Mistake in Satellite Placement Used To Further Confirm Relativity

The incorrect placement of ESA satellites in orbit has been used to confirm general relativity to the highest precision yet. (click for credit)

One of the things I continually stress with my students is that science doesn’t have to make sense. In fact, most of the theories in my scientific field make no sense at all. Why do I believe them? Because they make predictions which are later verified by the data. That’s the acid test of a scientific theory. If it can make predictions about something that is not known and those predictions can then be tested by experiment or observation, the theory is scientific. If observations or experiments actually confirm the predictions, then it is a reliable scientific theory. For example, young-earth creationism is a reliable scientific theory, because it makes predictions which are later confirmed by the data.

The same can be said of Einstein’s theory of general relativity. Make no mistake: It’s a very strange theory. It says that what we see as the force of gravity is not really a force at all. It is a consequence of how mass warps space and time. Now that’s just crazy. We know that we stay on the surface of the earth because the force of gravity continues to pull us to the center of the earth. An apple falls from a tree because the force of gravity pulls it to the earth. The earth stays in orbit around the sun because the force of gravity keeps it there. Sir Isaac Newton himself gave us an equation for gravity, and that equation has been tested over and over again and found to be reliable. It begins “F =”. The “F,” of course, stands for force. Why,then, would you believe something as silly as what Einstein said? Because his theory made several testable predictions, and when those predictions were tested, they were confirmed.

One of the stranger predictions of general relativity is that mass warps space and time enough that it actually affects the passage of time. When you are near a large mass, time passes more slowly than when you are far from that same mass. According to Einstein, then, time is not constant in the universe. It ticks at different rates, depending on the mass in the area. Once again, to you and me, that’s just crazy. However, it has been confirmed in many different experiments. Indeed, the Global Positioning System would not work if we didn’t take into account that time is ticking differently on the GPS satellites than it is on the surface of the earth. Of course, one hallmark of good science is to continually test your theories, even when they have been confirmed. My publisher told me about a recent example of this being done, and it is worth discussing.

Back in 2014, the European Space Agency launched several satellites into orbit around the earth. Satellites are generally put in a circular orbit, so their distance from the earth never changes. However, a malfunction in the rocket used to place two of the satellites caused them to be put into an elliptical orbit. As a result, their distance from the earth regularly varied. The ESA corrected the orbits as much as they could, but they remain elliptical to this day. The difference between their closest and farthest distances from the earth is about 8,500 kilometers.

While this was a disappointing mistake, two physics research teams realized that they could use it to further test Einstein’s prediction of time being affected by how close you are to a massive object. After all, at regular intervals, these satellites moved closer to and farther from earth. Their position could be accurately measured in real time, using the International Laser Ranging Service, which shoots lasers at the satellites and measures the time it takes for the light to reflect off them and return.

The teams independently examined the time measured by the clocks aboard the satellites, and they each produced a graph similar to the one at the top of this post. Both of them showed that the time measured by the clocks aboard the satellites varied just as Einstein had predicted: As the satellites drifted away from the earth, time started passing more quickly for them. As the satellites drifted towards the earth, time passed more slowly for them. What makes their results noteworthy is that this test is more precise than any other that has ever been done. Their results tell us that the maximum error in Einstein’s prediction is about 0.003%.

Like it or not, the general theory of relativity is the best description scientists have for gravity, as these misplaced satellites have further confirmed.


  1. James A Goering II says:

    This is very much a technicality that does not change the overall message of the post, but orbits are never circular. They can be roughly circular, but all orbits are somewhat elliptical. The orbit of the satellites in the incorrect orbit are simply MORE elliptical than they should be.

    1. Jay Wile says:

      Could you give me a reference for that? I realize that the orbits of natural satellites are elliptical, but what I have read indicates that human-made satellites are usually in a circular orbit. For example, how can you have a geosynchronous satellite that is not in a circular orbit?

      1. James A Goering II says:

        I did a bit of reading to check myself, and it does appear that orbits can theoretically be circular. In the real world, however, even geostationary satellites do have slightly eccentric orbits. Here is a link to some information about the geostationary satellite Intelsat 16. https://www.n2yo.com/satellite/?s=36397

        1. Jay Wile says:

          Thank you so much for the link. I honestly thought that geosynchronous satellites had to have a perfectly circular orbit. According to those specifications, that one has a 0.04% deviation from being perfectly circular. That’s small, but it’s definitely not zero!

