# Is there an anomalous variation of distance between Earth-Moon during a lunar eclipse?

Apart from normal (expected) variation of distance between Earth and Moon in any given time interval, what happens during a lunar eclipse by way of some unexpected (anomalous) deviation? Have lunar ranging measurements been used to detect the smallest, if any, deviation of the distance that is projected from before and after the lunar eclipse orbit?

Put another way: If the distance is measured at regular intervals short enough to plot the distance starting a few hours before, during and ending a few hours after the lunar eclipse, a "bulge" or "trough" on the curve, if present, would be of great interest. Has this been done?

• You think there's an influence of light pressure? Because in all other respects lunar eclipse doesn't differ from regular Full Moon that happens every 28 days, it just so happens the Moon, Sun and Earth are all in straight line from each other, not minimally offset from it.
– SF.
Nov 9 at 11:03
• @SF - I suppose an answer would be to calculate the light pressure that the Moon receives on average in its orbit, vs the light pressure that it receives during a typical total lunar eclipse. Then compare the difference in force to the force needed to change the Moon's orbit enough to be detected. Likely any change would be undetectable even over time, but if someone can provide some numbers that would help illustrate the point. Perhaps the change in orbit would be so small as to not be noticed for centuries, by which time it would be undecipherable from other effects on the Moon's orbit. Nov 9 at 13:11
• gerryD - my previous comment to @SF was based on the extremely thin possibility that reduced light pressure during a lunar eclipse could cause a change in orbit measurable over long periods of time, like decades. However your recent edit now says that you are looking for immediate measurable changes in the Moon's distance during an eclipse. The answer you received from PM2Ring estimates that at best there might be a change in distance of maybe a few dozen nanometers (a nanometer is a millionth of a millimeter). I think your edit pushes the question outside of reasonable possibility. Nov 10 at 4:31
• @Steve Pemberton: No problem with me and thank you. Only to say that my question (in three forms) is about the same thing with no mention to light pressure (I could not have it clarified earlier). Nov 10 at 6:02

The LLR experiment data can be downloaded from Paris Observatory Lunar Analysis Center. Comparing this with NASA Lunar Eclipse catalogs shows that the experiment has been active on the same date as a total lunar eclipse on 15 occasions:

1971-02-10, 1971-08-06, 1975-05-25, 1975-11-18, 1979-09-06, 1990-02-09, 1996-09-27, 2000-01-21, 2008-02-21, 2010-12-21, 2014-04-15, 2015-09-28, 2018-01-31, 2018-07-27, 2019-01-21

I plotted the raw data from 2019-01-21:

As expected, there are no obvious anomalies visible at this resolution. Total lunar eclipses will usually occur near the time when the Moon is closest to Earth. In this case you can see the closest approach occurring at 07:30, two hours after the end of total eclipse.

Note that the available ranging data begins after and ends near the penumbra contact times P1 = 02:36 and P4 = 07:48. This is because the light of the full Moon masks the laser returns. The Apollo 15 retroreflector has the largest surface area, providing the brightest return pulse.

Of course this is just a crude analysis and more careful correlations with lunar orbit models could reveal more. But I suspect they don't, and I haven't found any published papers on the subject.

Here is a comparison against simple parabolic fit on the Apollo 15 reflector data, allowing a more detailed look at the microsecond level. As can be seen, the motion of the moon has complex variations at every level.

• Thank you so much for the closest answer I could get. The databases you provided will keep me busy for some time. I will try to add to your plot a few extra hours before and after the peak of the event, just in case it might reveal something new. At any rate, if you feel inclined to delve a bit deeper at a later stage, I would be delighted to hear from you again. Without prejudice, my aim is to see if there is a gravitational deviation from known theory. The big problem is that various models are used to fit the experiment, but models can also fudge unknown influences. Nov 10 at 11:43
• @gerryD Nice to be of help. I don't think I'll dig deeper, but it was an interesting thing to check out. The lack of LLR data of full moons without eclipse is a bit annoying, otherwise it would provide a nice reference to compare against.
– jpa
Nov 10 at 13:01
• @gerryD You're checking if the Earth blocks gravitons between the sun and the moon? lol, although most new physics ideas sound absurd, this one actually makes so much sense I'm surprised it hasn't been done. Nov 10 at 13:57
• @JollyJoker: Almost. Nov 10 at 21:19
• @gerryD No, I'm not able to say that there is no anomaly. Only that the motion is complex enough that there is no trivial analysis that can provide proof of an anomaly. Considering how accurately we now know positions and masses of all major bodies in our solar system, it seems that it should be possible to create an accurate model - but it certainly isn't a small task!
– jpa
Nov 11 at 11:51

The deviation in the Moon's position due to the reduced light pressure during a lunar eclipse is too small to measure, even with Lunar Laser Ranging (LLR). However, the reduced surface temperature may have an effect on the lunar orientation (hot rock expands, raising its centre of gravity), but I suspect that would be hard to separate from the effects caused by the increased tidal force on the Moon when the Sun, Earth, and Moon are aligned during an eclipse.

