiment is interesting and rephased some of my sentences.
I would much appreciate comments to my actual idea and calculations.
We know the gravitational interaction between two bodies is given by F=GMm/r^2. From this we can determine the orbital period of one body about another. Or for that matter, the orbits of two bodies about another. However, it tells us nothing about the speed of propagation of gravity.
As both the Earth and the satellite have an effective angular momentum about the Sun, you not are actually measuring the speed of gravity but their relative speeds of rotation as a result of the inverse square law used for gravity. With the satellite at the Lagrangian point, this speed is the same.
The evidence for gravity propagating at the speed of light is primarily theoretical and, as far as I know, not proven conclusively by any observational evidence.
The evidence for gravity propagating at the speed of light is primarily theoretical and, as far as I know, not proven conclusively by any observational evidence.
Regards, Rob.
Hi,
Certainly not proven conclusively, true.
Just to add a bit, I had read about the observations of a rare pair of binary pulsars, the orbits of which are decaying. By attributing this to gravitational radiation, or a drag on the orbits due to gravity, we get a speed for gravity the same as c to within 1%. But this is not conclusive yet.
For instance, critics claim that observations like this just confirm the speed of light to be the same as itself!! Rather self-evident.
Then, is the speed of gravity constant, in all circumstances?
After that, is gravity due to a particle which interacts with a field, or something more mysterious? So far we can't find the graviton, and more generally its speed depends on the particular theory you assume for it.
Does relativity effect the calculations? I feel it would be insignificant. Have I made some gross assumptions? Are the calculations correct? Appreciate your comments.
Relativity effects would be significant.
In order to sync the two clocks in this situation you must account for both General & Special Relativity. Time correction calcs must be done for the clock (pulse) information.
Because the satelite at L4 needed to be accelerated to get there, Special Relativity states that IT'S clock must have slowed down (relative to control clock on Earth) during that acceleration.
Because the satelite at L4 is now spatially located in a different (lesser)gravitational-well from where is started from (Earth), General Relativity states that IT'S clock must speed up (relative to control clock on Earth).
I'm unsure if your experiment would work and will give it some thought.
But, Both Special & General Relativity corrections must be applied.
Also note that the corrections for the accleration (Special Relativity) would only be needed during it's acceleration (both +, -) with respect to the control clock on Earth.
The corrections for being in a different gravitational-well compared to Earth (General Relativity) would be ongoing.
Note:This value would also be changing during any change in distance with respect to the control clock on Earth.
Upon initial reading and looking at the diagram I think in a non-relativistic universe, it would have merit.. relativity does make a bit of a mess of it..
Also - Making the assumption that the speed of gravity = C in an experiment designed to measure the speed of gravity seems a little odd. If you're going to assume the speed is C from the onset, why then carry out the experiment.. Also - You would need to factor in the radio time delay. Radio signals do not travel at C.
I think the equations need to be a lot more complex in order to accurately measure the speed of gravity. More to the point, You're accurately measuring the speed of gravity within the solar system, closer to earth. The numbers would change if you got closer to the sun. The numbers would be VERY VERY different if you were within a few light hours of a neutron star or a pulsar..
Lots more to do, but your equation, (if you take the assumptions as a given, and ignore relativity (Special and General) for a moment) works.. There are just a few finer points to be factored in.
Also - Making the assumption that the speed of gravity = C in an experiment designed to measure the speed of gravity seems a little odd. If you're going to assume the speed is C from the onset, why then carry out the experiment..
Well, this is how science works..
First you make assumptions (that is hypothesis) , then you do some calculations based on those assumptions (that is theory) , then you measure the outcome (this is experiment).
If the outcome of experiment confirms calculation results, theory is correct.
If not, theory is not valid.
BTW, radio waves travel exactly at speed of light (in vacuum.. because they are also electromagnetic radiation, as well as visible light, x rays, gamma rays etc ).
As far as radio waves are concerned, yes, within the vacuum of space they travel at the speed of light, then they enter Earths atmosphere and slow up... There would be a delay involved between sending a signal from the satellite and it reaching earth.
So the experiment would be "confirming the speed of gravity = c, according to SR assumptions" ?
Taking nothing away from the brilliance of SR and GR theory... but could these fundamental assumptions form part of the difficulties in experimentation, mentioned above; ie gravity probes failing to reduce their errors to something meaningful, lido finding nothing, although according to the "theory" and cheque book it should've...etc... ?
As far as radio waves are concerned, yes, within the vacuum of space they travel at the speed of light, then they enter Earths atmosphere and slow up...
Just to be clear, the speed of light (radio in this case) in a given medium, is proportional to the speed of light in a vacuum (299792458m/s), and inversly proportional to the Refractive Index of that medium.
When an electromagnetic wave transitions between different medium boudaries, it's velocity (speed & direction) must change. We still call this speed 'c' as it is the fastest speed posiable in that medium, even though it is now less then 299792458m/s.
Also, a simple way to determine the amount of directional change is to apply Snell's Law:
n SIN(i) = n' SIN(r)
Where n & n' are the respective Refractive Indices, and i & r are the deviation from perpendicular of the Incident ray & the Refracted ray.
I say simple because the more exact way to measure refraction is very complex and involves calculating the values of the wave phase and transition mediums at quantum levels and treating all points as harmonic oscillaters.
Hmmm
Could you be more specific?
Could you provide me (us) with more accurate information?
The absence of gravitational aberration has nothing to do with the speed of gravity greatly exceeding the speed the light but rather the motion of the body in the field.
A common "pictorial" misinterpretation is to think of a planetary orbit like throwing a slingshot. The rope is represented as a single line of force which rotates around a centre. If gravity is represented this way then yes aberration is an issue.
The reality is we need to refer to a gravitational field instead of an individual line of force. A gravitational field can be represented as field lines radiating from a centre. An object in orbit around this centre moves from one field line to the next instead of being "confined" to a single (rotating) line of force. The movement of the object in the field cancels out the aberration effects due to gravity.
While this is a crude description (I can't make it any simpler) the full description is given here.
FYI: Interesting recent views and lists of papers on the Quasar-Jupiter effects observations, also gravity measurement concepts in general from Washington Uni... http://wugrav.wustl.edu/people/CMW/SpeedofGravity.html
Would I be greatly mistaken if I state that gravity field moves along with the body which is cause of this geometry " defect" of the space-time? So, in effect, the gravity influence is (almost) instantaneous, and for an object causing it we have to wait until light reaches us to see it? (as described in document http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909087v2.pdf)
Could it be that the inflation that happened after BB has something to do with this?
Arr we meet again Alex where do you get these links, one can only imagine you have somthing against mainstream science. Meta research is the clearing house for nutty ideas most famous for the founders belief in the "face of Mars".
Once we get instruments that are able to either detect gravity waves, or we find a GUT which might shed some light on other way to measure the messenger particles of q gravity.
How to directly measure the speed of gravity
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