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Concepts in Special Relativity (1905) and of General relativity (first developed between 1907 and 1915) substantially predated spaceflight; they were well known and had been tested well before objects were put in space.

I'd like to ask when relativistic corrections were first required in spaceflight mission calculations, and if possible which missions absolutely required relativistic corrections in order to not fail.

uhoh
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I think that the timing of GPS signals was the first real necessity to apply General Relativity to spaceflight, or else precision would be much lower.

According to (Ashby, 1997) and other sources I found the first GPS satellite launched in 1977 was used to prove that General Relativity will have a noticeable effect on the clocks. It turned out that the clock onboard it was off by 38 microsec/day or a resulting positional error of 11km/day. This would make the GPS the first space application that required relativistic corrections.

Brian Tompsett - 汤莱恩
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  • Do you think the Mariner missions might have had some difficulty with calculations based on only Newtonian mechanics? Or is that what they used? – uhoh Dec 09 '19 at 11:47
  • Do you think they "absolutely required relativistic corrections" for the missions ? If that is the case, then my answer is wrong. –  Dec 09 '19 at 11:52
  • Were the corrections needed for the mission calculations, or just for the onboard clocks? –  Dec 09 '19 at 12:06
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    Guys, are you trying to corner me ? How about a helpful discussion to find out what mission "abolutely needed relativistic corrections". GPS in its current confiduration would not work without them, so that's a point (right ?). Mariner performed experiments to test GR/SR, but did not rely on oit (right ?). If you think that i am wrong, why not post a counterproof or name my failure and we can all move on ? I don't pretend to be right and i can easily take a counter proof, no question. We are not writing publication for peer review here. –  Dec 09 '19 at 12:17
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    I still up voted your answer, don't worry, your answer isn't "rejected" ;-) After the edit I think that you can leave it here as-is, if you like. The title reads "When was Newton “not good enough” for spaceflight; first use and first absolute requirement for relativistic corrections?" and the second half of that clarifies the first half. Your's is an excellent example of a mission that required relativity in calculations to be a success, but it's probably not a "first". I think additional answers will be posted over time. Welcome to Space! – uhoh Dec 09 '19 at 12:26
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    Does launching GPS satellites require relativity, or just the usage of the protocol? My understanding was that it's the latter, which means relativity was not needed for the spaceflight. – BlueRaja - Danny Pflughoeft Dec 09 '19 at 23:35
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    @BlueRaja I like that distinction - and I believe you're correct with that. Although it does depend on your definition of mission calculations, because there is weasel room in the principles of the GPS system being part of those calculations. (Other mustelids available on request.) – Graham Dec 10 '19 at 01:09
  • @BlueRaja-DannyPflughoeft there are only two sentences in the body of the question, and they clarify the title: I've asked about "...in spaceflight mission calculations..." so as not to restrict to orbit/trajectory design. – uhoh Dec 10 '19 at 01:10
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    Kinda interesting that the effect is so huge compared to the required accuracy. The current accuracy goes down to 30 cm according to Wikipedia, while the oldest operational satellite was launched in 1997, for a potential error of 90 000 km so far, a whopping nine orders of magnitude above the current best accuracy. – JollyJoker Dec 10 '19 at 09:05
  • Thanks, @Brian Tompsett, for editing my stammering :-) Looks like it depends a little on the viewpoint to answer which mission really needed gr ... –  Dec 10 '19 at 10:44
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    FYI, the 11km/day error is not correct, the error would be closer to 10cm/day or so. GPS positions aren't obtained by comparing their clocks to a ground clock, but by computing time of flight information from multiple satellites. Each satellites clock would be "off" by about the same amount, so the remaining relativistic errors would not be so big. – whatsisname Dec 10 '19 at 19:08
  • or else precision would be much lower. It's not that the precision would be lower, it's that the system wouldn't work at all. Without the GR corrections, the clocks would drift more and more, and eventually positions would be off by thousands of miles. –  Dec 10 '19 at 19:55
  • I see it the same way @Ben Crowell, and i wanted to write the passage in a more apodictic way. But somehow my neckhair tickled, usually a sure sign that trouble lies ahead if i proceed without caution ;-) –  Dec 10 '19 at 20:11
  • @BenCrowell You're right, although it would take tens of thousands of years for the accuracy to be that off. If you just send an update to each satellite once a week, the error (at least due to GR-denial) is at most a meter. – Arthur Dec 11 '19 at 13:44
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As far as I know, there has not been a space mission that would have been impossible without a theory of relativistic physics.

It is true that the relativistic effects are clearly visible in GPS clocks. However, if the theory didn't exist, they'd just classify it under "weird observation" and trim the clocks to match ground station clocks. The weird observation could very well lead to the development of a new theory, but even if it didn't, GPS could be made function just as well.

It is conceivable that there could be a mission that would have needed relativistic physics for e.g. orbit planning in advance. Normally small inaccuracies would just be corrected mid-course. In very long distances, fast speeds or high gravity, the course corrections needed would be so large that fuel would run out if theory didn't give accurate predictions. Only at that point I would call it "absolutely required". But so far all space missions have been quite firmly in the Newtonian range of speeds.

Some records so far:

  • Juno: Speed of $209\,000\text{ km/h} \approx 0.0002 \cdot c$. According to "A possible new test of general relativity with Juno", the relativistic effects in orbit are less than 900 meters. Closest approach to Jupiter's "cloud tops" is 3500 km, so the difference doesn't sound large enough to cause a mission failure.

  • Parker Solar Probe: Speed of $343\,180\text{ km/h} \approx 0.0003 \cdot c$. It's also close to the most massive body in our solar system, and executes multiple Venus flybys to change orbit over several years, so any errors can accumulate for a long time. I didn't find a calculation on how much of an effect it would have.
    According to this answer, relativistic effects due to gravity are, however, quite critical to accurately determine the orbit. So it is quite likely that the science results obtained by this mission would be inaccurate if relativity wasn't accounted for, even though we might not detect it.

jpa
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  • How far off would deep space missions have bene from their targeted planetary flybys using only Newtonian physics? For example could this have worked? I'd like to see some math behind "But so far all space missions have been quite firmly in the Newtonian range of speeds." I don't believe this is true. One needs to be within a few km or less of the desired position and time after traveling years and hundreds of millions of km. That's accuracy of 1 part in 10^8 or more. – uhoh Dec 09 '19 at 16:37
  • @uhoh Hmm, I'm not sure what part of the Venus question you are referring to. But I added some calculations of the two fastest probes so far, and yeah, I guess science objectives would fail for Parker Solar Probe even though it wouldn't literally crash into anything. – jpa Dec 09 '19 at 16:56
  • Eventually I may try to run this with relativistic corrections turned on and off to see how much difference there is, but from what I recollect the accumulated error over years will be a lot more than 900 meters for something like Juno's rendez-vous with Jupiter. But I could be wrong. At the time when I wrote this Universal Sandbox didn't have relativistic effects, but maybe it does now. – uhoh Dec 09 '19 at 17:02
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    @uhoh Yeah. It's further complicated by the fact that without a theory of relativity, our estimates for the mass of planets would be different, which would mask part of the error. – jpa Dec 09 '19 at 17:24
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    @uhoh, the total error doesn't matter much. A better comparison would be the relative error compared with other sources. Your comments seem to suggest pinpoint precision at launch leading to a bullseye, when instead the trajectory is corrected along the way as new information is learned. I suspect any relativistic errors are dwarfed by the uncertainty in DV during a firing maneuver. – BowlOfRed Dec 09 '19 at 17:29
  • @BowlOfRed that's a very good point! While I don't believe that it would be too small to have a meaningful effect, I'm sure you are right that it would have been small enough to have been corrected for at regular intervals along with all the other errors. So this answer might be right-ish, but not yet for the right reason. – uhoh Dec 09 '19 at 17:36
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    That's what I tried to convey, like with error in GPS it would just be compensated once detected. But if the error would be so large that a correction would be infeasible, then the theory of relativity would become mission-critical. – jpa Dec 09 '19 at 18:22
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    The orbit of Mercury is not correctly predicted by Netwonian physics, none of the spacecraft bound for Mercury would have hit their target if this wasn't corrected. Speed isn't the only factor, mass is also, and the Suns mass does have a noticeable effect on Mercury. – Polygnome Dec 09 '19 at 19:46
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    Just because there's lots of questions regarding the meaning of terms: Personally, I would consider adjusting the GPS ground clocks regularly to qualify as "relativistic corrections." Maybe that's just me taking it literally as corrections made to deal with errors deriving from relativity. (The whole discussion on all of the answers is rather fascinating to me, because I figured "required to not fail" was such a well defined concept when I started reading the question. Now, I'm not so sure.) – Cort Ammon Dec 09 '19 at 22:24
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    @Polygnome as others have said, it's perfectly possible to "hit" Mercury without GR calculations. The error in trajectory prediction is masked by the uncertainty in the launch thrust. You make course adjustments en-route. – OrangeDog Dec 10 '19 at 12:21
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    @CortAmmon-ReinstateMonica if we didn't know about GR we'd just call them "error corrections". Hopefully they'd further inspire someone to realise GR, but equally people would go down a lot of dead ends looking at stellar wind impact on caesium transitions etc. – OrangeDog Dec 10 '19 at 12:24
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    @StopHarmingMonica Whats the material difference between "Oh we use this error correction formula" and "oh yeah, this is because of GR?". just the name is different. – Polygnome Dec 10 '19 at 12:35
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    Yeah, I see now that I've essentially answered "when was a theory of relativity needed", and not "when were corrections for relativistic effects needed". – jpa Dec 10 '19 at 13:22
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    @Polygnome the main difference between Newtonian and GR orbits of mercury is the precession of the perihelion, the disagreement between them is about 43 arcseconds per century relative to earth's orbit. It is not a significant correction unless you're flying there via a stop at proxima centauri or something https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury – llama Dec 10 '19 at 22:31
  • The question is not "which mission would have been impossible..." but, simply and clearly, in which instance were such corrections first used. – Fattie Dec 11 '19 at 18:48
  • @Fattie Well, in title the question is "When was Newton 'not good enough'" - if the mission succeeds with just Newton's theory + normal corrections for inaccuracies, isn't it good enough? It's just a classic case of subtly different question in title vs. body. – jpa Dec 11 '19 at 18:58
  • @jpa - quite right on the poor title, good one – Fattie Dec 11 '19 at 19:10
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JPL's DESCANSO website links to online books describing spacecraft navigation. Page 4-19 of Volume 2 states "The point-mass Newtonian acceleration plus the point-mass relativistic perturbative acceleration ... is given by Eq. (54) of Moyer (1971)." So JPL was incorporating relativistic effects in its navigation calculations at least as early as then.