  2. Jennifer Matheson says:

    Question from a homeschooing mom: How do scientists know for sure that the difference in time measured is a result of time passing differently farther from a large mass, and not the result of distance from a large mass affecting the equipment being used to measure time?

    1. Jay Wile says:

      That’s a great question! The first confirmation of time passing differently didn’t even depend on clocks. It had to do with the way the planet Mercury moves in the night sky. It’s movement was inconsistent with Newton’s Laws, but Einstein showed that when you account for time passing more slowly for Mercury than for the earth (because it is closer to the sun), then Mercury’s motion was completely consistent with Newton’s Laws. So it does seem to be an actual change in how time is passing, not just a change in how the clocks are ticking.

  3. Jim Pemberton says:

    I wonder to what extent the earth homogenizes the macroscopic (and perhaps even the quantum) passage of time for all of us immediately connected to the planet. Or perhaps the opposite question would be more pertinent: How differently do objects in interstellar space with negligible gravitational influences experience the passage of time?

    For example, given that time is a factor in the production of electromagnetic radiation, how should this change our understanding of what we observe? Observing the refraction of light around a large object is one thing. Thinking about how a particularly massive sun produces light differently than a small sun may be another. Are certain wavelengths noticeably changed in the process? We have a certain predictive quality to discerning elements based on the wavelength, and we also observe a shift based on how much we expect the universe to be expanding. Are scientists taking any shifts due to gravity into consideration based on the size of the source star?

    1. Jay Wile says:

      The initial wavelength of light emitted by an excited system depends on the energy of the system. So, for example, the wavelengths of light emitted by the star depends on the elements that make up the star. Time doesn’t affect that. Those wavelengths are then shifted due to the expansion of the universe (as you say). There are also other factors. Light is red-shifted due to gravity, but once again, that is not a time effect. It is a gravitational effect. Gravity would affect the time it takes for the light to get to us, but it shouldn’t affect wavelength.

      1. Emory Grove says:

        Pardon my lack of knowledge on the subject. Wouldn’t an object with enough gravitational force change the wavelength of light? An example being a black hole pulling light in, if we can’t detect the already absorbed or captured light, but perhaps the light that might be on a path of escape, would that gravity on the light have a reversing effect on the wavelength before it reaches us or would that be impossible since any light that is caught by the gravity of a black hole would have no chance of escape, therefore, observance? Enjoying your posts BTW.

        1. Jay Wile says:

          Gravity does cause light’s wavelength to lengthen. That’s called the gravitational redshift of light, and it’s one of the many successful predictions of General Relativity. However, that occurs after the light has been made. So, when light from a star is made, its wavelength is determined by the energy of the process that is happening (thermonuclear fusion), and that is independent of gravity. Once the light starts travelling away from the star, its wavelength is lengthened, but that happens to all wavelengths of light coming from the star. Thus, when we receive light from the star, we can account for the gravitational redshift, once we take other things into account (like the expansion of the universe).

  4. Bruce Rennie says:

    Greetings Jay,

    How does the gravity map of the planet Earth affect the readings that they found? Since the Earth is not homogeneous nor is it spherical or even oblate, did the calculations take the surface variation and hence the altitude variation in gravitational field strength?

    The fundamental problems that I have with General Relativity are the non-linearity of the model, the inability to describe any n-body interaction (without the introduction of perturbation theory) and that a number of predictions made for which the evidence supposedly supports GR but doesn’t actually match.

    There may only be a small number of researchers looking into alternatives but there is a growing number of questions that are not being satisfactorily answered by GR or SR. The real world is “chaotic” whereas GR expects the real world to be “smooth”.

    GR is a map but it is not the territory. It can be a useful tool but what it describes is only a map, a simplified view of the reality around us. It is an unfortunate aspect of “science” today (as you have have shown often enough yourself) that belief is the essential “truth” of any specific model. Instead of teaching that these theories are a current understanding of the universe about us and that there are alternative models that provide insight for us, we teach these things as “truth”.

    As a simple example, “black holes” are touted as being the cause of various astronomical phenomena being observed. These entities are purported to be based on various developments of GR. Yet the fundamental underpinnings of these theoretical entities are not based on the observable universe but on a model that we fully know is “false”.

    Yet, once the idea came to be accepted, it is applied without consideration to the real universe as if these theoretical entities have a reality.

    Mathematics is a wonderful tool, but it makes all sorts of simplifying assumptions to give us approximate answers that are useful for us. Both Newtonian and General Relativity give useful approximations to the evidence we see, but neither can predict accurately the orbits of the planets around our sun. Both require additional tools and models to explain what we see.

    Whether or not GR provides a “better” approximation to what we see, it has its failure points – the evidence is there and has been collected over many years by many different researchers.

    What we are in many ways missing today is the generation of excitement that there is much more to be discovered. The way GR is touted works against building this excitement. It is just one model that gives match to the experimental results we obtain. It, may at this time, give the best match to the experimental results we currently obtain. However, it misses in some very large essentials.

    Finally my apologies at not responding to your comments in your earlier post, I have been under the pump for some considerable time.

    My our Great, Holy and Magnificent God (Father, Son and Spirit) cover you and your family in the weeks and months ahead. May His blessings keep you in His Peace in the days that are coming.


    Bruce Rennie

    1. Jay Wile says:

      Hi Bruce,

      The variations of the earth’s gravity because of its shape play a minor role, but as the scientific paper indicates, they are taken into account. That’s one of the many reasons they used laser distance determination in their calculations.

      Could you explain what you mean by “…a number of predictions made for which the evidence supposedly supports GR but doesn’t actually match.”? I am not aware of any data related to GR where the model doesn’t match the observations to the limit of the measurement’s precision. Also, I don’t know what you mean by GR expecting the world to be “smooth.” It has no expectations on the world, except that it is made up of a 4-dimensional construct. You might be confusing GR with the Big Bang, but they are completely different things. The Big Bang depends on GR, but GR doesn’t depend on the Big Bang in any way.

      Also, I have no idea what you mean when you say that black holes are based on a model that we fully know is “false.” Black holes were predicted by the equations of GR, which is why it was thought that they might exist. GR has is not fully known to be “false.” Indeed, it has been accurate in every one of its predictions that have been tested, and the accuracy is uncanny. Thus, it is certainly not “false.” Also, the existence of black holes is backed by a lot of observational evidence. Even the equations of Newtonian physics show us that there are entities whose mass and size are exactly what is predicted for certain kinds of black holes. Thus, from an observational point of view, black holes are not theoretical entities. They exist, whether we like them or not.

      You say that “Newtonian and General Relativity give useful approximations,” but they don’t. Once again, the data in this analysis indicate that the equations of GR are accurate to the level of precision allowed by measurement. Thus, as far as we can observe, they are not approximations of the universe. They are exact depictions of the universe, at least when it comes to time dilation. Now, of course, more precise experiments might eventually show some deviation from the equations of GR, but if you are being guided by observation, then as far as we can tell, GR gives us an exact explanation of time dilation.

      I also don’t understand what you mean by this generation losing the “excitement that there is much more to be discovered.” In fact, one of the motivations of this experiment was to test GR to see if it deviates from reality in any observable way. If it had deviated, that would have been really exciting. However, it did not. Even if GR is a full description of gravity, that doesn’t mean there is nothing left to discover. The application of GR to the universe leads to all sorts of discoveries. Discoveries that have been made (black holes, gravitational lensing, the gravitational red shift of light, frame dragging, etc.) were all the result of applying GR to the universe. There are lots of other things out there to discover, even if we do have a fully-complete model of gravity. Now, of course, I am not saying we do. All I am saying is that from an observational perspective, GR is by far and away the best description of gravity that exists.

      In the end, you might not like GR. That’s fine. I encourage anyone who is interested to come up with an alternative model. However, to “beat out” GR as the best description of gravity that we have so far, you need to come up with a theory that is at least as wildly successful as GR has been about making predictions that are later confirmed by the data, even to the limit of the measurements’ precision!

  5. John D says:

    I love to disagree with you on this : )

    First off I’d like to suggest that a theory can be correct in both math and phenomenon whilst being way off in it’s conceptual abstract.

    Whilst there might be evidence if time dilation, that phenomenon could easily be produced by any number of field theories which depend on a stronger field near massive bodies. Warped space could easily be swapped out with heavy aether.

    We have to remember that Relativity was a theory that was created to explain an enigma. The failure of the Michelson Morely experiment.

    Also, correct me if I’m wrong but there is no evidence of length contraction.

