# When was Newton "not good enough" for spaceflight; first use and first absolute requirement for relativistic corrections?

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.

• You seems to be specifically asking about orbit/trajectory design and planning. A mission have more to do with just trajectory, e.g. the operation of the payload, e.g. GPS clocks described by the below answer. If you want to know GR/SR's impact on trajectory calculations, you should be more specific. Dec 9 '19 at 16:21
• @user3528438 I've written the question exactly how I intended, without specifying or restricting to orbit/trajectory design. I did that on purpose. This is why I've up voted the answer about GPS clocks. It may not be a "first", but it does address the question because relativistic corrections are essential for a GPS satellite's mission success.
– uhoh
Dec 9 '19 at 16:26
• Would you like to weigh in on the subtle distinction captured in the comments on jpa's answer regarding the difference between needing a theory of relativity to complete the mission or merely needing to correct for relativistic effects? I think that distinction is a rather neat one that I didn't expect to come up until reading the answers. Dec 10 '19 at 14:44
• See the related question Could we send a man safely to the Moon in a rocket without knowledge of general relativity? on the Physics Stack Exchange. Dec 10 '19 at 15:52
• Nov 18 '20 at 21:30

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.

• 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.
– user34174
Dec 9 '19 at 12:17
• 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 9 '19 at 12:26
• 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. Dec 9 '19 at 23:35
• @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.) Dec 10 '19 at 1:09
• 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. Dec 10 '19 at 19:08

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.

• @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 9 '19 at 17:24
• @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. Dec 9 '19 at 17:29
• 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. Dec 9 '19 at 19:46
• 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.) Dec 9 '19 at 22:24
• @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 en.wikipedia.org/wiki/… Dec 10 '19 at 22:31

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.

• Excellent! Equation 4-26 is the fourth bullet in my list here I wonder if Moyer should be added as well
– uhoh
Dec 9 '19 at 18:01
• Outstandsing answer. Dec 11 '19 at 18:48

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 ...
– user34174
Dec 10 '19 at 22:13
• @idk: In both the GPS exam and this example, the effect is small, and the trend is straightforward.
– user687
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. Dec 11 '19 at 8:50
• 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 :-)
– user34174
Dec 11 '19 at 10:07
• It seems to me that this answer overlooks mid-course corrections. Dec 12 '19 at 3:19

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

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.

• "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 2:58
• ... 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. Dec 10 '19 at 6:51
• I'm about to add some references and make a few tweaks to address some complaints. Dec 10 '19 at 19:40
• @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? Dec 12 '19 at 10:50
• @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. Dec 12 '19 at 11:35