I don't know which mission was the first to require such corrections.

Bob Werner
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As others have pointed out, a civilization with zero knowledge of relativity could have carried out all space missions so far, and even constructed the GPS network, if they had simply added in various ad hoc corrections based on experience, without any understanding of the underlying physics. However, it's easy to come up with examples where if you failed to do these ad hoc corrections on the fly, there would be big effects.

As a silly example, suppose that the Mariner 10 mission in 1975 had been planned based on orbital elements of Mercury that had been measured in 1875. These data would have been a century out of date. Now suppose that they understood the dominant reasons for the precession of Mercury's perihelion, which have to do with Newtonian effects from other planets' gravity, but they didn't understand enough GR to know about the anomalous precession. Let $e=0.2$ be the eccentricity of the orbit, $a$ the semimajor axis, and $\delta\theta=2\times10^{-4}$ rad the anomalous precession of its perihelion. Then the error in predicting Mercury's position would be on the order of $ea\delta\theta\sim10^6$ m, which is certainly enough to make the mission fail. Of course this is a silly example, because there's no reason they wouldn't have updated their data on Mercury's orbit for a whole century.

  • If an unexpected deviation was observed for a certain satellite, and a slightly different one for another on a slightly different orbit, wouldn't people stop then ? Besides the military nature, imagine the use for precision approaches or in construction, surveying and mapping, wouldn't the project be stopped until the cause has been found and can exactly be quantified, simply because it's expensive and other means to obtain a position are cheaper and more accurate ? idk ... –  Dec 10 '19 at 22:13
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    @idk: In both the GPS exam and this example, the effect is small, and the trend is straightforward. –  Dec 10 '19 at 22:21
  • @ebv Not only is the problem easily corrected with a simple fudge factor (easily determined experimentally - they might not even notice a discrepancy if they relied on calibration in the first place), it's also very common for engineering to plow forward when the science is lacking and vice versa. The two disciplines are complementary, but we have plenty of engineering without the science to guide and/or explain it and plenty of science without any practical engineering. But mainly, as Ben said, the error is easily and exactly quantified, and alternatives to GPS are far worse. – Luaan Dec 11 '19 at 08:50
  • Neing provocative: a measuring tape is more exact than any gps, though it needs more thought. Not speaking of total stations for terrestrial application or precision approaches guided by radio technology (in conjunction with differential gps). But aren't we looking for the first space application ? :-) Sorry for talking old, i know some things require discussion, relativity is one of them :-) –  Dec 11 '19 at 10:07
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    It seems to me that this answer overlooks mid-course corrections. – Itsme2003 Dec 12 '19 at 03:19
  • @ebv , yep, and with the Mercury precession problem, we had already quantified the size of the correction factor needed to adjust the older predictions and bring them into line with observation. Einstein's 1916 theory provided an explanation for the already-known anomaly, but if we'd stopped watching Mercury in 1912, a 2012 Mercury mission might still have a decent idea where to aim for. During the development of the general theory, Einstein is supposed to have been keen that the new theory would explain the known (mis)behaviour of Mercury. – Eric Baird Dec 14 '19 at 00:30
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I'm not sure that any spaceflight missions to date have really needed SR/GR.