    Tesla thought the phenomenon could be explained via electromagnetism and hated relativity.

    Regarding GPS,

    GPS technology is not “built around” relativity as is so commonly espoused by people (Neil Ashby) who hail it as proof of relativity. It’s true that relativistic time dilation corrections are programmed into GPS algorithms but GPS works just fine without them. In fact it’s the assertion of people that work on GPS that corrections for relativity are completely ignored by GPS systems and have no bearing on the results whatsoever. One of these men is Ronald Hatch – As an originator of many of the original GPS algorithms and creator of the GPS Hatch filter.


    Also just to approach this with common sense we must understand that GPS is constantly making large corrections for drift, ionospheric effects, solar radiation, magnetic anomalies, etc, etc, etc. And then in spite of all these corrections it uses trilateration to check in.. and ultimately will reset with the atomic clock on the ground. Do you actually think the tiny micro second corrections for relativity mean anything in light of these larger corrections and then ultimate synchronization through triangulation? No. A few mico seconds a day adds up to nothing if the satellite is corrected daily by more accurate ground based clocks. Here’s a little tutorial 2 page tutorial that shows all the real corrections that are being made.. corrections that actually make a difference

    1. Jay Wile says:

      I certainly agree that there are other ways to produce time dilation, but that’s not what General Relativity has done. It didn’t explain the phenomenon once it was discovered. It predicted the phenomenon. Not only that, it predicted the precise way in which time is dilated. That is an extraordinary feat, which has not been matched by any other theory. That’s the point. Also, heavy aether doesn’t work, because the Michelson-Morley experiment showed that if aether exists, it’s in the reference frame of the earth. Thus, it is moving faster than the speed of light for most of the universe. There’s no way light can travel in straight lines in a medium that is already moving faster than light.

      And no, relativity was not created to explain the Michelson-Morley effect. Einstein himself said that he developed special relativity as a first step to producing general relativity. His motivation was because he realized that since the effect of gravity can be removed by being in an accelerating reference frame, gravity cannot be a real force. That’s why relativity was produced. He chose the speed of light as a constant in special relativity because Maxwell had derived the electromagnetic wave equation and showed that the speed of light is, in fact, a fundamental constant.

      And yes, there is strong experimental evidence to support length contraction, which is about special relativity, not general relativity. Nevertheless, experiments at RHIC can only be explained if the nuclei are experiencing length contraction. The energy of beta particles can only be explained by length contraction. Modern synchrotrons also depend on length contraction.

      You are quite wrong about the GPS, as I have pointed out many times before. Hatch is wrong as well. Dr. Fred Singer is the man whose GR treatment is used for the GPS. He discusses it here. Here is one of the original engineering papers that describes how it is done. You can deny it all you want, but that doesn’t change the fact that general relativity is required to keep the GPS working properly.

      The very fact that you don’t know the required time accuracy for the GPS shows that you don’t understand what is going on there. You say, “A few mico seconds a day adds up to nothing if the satellite is corrected daily by more accurate ground based clocks.” That is simply false. The GPS requires an accuracy of 20-30 nanoseconds in order to function properly. Thus, microsecond changes would completely destroy the GPS. Yes, lots of corrections have to be made, but any effect that produces even a few nanoseconds of difference must be taken into account. As the link I give in the original article tells you:

      This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

      So yes, the GPS is one of the many, many confirmations of the equations of general relativity.

  6. Erik Tucker says:

    What was the percentage difference in time ticking speed between closest and furthest distance?

    1. Jay Wile says:

      It’s roughly 0.00004%.

  7. Chris says:

    Dr Wile,

    You say the universe is expanding. What is it expanding into?
    Thank you

    1. Jay Wile says:

      That depends on who you ask, Chris. In the standard Big Bang model, the universe is all there is, and it is expanding. Thus, it isn’t expanding into anything. Everything is simply expanding together. As a result, there is no geometry to the expansion and no “edge” to the universe. Of course, that would make the universe’s expansion different from every other expansion we have ever studied. I consider it more reasonable to assume the universe’s expansion is basically like every other expansion we have ever studied, so the universe is expanding spherically. If that’s the case, then it must be expanding into something. In my mind, the universe is defined by the fabric of spacetime. Wherever there is spacetime, there you find the universe. Past the edge of spacetime is nothing: the void. That’s what I think the universe is expanding into.

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