The Moon’s Subtle Influence

Science or fiction, sometimes it is hard to tell. In 1997, a group of Chinese scientists hooked up a sensitive gravimeter, to automatically record the earth’s gravitational field (or more accurately, the local acceleration of the earth’s crust) in the obscure northeast China town of Mohe, Heilongjiang (Black Dragon River) province. They chose this town because it was near the center of the 1997 solar eclipse, achieving totality for about 2 minutes. They chose the most accurate unit available, it can detect the reduction in gravitation when it is raised 1cm.

After the eclipse they examined their data. They found the usual tidal effects and slow drifts but they also found an interesting signal at the beginning and end of the eclipse, a signal that indicated that the earth’s gravitation field weakened slightly, or that the location was lifted into the air a few cm, or, perhaps, the gravitational field of the sun or moon had increased slightly. Their data, published in Phys Rev D 62, 041101, in units of 10^{-6}cm/s^2 looked like this:

Mohe gravimeter eclipse data

Mohe eclipse data

Let’s look at the data. Our first step will be to look at the elevation of the sun.

Elevation of the Sun
If the Mohe anomaly is due to gravitons emitted from the sun and or moon, then we need to adjust for how far off the horizon these bodies are. The eclipse was observed at latitude 53°29’20” N and longitude 122°20’30” E, on March 9, 1997. Sunrise was at 06:20:00 local time, with first contact at 08:03:29, totality from 09:08:18 to 09:11:04, and fourth (last) contact at 10:19:50. The first anomaly peaked at around 5\times 10^{-6}\; cm/s^2 at around 7:30 while the second anomaly goes to 7.5\times 10^{-6} at 10:20.

To see how far off the horizon the sun was at 7:30 and 10:20, we go to John Walker’s convenient applet Your Sky, and find the sky map for that spot on the earth at that time. Whoops, he doesn’t quite manage to get the numbers exactly right. Here’s his picture for the center of totality, showing the sun erroneously peeking out underneath the moon:

John Walker's eclipse image

John Walker's eclipse image

Okay, so let’s go to Chris Obyrne’s Javacript eclipse calculator and select the 1997 data at the given longitude and latitude. We find that first contact has the sun 14 degrees of the horizon while fourth contact is 28 degrees. This is compatible with Walker’s program having the sun 21 degrees over the horizon at the center of totality.

Now, if the Mohe measurements are to be interpreted as modifications of the total gravity strength due to (a change in) the sun and moon, then, since the earth’s gravity dominates, we need to divide by the sine of the elevation of the sun. At first contact, this is a factor of 4.13, and at fourth contact 2.13; adjusting the anomaly peaks, this gives the first contact peak at around 21\times 10^{-6}\; cm/sec^2 and the fourth contact goes to 16\times 10^{-6}\; cm/sec^2. These numbers are somewhat closer to symmetric than the originals.

Tides and Gravimeters

But we can’t interpret the data as measurements of the force of gravity. It is impossible, in a certain sense, to measure the force of gravity at a single point in space. What a gravimeter actually measures, at best, is an acceleration. Installed properly, this acceleration is the force applied to the base of the gravimeter. Consistent with Einstein’s Equivalence principle, a gravimeter in free-fall will measure no gravitational force.

Consequently, interpreting the anomaly peaks as corresponding to changes in the flux of gravitons is simplistic and wrong. But before we discuss what gravimeters actually do measure, let’s discuss the timing of the anomalies.

Gravitational Timing

A significant difference between Einstein’s theory of gravity and Newton’s is that in Newton’s theory, the force is instantaneous at a distance. For theories based on superluminal gravitons, the timing of the pulses needs to be adjusted.

It takes light from the sun about 8.3 minutes to reach the earth. Consequently, while we detect the center of the total eclipse at 09:09:41, the sun actually emitted that light at 09:01:23. This was the time at which the bodies were in alignment.

Thus, if gravitons travel at very high rates, we would expect that the eclipse’s modification of gravity would be symmetric not around the time of deepest eclipse, 09:09:41, but instead around the actual time of alignment, 09:01:23. Thus those who believe in faster than light gravitons expect the gravitonal eclipse effects to appear around 8 minutes before the photon eclipse effects.

Returning to the Mohe gravity data, we see that the first pulse is almost entirely over by the time of first contact, but that the second pulse is close to coincident with fourth contact. To make these two pulses symmetric with respect to the photon measurements of the time of the eclipse, we have to shift the gravity measurements later by around 7 or 8 minutes.

The Acceleration of the Sun and Moon
In preparation for discussing tides and gravimeters, it’s useful to calculate the acceleration, on the earth, of the sun and moon. Since I am a (hopefully soon to be published) general relativity theorist, I will make these calculations in the professional way, using units of centimeters only. To convert from cm to those ugly pedestrian units involving grams and seconds, we will be setting to unity, the gravitational constant G, and the speed of light c:
1 = G = 6.674\times 10^{-8}\;cm^3/s^2/g,
1 = c = 2.997\times 10^{10}\;cm/s, and so
1 = G/c^2 = 7.43\times 10^{-29}\;cm/g.

Looking in wikipedia’s collection of Solar System values, the masses of the sun and moon, and their distances from the earth, are:

Mass Sun: 1.47798\times 10^{5} cm,
Distance: 1.496\times 10^{13} cm,

Mass Moon: 5.46\times 10^{-3} cm,
Distance: 3.844\times 10^{10} cm.

In theoretical general relativity, the formula for (Newtonian) acceleration is very simple; A = M/r^2. Applying this formula to the above, we get the force that the sun and moon apply to the earth, in units of 1/cm. We can convert these into cm/s^2 by multiplying by c^2. We find:

Sun accel: 6.6\times 10^{-22}/cm = 0.593cm/s^2.
Moon accel: 3.7\times 10^{-24}/cm =   0.00332 cm/s^2.


Sailors know that the moon makes stronger tides than the sun; so it is a little surprising that the gravitational acceleration of the sun is stronger in its effect on the earth. The tidal effects of the moon are stronger because the moon is so close.

Tidal forces are caused not by gravitational accelerations, but instead by differences in gravitational accelerations. The strong tides of the moon are caused by the difference in gravitational acceleration between the side of the earth closest to the moon and the side farthest away. As far as tides go, gravity is a 1/r^3 force, not a 1/r^2.

Gravimeters show tidal forces rather handily. They cannot measure actual gravitational forces. Consequently, when we use a gravimeter to look for gravitational anomalies, we need to interpret what we measure not as a gravitational force, but instead as a tidal force.

Since eclipses last several hours, the data for these sorts of experiments has to be corrected for the usual tidal forces. This means that there are lots of opportunities for getting the wrong answer. Later experiments, particularly with the European eclipse of 2003,

Like I said, I don’t know if this is significant. At least it is interesting. For a recent review of conventional explanations for these sorts of observations, see A review of conventional explanations of anomalous observations during solar eclipses by Chris P. Duif, and Review on Possible Gravitational Anomalies by Xavier E. Amador.

Corpuscular Gravity Shielding

The corpuscular graviton shielding theory is that gravity is a shielding effect; two masses are attracted to each other by their shielding of each other from the effect of an isotropic and universal sea of gravitons. This sort of theory expects to see a reduction in the effect of the combined sun and moon gravitational attraction during an eclipse.

Such a reduction would mean that the earth’s gravity field would become stronger. This is the opposite of the observation above, but there is evidence for a decrease in other gravimeter measurements. See Un Résultat Gravimétrique pour la Renaissance de la Théorie Corpusculaire “An Experimental Gravimetric Result for the Revival of Corpuscular Theory “, Maurice Duval, (in French). These are difficult measurements and difficult interpretation.

For how corpuscular theories of the graviton fit with these observations, see Un Résultat Gravimétrique pour la Renaissance de la Théorie Corpusculaire “An Experimental Gravimetric Result for the Revival of Corpuscular Theory “, Maurice Duval, (in French).


Filed under physics

10 responses to “The Moon’s Subtle Influence

  1. andy.s

    There seems to be some material omitted between

    “Later experiments, particularly with the European eclipse of 2003,”


    “Like I said, I don’t know if this is significant. At least it is interesting.”

    [Carl: I thought that the data from Europe was sketchier than the Chinese data for three reasons. (a) They did not publish their raw data. This is a problem because the effects are a result of subtracting off the much larger known tidal effects. (b) Most of the European data was cut off immediately before and after the eclipse, right where the Chinese data was most interesting. (c) There is a very strong bias in experimental physics to try and interpret data in such a way that it verifies the current paradigm. When you say something else, the implication is that you made a mistake. This makes it difficult to publish, etc. So from a sociological basis, it’s a lot easier to get people to say that they got a null result.]

  2. Todd P

    “Consequently, while we detect the center of the total eclipse at 09:09:41, the sun actually emitted that light at 09:01:23. This was the time at which the bodies were in alignment.”

    hmmm….if the bodies are all moving relative to each other, then the moon and the earth don’t stop moving when the photons leave the sun. Rather the moon is in the path of the light emitted from the sun at 09:01:23 at the moment the photons reach the moon. When the graviton path is eclipsed would depend on the speed and path of the gravitons.

    [Carl: I’m assuming infinite speed for the gravitons, among other things.]

  3. Nige

    In the graph, I presume that the curve the mean of the data points, but there are no error bars for data points. The range of the data point scatter may indicate a type of mean, but that would be implicitly assuming that each data point was 100% accurate. I’m wondering if there is any other effect at play.

    E.g. during the 1919 eclipse which verified Einstein’s general relativity, Eddington et al. found that the cooling effect during the eclipse period (accompanied by an absence of radiant warmth from sun, not just sunlight) produced small thermal contractions in the metal bodies of the telescopes, which nevertheless were larger than the deflection of the starlight by gravity. Therefore, the compensation for these effects introduced some controversy (later measurements were more accurate and provided better evidence).

    Similarly, some kind of thermal effect on the instrument (even just changes in electrical resistance of components, since resistance is temperature dependent) during the cooling period could possibly account for the wariations, seeing that measured effect is so small. It reminds me a bit of the “yes we have no neutrons” Cold Fusion discovery in 1989. (In the video every time the discoverers picked up the neutron counter probe and placed it near the beaker, the neutron count slowly increased as the probe warmed up to hand temperature. In another lab, they got the same effect with no beaker: the neutron probe simply has a very slight dependence on temperature on its efficiency at detecting neutrons in natural background radiation, something the discoverers knew nothing about!)

    So it would be interesting to know if these guys made any attempt to repeat the experiment with a simulated eclipse-type transient temperature rise and fall, to see if the purely thermal effects of the eclipse had an effect on gravity measurements? (I’m temporarily off Facebook while I try to write up a paper, by the way.)

  4. Nige asks “… if these guys made any attempt to repeat the experiment with a simulated eclipse-type transient temperature rise and fall, to see if the purely thermal effects of the eclipse had an effect on gravity measurements? …”.

    Tang, Wang, Zhang, Hua, Peng, and Hu in
    “Gravity Effects of Solar Eclipse and Inducted Gravitational Field”,
    American Geophysical Union, Fall Meeting 2003, abstract #G32A-0735
    “… During the total solar eclipse of March 1997, we conducted a comprehensive geophysical observation at Mohe … From the data we recorded, we found two valleys about 5 to 7 μ Gal.
    Unnikrishnan et al. inferred this gravity anomaly was caused by the environment changes.
    We know that the observation had been conducting in a room inside a small building with a stable coal heating system; the temperature variation inside the experimental room was less 10C during the eclipse.
    Moreover, the measured atmospheric pressure change was less 1hPa during the eclipse.
    It is reasonable to believe that surrounding environment of the observatory excluded the significant gravity variations caused by temperature, pressure variation and local moving of persons and vehicles.
    To further study the gravity effects related to solar eclipses, our scientific team took more observations during Zambia total solar eclipse of June 2001 and Australia total solar eclipse of December 2002.
    After data corrections, we found respectively two gravity anomalies, with 3 to 4μ Gal for Zambia eclipse and 1.5μ Gal for Australia eclipse.
    As many scientists have pointed out that pressure-gravity factor is lower than 0.3μ Gal / hPa,
    it means that any gravity anomaly great than 0.5μ Gal could not be inferred as the results of atmospheric pressure change.
    The two more gravity anomalies recorded during the solar eclipses provided us strong evidences that some gravity anomalies could not simply be inferred as atmospheric pressure change.
    We have tried to explain those anomalies by the induced gravitational field. …”.

    As to what they meant by “the induced gravitational field”,
    maybe it is described by Chen Shouyuan in a paper
    “Induction Gravity From Temporal Variations in Gravity Field During Total Solar Eclipse”
    which said:
    “… The … variation … maybe similar to Faraday’s electromagnet induction … As the moon thrusts between Earth and Sun, the temporal variation occurs …”.

    Tony Smith

  5. Nige

    “We know that the observation had been conducting in a room inside a small building with a stable coal heating system; the temperature variation inside the experimental room was less 1 [degree] C during the eclipse.”

    Thanks, Tony! The temperature change is stated to be less than 1 degree C not 10 C in the abstract you link to. I think that they ignored the effect on the electronics in the instrument. Even less than 1 C change can produce easily observable effects on resistance of some components, particularly when the gravity variation is being measured is so tiny.

    What they have done is to ignore the direct effect of temperature on resistance in affecting the calibration of the instrument for measuring such small gravity variations with a hand-waving dismissal (‘it is reasonable to ignore such small variations’), without actually doing any control experiments with just temperature being varied to see how the instrument response is affected. As the 1989 Cold Fusion ‘discovery’ where a small thermal dependence on neutron count rate caused a hoax claim that fusion neutrons were being detected (when in fact the hand-heated probe was merely more sensitive to background radiation), where you have startling claims from small measured variations, it pays to carefully check all possible sources of experimental error.

  6. Sorry for my typo error that looked like
    “10 degrees C” when it really is “1 degree C”.

    I had done a cut-and-paste from the abstract and the 0 of “10C” came from typography using something like 0 for a degree sign.

    I have not found anything beyond the abstract for the AGU Fall 2003 meeting article,
    so I don’t know the details of how careful (or not) they were about temperature variation effects over the hour or so at the beginning and the end of the eclipse (the times of the observed variations).

    Also, I don’t know what was their exact experimental setup a the two subsequent solar eclipses (Zambia June 20o1 and Australia December 2002) where they claim to have seen similar gravity anomalies.


  7. I also found at
    a link to a pdf file at

    Click to access tangtalk.pdf

    of some slides of a presentation by Tang et al
    that shows some pictures of eclipses in 1997 and 2001 Zambia and 2002 Australia. The data slides for 2001 and 2002 do not look as convincing to me, but there is no explanatory paper and some the caption for 2002 is in Chinese.

    There is also a New Scientist space blog article dated 7 August 2008 that says:
    “… While taking in the 1 August solar eclipse from atop the Great Wall … I ran into … Geophysicist Keyun Tang of the Chinese Academy of Sciences [who] believes that during a total solar eclipse, the gravity … drops … To try to confirm the momentary decrease in gravitational pull, Tang and colleagues set up some extremely sensitive accelerometers, which can measure minute changes in gravity, just a few miles from where we viewed the eclipse. To eliminate as much outside disturbance as possible, they placed their instruments underground, in the basement of a friend’s apartment building.
    It will take them a couple weeks to analyse the results from this year’s eclipse, but tests they’ve done elsewhere – in northern China in 1997, Zambia in 2001, Australia in 2002 – have all shown slight, momentary dips in gravity.
    … Tang … admits even his group’s published results from recent eclipses don’t prove the effect. …”.

    Also, it seems that there will be a total solar eclipse in China on 22 July 2009, so maybe there will be interesting data from it.


  8. Sorry for so many posts (I promise to stop here for now), but further web searching led me to an article by Yang and Wang at

    Click to access yangwang.pdf

    published as Astrophysics and Space Science 282 (2002) 245-253
    which described temperature variations during the 1997 eclipse gravity measurements in a less hand-waving and more specific way:

    “… The outer environment of the observation station: the gravimeter during observations was placed in quiet, dry room without any interference at a room temperature of 15◦ C. The power supply was stable and the gravimeter was kept at a constant temperature.

    The equipment was kept in a constant temperature with +/- 0.1 degree C inside an undisturbed room

    According to the calibration precision of the LaCoste-Romberg (L & R) gravimeter provided by the manufacturer, the variation of 8 degrees C in temperature would lead to 5 μgal change in gravity reading. …
    The actual temperature change in controlled room temperature (15 degrees C) during the eclipse is within +/- 1 degree C, so the actual effect of temperature change is less than 1 μgal .
    Therefore, it is not necessary to make the correction due to temperature variations. …”.


  9. carlbrannen


    thanks for the links. I agree that temperature isn’t likely to be the explanation.

    Theoretically, if gravity is shielded, you should see a big increase in the acceleration in the middle of the eclipse. What’s going on in the nice data I included the plot for, is that the acceleration is instead weak, and that only going into and out of the eclipse.

    To get the observed effect, we would have to have a sort of refraction of gravity, a sort of scattering. This is sort of compatible with my paper in that the paper assumes that gravitons scatter off of gravitons to make new gravitons pointed in the same direction. In any such interaction, there needs to be a characteristic angular diffraction. That is, the gravity-gravity interaction needs to exist for gravitons that are slightly offset in direction. From the Chinese data, the diffraction needs to be something like 1/4 degree or 0.004 radians, i.e. roughly half the diameter of the moon or so.

    Electric charge doesn’t do this; it doesn’t depend on the direction of orientation of the photons. So instead of covering 4 pi ster radians, one ends up with only \pi 0.004^2 = 6×10^ -5 or a reduction of about 1/ 200,000 compared to a force that doesn’t depend on direction.

    Maybe this is why the observed strength of the graviton flux change is so large compared to the pull of gravity and the weakness of relativistic effects.

  10. Nige

    Tony, thanks for that last quotation, which knocks my objection on the head. Carl, could I question the following in your post:

    “The corpuscular graviton shielding theory is that gravity is a shielding effect; two masses are attracted to each other by their shielding of each other from the effect of an isotropic and universal sea of gravitons. This sort of theory expects to see a reduction in the effect of the combined sun and moon gravitational attraction during an eclipse.

    “Such a reduction would mean that the earth’s gravity field would become stronger.”

    I don’t understand this. Possibly you are making some assumptions about the details of the shielding model which you haven’t stated in the post? [Carl: Actually, my model is not the corpuscular. I should have noted that. In the corpuscular model, there is a static background of things that get shielded by gravitational matter. The absence of corpuscles causes attraction. This theory would imply that the background steadily is eaten up by matter which effect is not seen.]

    If you have a theory of shielding which yields F = GMm/r^2 for two fundamental particles, then it will give the same result as as the regular law of gravity for large masses too. I don’t see how there is a departure when the Moon intervenes between Sun and Earth, unless you are assuming that there is a significant shielding of gravitons.[Carl: You’re looking here at graviton-matter interactions. In addition, there could be graviton-graviton interactions. That’s the topic of my paper. It would tend to increase the number of gravitons when the Moon intervenes.]

    There is evidence that the cross-section per fundamental particle for graviton scatter will be extremely small. I.e. gravitons are an extremely penetrating form of radiation, so an enormous flux of them is required even to produce the relatively weak force of gravity. [Carl: Yes.] The 73% of the energy of the universe in dark energy would seem to be gravitons, acting like a gas in pushing matter apart in large scales but acting to push matter together on small scales. [Carl: My assumption is that the gravitons emitted by matter steadily build up imitating the effect of the big bang. Those gravitons interact with other gravitons to make more gravitons, hence the dark energy effect.]

    As a nice analogy, the force from 14.7 psi air pressure in a room would push the walls out explosively and thus “expand” the room if there wasn’t similar pressure pushing inward on the walls from outside. The same air pressure which would cause the room to expand will cause a rubber “suction” cup to be “attracted to the wall”, because the air pressure between the cup and the wall is smaller than that in the room.

    Because of the small cross-section for graviton interactions, the probability of two fundamental particles overlapping on any line of sight is effectively zero, unless you have immense masses (where gravitation needs modification with dark mass and dark energy anyway). [Carl: The only way you can get the graviton-graviton effect to work is if you assume that “orverlapping on any line of sight” means something like “have velocity vectors within a small angle”. To get the effect seen by the Chinese, that small angle has to be something less than 1 degree. To analyze the size of that angle from first principles, you would have to do something like analyze the uncertainty relation between angle and angular momentum. Hmmm.]

    LeSage’s theory predicts that gravity falls faster than the inverse square law, F = (MmG/r^2)exp(-r/x) where x in the exponential component is the mean free path of gravitons in the mass (this exponential equation is analogous to “Beer’s law”, or the simple radiation shielding by matter, considering just the “direct” or unscattered contribution).

    It is valid for the Yukawa strong attraction force mediated by pions, where each nucleon has a cloud of virtual pions created by pair production moving in the very strong electric field around it, so that when two nucleons are close together, the pion fields between them cover a smaller volume of space than on the opposite sides, and the nucleons are pushed together. This of course is why nuclei with many positive charges are held together. As you move two nucleons apart, virtual pions have enough space and thus time to be created between them and the force drops to zero very quickly.

    But with gravity, the mean free path is astronomical in size due to the small cross-section for graviton interactions. So the exponential term is effectively 1 unless you are dealing with immense masses like galaxies. So the quantum gravity law will be indistinguishable from Newtonian gravitation within the solar system, apart from well known general relativistic effects like a tiny (1.5 mm for Earth) radial contraction of masses. So I don’t see how putting the Moon between the Sun and Earth will lead to differences between quantum and Newtonian gravity. [Carl: Yes, the usual physics assumes that quantum graviton effects will be corrections to general relativity. I’m assuming general relativity itself is a quantum gravity effect. So all deviations from 1/r^2 are assumed due to quantum effects. Consequently, the bending of light, perihelion advance of mercury, and the Shapiro delay all have quantum causes. These are all solar system effects.]

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