The Apollo missions finished in ~1972. GPS didn't kick in until ~1978. The Hubble Space Telescope's Pointing Control System (PCS) uses guide stars for alignment. Interplanetary probes presumably don't rely on Earth GPS(!). The slingshot effect tends to be presented as a Newtonian exercise in momentum exchange, partly for simplicity, and partly because GR has some issues with velocity-dependent gravitomagnetic dragging effects, http://maths.dur.ac.uk/~dma0rcj/Psling/sling.pdf :

"... by its usage the slingshot effect is a modern triumph of Newtonian Mechanics."

The fastest ever space probe seems to be the Parker Solar Probe, listed as having reached 692,000 km/h ( ~192 km/s? ) . By comparison, the the speed of light is more like 300,000 km/s So we're talking about less than a thousandth of the speed of light. At v<0.001c, differences between SR and Newtonian calculations are likely to be small compared to other errors (chemical rockets!). NASA don't expect their initial probe trajectories to be perfect, and the craft have manoeuvring thrusters to make changes and trajectory corrections during their multi-year missions.

GPS and GR

GPS calculations are designed to incorporate SR/GR corrections, but analogous effects also show up under Newtonian-based theory. The two "important" GPS corrections that GR folk like to talk about are the gravitational time dilation effect down on the Earth's surface (which makes GPS' orbiting atomic clocks tick faster than us) and the SR transverse redshift (which slows them down again). The clocks are typically adjusted to compensate for these effects before launch.

The "Newtonian" gravitational shift effect that changes the energy of light as it crosses a gravitational gradient was described by John Michell back in 1783 (paper). Einstein then seems to have rediscovered the effect and in 1911 pointed out that the unavoidable consequence was gravitational time dilation ("On the Influence of Gravitation on the Propagation of Light"), but for simplicity Einstein's 1911 paper derives the effect within Newtonian gravity. So while gravitational time dilation isn't usually "historically" considered to be Newtonian theory, the Newtonian version predates GR by a few years, and could and should have been a Nineteenth-Century prediction, and presumably would have been if not for human fallibility.

Earth gravity is almost certainly going to be probably too weak to tell the two predictions apart, because the Earth's gravitational terminal velocity is only about 11 km/s (as opposed to light's three hundred thousand km/s).

Newtonian theory also gives a counterpart to the second "relativistic" GPS correction, the SR transverse redshift effect. The Newtonian version of this is an "aberration redshift" caused by the forward deflection of rays, which causes the light entering a "transverse-aimed" detector to receive a ray that has a slight recession redshift component. Oliver Lodge "The Ether of Space" p134-136:

"... a spurious or apparent Doppler effect due to common aberration. " http://www.gutenberg.org/files/40911/40911-h/40911-h.htm

The Newtonian "transverse" effect appears identical to the SR effect other than it's a Lorentz-squared redshift rather than a single Lorentz redshift.

As a result there's no obvious reason to believe that GPS wouldn't work just as well outside the SR/GR context, and Ronald Hatch, one of the independent GPS technical experts who served on the GPS board until he died this year (2019), spent some years arguing this point.

In general, in practical situations, we use the Newtonian relationships for astronomy rather than the SR/GR set, because the Newtonian set are simpler, and the differences are so small at normal relative velocities that there's no appreciable difference between them: http://spiff.rit.edu/classes/phys301/lectures/doppler/doppler.html

"... because the velocities of planets, binary stars and clusters of stars are hardly ever more than a few hundred kilometres per second, the classical red-shift equation is accurate enough for most astronomical problems". Foundations of Astronomy, Third edition, Michael A. Seeds (1992)

If we ever manage to get spacecraft travelling at "full percents" of the speed of light, then maybe the difference might start to be important.

Eric Baird
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    "There's a guy called Ronald Hatch who says that GPS would work fine without SR/GR ... he has a stack of GPS patents, and they probably don't have any" - having patents means nothing more than getting a patent application approved. It says nothing about their usefulness or even their novelty or realistic validity. – Nij Dec 10 '19 at 02:58
  • Hatch appears to have recently died: GPS.GOV U.S. Official U.S. government information about the Global Positioning System (GPS) and related topics - "Ron Hatch passed away on September 25, 2019, while serving his fifth term as a member of the National Space-Based PNT Advisory Board." https://www.gps.gov/governance/advisory/members/hatch/ – Eric Baird Dec 10 '19 at 06:32
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    ... FYI, that's the official US Government website for the GPS system. Hatch was on their advisory board: "The National Space-Based Positioning, Navigation, and Timing (PNT) Advisory Board provides independent advice to the U.S. government on GPS-related policy, planning, program management, and funding profiles in relation to the current state of national and international satellite navigation services." In other words, Hatch was one of the board of independent experts that the US Government appointed and paid to tell them how they should be running, maintaining and upgrading the GPS system. – Eric Baird Dec 10 '19 at 06:51
  • I'm sorry, but there's a lot in this answer that's either misleading or incorrect. For example, Michell did not predict gravitational time dilation; the Galilean-invariant theory that he used to calculate gravitational redshift (note the difference) assumed that time was absolute in every reference frame. The notion of the passage of time being different from different reference frames is explicitly incompatible with the assumptions of the supporting theory, so they couldn't have had anything to do with gravitational time dilation. – probably_someone Dec 10 '19 at 13:34
  • For that matter, qualitative accuracy, especially in the face of a limited set of observations, means almost nothing without quantitative accuracy. Aristotelian mechanics, where objects fall because "their natural state is on the ground" and objects slow down because "their natural state is standing still", is also qualitatively accurate for terrestrial observations, even though its explanations of how nature works are completely incorrect. Michell's "predictions" hold exactly as much value in explaining nature as Aristotle's do. – probably_someone Dec 10 '19 at 13:42
  • dear, probably_someone . I wrote, "The gravitational shift effect was first predicted by John Michell in 1783 ... Einstein published an NM-based derivation of gravitational time dilation in 1911". So you can't complain, "Michell did not predict gravitational time dilation", because that wasn't the claim. However, Einstein argued that once you had gravitational shifts, gravitational time dilation was logically unavoidable. PS if you read Principia, you'll find that Newton defined both absolute and relative time - his absolute time was not claimed to be the rate at which clocks ticked – Eric Baird Dec 10 '19 at 19:38
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    I'm about to add some references and make a few tweaks to address some complaints. – Eric Baird Dec 10 '19 at 19:40
  • "Michell's "predictions" hold exactly as much value in explaining nature as Aristotle's do". Actually, a Michell dark star makes quantitive predictions about light-energies and behaviour, you just have to fix Newton's screwup over how energy relates to frequency, and then "smooth" lightspeeds to force wave-compatibility. The first correction brings Newtonian gravity into the Nineteenth century, the second creates an acoustic metric and brings it into the C21st. Did you know that C18th dark stars and C21st acoustic metrics generate the classical version of Hawking radiation? GR can't do that. – Eric Baird Dec 11 '19 at 01:20
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    @EricBaird First of all, you're going to need a source for the "C21st acoustic metrics" and "Newton's screwup over how energy relates to frequency" and the notion of "wave-compatbility" you're citing. Second, Michell's quantitative predictions are incorrect, so his explanation is incorrect. Third, this isn't particularly surprising, as Michell's assumptions are in contradiction with the Michelson-Morley experiment and others demonstrating the invariance of the speed of light. Fourth, considering we've never measured Hawking radiation, how can you say that "the classical version" is correct? – probably_someone Dec 12 '19 at 10:50
