How much of a wavelength change does our sun’s gravity cause in the light it emits? I imagine this could be measured by the shift in its spectral lines. And by extension, does the earth’s gravitational field cause a minuscule blue shift- or does this add a bit more redshift?
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3$\begingroup$ en.wikipedia.org/wiki/Gravitational_redshift has a lot of good info, and various formulae. "Measuring the solar redshift is complicated by the Doppler shift caused by the motion of the sun's surface, which is of similar magnitude as the gravitational effect". $\endgroup$– PM 2RingNov 28, 2021 at 7:40
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1$\begingroup$ I'll tell you more, the gravitational redshift of our Earth (two orders of magnitude less) is pretty much measurable, too. Otherwise your phone won't know what to report as your location to our digital overlords. $\endgroup$– fraxinusNov 28, 2021 at 23:50
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1$\begingroup$ @PM 2Ring Thank you for that wiki ref. I found it interesting that it said this about the PoundRebka expt “ Since this prediction arises directly from the equivalence principle, it does not require any of the mathematical apparatus of general relativity, and its verification does not specifically support general relativity over any other theory that incorporates the equivalence principle.” $\endgroup$– aquagremlinNov 29, 2021 at 3:46
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1$\begingroup$ @fraxinus I don't think redshift is needed for GPS. GPS is based on calculating distances to the satellites. Finding one's location is a matter of finding the intersection of the resulting spheres. $\endgroup$– AcccumulationNov 29, 2021 at 6:52
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$\begingroup$ @Acccumulation the GPS signal blueshift (it is not really red-shift) is pre-calculated in the GPS clocks. $\endgroup$– fraxinusNov 29, 2021 at 8:54
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2 Answers
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Yes. It can be measured in spectra of the moon.
A paper The solar gravitational redshift from HARPS-LFC Moon spectra describes the measurment of red-shifts in Iron absorption lines in the spectrum of the moon which result from gravitational redshift from the sun.
The difficulty in measuring these redshifts is not their scale (equivalent to motion of about 630 m/s) but because there are lots of other motions, of the convection in the sun, the moon's orbit, the Earth's rotation, that need to be accounted for.
When this was done, the authors conclude:
$v_{GRS,3D} = 638 ± 6 m s^{−1}$ from the mean of observed global line shifts of 97 Fe lines with 10 < EWs[mÅ] < 180, and $v_{GRS,obs} = 639 ± 14 m s^{−1}$ from the mean line core shift of 15 strong Fe lines with EW > 150 mÅ. Both measurements are in perfect agreement with the theoretical value of the solar gravitational redshift, $v_{GRS,theo} = 633.1 m s^{−1}$, representing an observational test of the general theory of relativity.
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$\begingroup$ Thank you. Also See my comment above about The PoundRebka expt. Am I to conclude that ANY Theory that incorporates the equiv principle could account for this? $\endgroup$ Nov 29, 2021 at 3:54
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$\begingroup$ Thank you, exist any document that show how to detect direction of sun respect to earth north pole ? $\endgroup$– Adrian RNov 29, 2021 at 18:33
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Yes, gravitational redshift (and blueshift for photons travelling downwards) from the Earth's gravitation field has been experimentally detected. See https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment