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    @EricBaird Also, now that you've provided a source for the Einstein citation, if you actually read it, he is emphatically not giving a Newtonian treatment of gravitational time dilation. Just because he mentions Newton's name once in the second paragraph doesn't mean all subsequent physics is Newtonian. At the time, the notion of an inertial reference frame was not as formalized as it is today, and what Einstein is saying there is that free-falling reference frames can be called inertial, which is a fundamental tenet of GR (generalizing SR's equivalence principle). – probably_someone Dec 12 '19 at 10:54
  • @EricBaird The static "luminiferous aether" assumed by Oliver Lodge and others was disproved using the Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell experiments; the only versions of those theories left are so convoluted that Occam's Razor disfavors them. – probably_someone Dec 12 '19 at 10:58
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    @EricBaird "Earth gravity is almost certainly going to be probably too weak to tell the two predictions apart" - Do you have a source for this? Because it certainly sounds like this is a claim being made with no evidence to support it at all. – probably_someone Dec 12 '19 at 10:59
  • @EricBaird After looking him up, Ronald Hatch illustrates the principle of "An expert in one thing is not automatically an expert in all things" quite well. You haven't cited any specific arguments he makes, and I don't have the space here to address every single one, so instead I'll bring up one of his other works, that may be illustrative: The Long Day of Joshua and Six Other Catastrophes, in which Hatch proposes that in biblical times, Mars repeatedly passed very close to/between the Earth and Moon, and precessed Earth's axis of rotation. – probably_someone Dec 12 '19 at 11:16
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    @EricBaird "In general, in practical situations, we use the Newtonian relationships for astronomy rather than the SR/GR set" - No, we don't. Maybe for things within our own galaxy this is true, but for any extragalactic source, the expansion of the universe (which can only be described using GR) gives faraway galaxies apparent recessional velocities that are appreciable fractions of the speed of light, leading to very, very high redshifts that couldn't be reached using the "Newtonian" formula. Only SR/GR can explain why we see radio galaxies. – probably_someone Dec 12 '19 at 11:35
  • @EricBaird In addition, only the relativistic Doppler shift formula predicts that a Doppler-shifted blackbody spectrum is still a blackbody spectrum. This result relies on the fact that the power spectral density divided by the cube of the frequency is Lorentz-invariant, which is explicitly an SR prediction. The fact that the cosmic microwave background is still a blackbody even at a redshift of $z=17$ can only be explained using the SR/GR definitions. You're really ignoring about half of astronomy if you think the SR/GR formulas aren't used. – probably_someone Dec 12 '19 at 11:39
  • @probably_someone said "... the expansion of the universe (which can only be described using GR) gives faraway galaxies apparent recessional velocities that are appreciable fractions of the speed of light, leading to very, very high redshifts that couldn't be reached using the "Newtonian" formula." No. https://en.wikipedia.org/wiki/Redshift#Gravitational_redshift "... cosmological redshift is not found using the relativistic Doppler equation ..." The Newtonian recession velocity shift is E'/E= (c-v)/c . You just got Newtonian theory and GR and modern cosmology wrong. – Eric Baird Dec 13 '19 at 22:29
  • PS: "Your cosmological shift" mistake is understandable if you've been told that the 1916 theory valid, because a workable general theory has to apply a single shift formula to both the curvature shifts associated with gravity, and those associated with cosmological expansion. GR1916 fails this condition: it uses "SR" shifts for gravity and "non-SR" shifts for Hubble shift. https://doi.org/10.13140/RG.2.2.26042.29128 This makes the 1916 theory geometrically inconsistent with modern cosmology. Which, to be fair, it was never designed for. – Eric Baird Dec 13 '19 at 22:31
  • @probably_someone ""Earth gravity is almost certainly going to be probably too weak to tell the two predictions apart" Do you have a source for this?" Your internet device should have a calculator app. The gravitational differential associated with the Earth's field, down to the surface, is quoted as ~11.186 km/s. c is 299792.458 km/s. Treating these as exact, the Newtonian gravity-shift is E'/E = (c-v)/c , for which Windows calculator gives E'/E=~0.9999626875... The SR-based prediction comes out as E'/E=0.9999626882... the two gravity-shift predictions only differ by ~7 × 10^-10 – Eric Baird Dec 13 '19 at 22:36
  • @probably_someone ... Compare this to the scale of the arbitrary gravitational anomalies that GPS has to correct using lookup tables. https://www.newscientist.com/article/dn24068-gravity-map-reveals-earths-extremes/ – Eric Baird Dec 13 '19 at 22:37
  • @probably_someone said: "The static "luminiferous aether" assumed by Oliver Lodge ..." No, the calculation in question was emphatically NOT for a static luminiferous aether. An sla gives no aberration redshift. Different aether theories at the time had arbitrary coefficients for dragging, etc., aether theory stopped being useful not because it was wrong, but because with the right choice of parameters you could use it to explain almost any result. SR's advantage was its lack of free parameters. You haven't understood the historical context, or the logic, or the math, or how they connect. – Eric Baird Dec 13 '19 at 22:45
  • @probably_someone said: "_ ... Einstein ... if you actually read it, is emphatically not giving a Newtonian treatment of gravitational time dilation_" Please look at Einstein's equation 1. There's no Lorentz factor. For the energy-increase in falling light, rather than the SR Doppler shift equation, he uses "a first approximation", E'/E = (c±v)/c ... the Newtonian calculation. So Einstein gave a Newtonian-math-based derivation of gravitational shifts and then argued that once you had those, gravitational time dilation was unavoidable. This was in 1911, his general theory was ~1915/1916. – Eric Baird Dec 13 '19 at 23:26
  • @probably_someone said: "...you're going to need a source for the "C21st acoustic metrics"" Try: https://arxiv.org/abs/gr-qc/0505065 . Acoustic metrics only started to be properly studied in the late 1990s, due to their ability to combine classical physics with behaviours (specifically Hawking radiation) more normally associated with quantum mechanics. Acoustic metrics have desperately nonlinear behaviour that allows them to radiate indirectly through a horizon. The hope was that by using acoustic metrics as a "toy model" for quantum gravity, we might be able to reconcile GR1916 and QM. – Eric Baird Dec 13 '19 at 23:29
  • ... Unfortunately, acoustic metrics turn out to be incompatible with the SR shift equations. The only classical relativistic set of Doppler equations that can generate Hawking radiation turns out to be the older Newtonian set. You can find a plot of HR-dependency vs. choice of relativistic equation here: https://doi.org/10.13140/RG.2.2.21885.67045 – Eric Baird Dec 13 '19 at 23:31
  • @probably_someone said: "_...you're going to need a source for ... "Newton's screwup over how energy relates to frequency" _" It's in Principa/Opticks. Newton assumed that bigger wavelengths corresponded to bigger energies, and that therefore the speed of light in glass had to be greater than in air, and by analogy that the SoL had to be greater in a strong-gravity region than a weaker-gravity region (inverse Shapiro effect). In around ~1800, a number of experimenters started to do the lightspeed-in-glass experiment and found that Newton's original system was wrong. – Eric Baird Dec 13 '19 at 23:33
  • ... So the community quietly fixed the error, changed the textbook predictions, and tried to pretend that the whole sorry episode had never happened. Opticks then stayed out of print until the ~1930s, when parallels between some of Newton's descriptions and QM (wave/particle duality, pilot waves) created a resurgence in interest in the book. – Eric Baird Dec 13 '19 at 23:35
  • @probably_someone said: "Michell's quantitative predictions are incorrect, so his explanation is incorrect." Michell's predictions for the shift in energy of light crossing a gravitational gradient weren't affected by Newton's screwup. You haven't yet demonstrated that the GR1916 energy-change equations are more accurate. Assurances, faith, what your teachers told you at school, and strongly-held beliefs don't count - give me correct mathematics. – Eric Baird Dec 13 '19 at 23:37
  • @probably_someone said: "After looking him up, Ronald Hatch illustrates the principle of "An expert in one thing is not automatically an expert in all things" quite well." Agreed. But what Hatch was an expert in was high-precision GPS systems. That was his specific area of expertise, and was what he did for a living. That's why the US Government hired him as a technical expert and board member, and why the GPS.gov website currently has an "in memoriam" notice for him. https://worldwide.espacenet.com/patent/search?q=ia%20%3D%20%22HATCH%20RONALD%20R%22 – Eric Baird Dec 13 '19 at 23:47
  • Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Dec 16 '19 at 15:35
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Consider NASA's Gravity Recovery and Interior Laboratory (GRAIL) mission. Not only would each probe's positions need to be precisely known, but the effects of lunar gravity at their locations. This pairing of position and gravitational measurement could qualify for Relativity being necessary for the success of the mission.

https://www.nasa.gov/pdf/582116main_GRAIL_launch_press_kit.pdf

Zuber and company will have to correct for pesky factors such as atmospheric drag, gravitational pull from other planets and general relativity, just to name a few.

https://science.nasa.gov/science-news/science-at-nasa/2008/22may_grail

uhoh
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