The JPL ephemeris calculations use a very sophisticated model of the Moon. The ephemeris is calculated by integrating the equations of motion of the major masses of the Solar System (including 343 asteroids), and then fitting the numerically integrated orbits to ground-based and space-based observations. For details, please see The JPL Planetary and Lunar Ephemerides DE440 and DE441, Park et al (2021), DOI 10.3847/1538-3881/abd414
in particular, section 2.4 Orientation of the Moon, and section 4 Rotational Dynamics of the Moon.

The motion of the Moon is quite complex, and we cannot model it analytically to the precision matching the LLR measurements. As I said recently on Astronomy.SE, the lunar theory of E. W. Brown, developed around the turn of the twentieth century, used over 1400 terms. The more recent Éphéméride Lunaire Parisienne (ELP), developed by Jean Chapront, Michelle Chapront-Touzé, et al, "contains more than 20,000 periodic terms, [but] it is not sufficiently accurate to predict the Moon's position to the centimeter accuracy with which that can be measured by LLR". Note that ELP was not fitted directly to observations but to the JPL DE, initially DE200, but it was later updated to DE405.

It's kind of hard to spot anomalies in the Moon's motion because our lunar motion models have been adjusted to match our observations. I suppose there might be terms in the ELP equations that correspond to light pressure, but I haven't studied the details of that theory.

Light pressure is important for modelling the motion of small bodies, including spacecraft, but its effects on large bodies is negligible, and effectively causes a slight reduction in the body's attraction to the Sun.

According to Wikipedia's article on radiation pressure the solar radiation pressure at 1 AU is ~$$9.08×10^{-6}\,\rm N/m^2$$. We can estimate the force this has on the Moon by multiplying that by half the Moon's surface area (~$$3.793×10^{13}\,\rm m^2$$), which gives a force of ~$$1.722×10^{8}\,\rm N$$. Dividing by the lunar mass (~$$7.342×10^{22}\,\rm kg$$) yields an acceleration of ~$$2.345 ×10^{-15}\,\rm m/s^2$$, which is pretty tiny. Over a 2 hour lunar eclipse, such an acceleration would cause a displacement of just under $$61$$ nanometres. (The lunar parameters in the above calculations are from Wikipedia).

I'm being generous in that calculation. We probably should use the cross-section area, which is approximately one quarter of the surface area. On the other hand, the pressure is doubled for a perfect reflector, but I've ignored that because the Moon's albedo is only ~$$0.136$$, so only $$13.6$$% of the sunlight is reflected and the other $$86.4$$% is absorbed. Also, at Full Moon, the Moon is further from the Sun than the Earth is, but the Moon's orbital radius is smaller than the variation in the Earth-Sun distance, and the radiation pressure value we're using is derived from a mean value for the solar energy flux.

I should mention that it is difficult to make LLR measurements at Full Moon. The LLR detectors only receive a small number of reflected laser photons, and at Full Moon the signal is swamped by sunlight. Also, the two Lunokhod reflectors are unusable at Full Moon, due to thermal expansion, so only the three Apollo reflectors can be used. However, the LLR observing stations do try to take advantage of lunar eclipses.

I should also mention that although we know the distances of the lunar laser reflectors to sub-centimetre precision, we do not know the location of the Moon's centre of mass to the same precision. At the centimetre scale, the Moon is not a rigid body, it's a big wobbly ball of looney mooney... stuff. ;) As mentioned in Park et al, the JPL model does account for the Moon's liquid core, but it's difficult to do that accurately over timespans >1000 years.

• FWIW, here's a nice article on LLR from 2020: Recent Progress in Lunar Laser Ranging at Grasse Laser Ranging Station. It's moderately technical, but should be (mostly) readable by non-specialists. Nov 9 at 16:04
• "although we know the distances of the lunar laser reflectors to sub-centimetre precision..." hmm for this section I'm not sure it's so simple. Yes the Moon is indeed made of looney mooney stuff, do we know at a given moment the distance to sub-centimetre precision from only a few photons received, or is it only after an extensive measurement campaign that we can fit a smooth trajectory of that spot on the Moon to say weeks or months of noisy measurements.
– uhoh
Nov 9 at 22:03
• Here's a fascinating article on differential lunar laser ranging, which expects to improve accuracy to 30 microns! Nov 10 at 0:12
• @gerryD Because of the power of its laser, the Apache Point site (APOLLO) is the best at handling Full Moon measurements. From the previously linked paper, "On five occasions, APOLLO has undertaken extended ranging sessions (e.g., during lunar eclipses) that have produced more than 20 NPs per session." Nov 10 at 8:26
• Note that there are improved retroreflectors in the pipeline. Next-generation Laser Ranging at Lunar Geophysical Network and Commercial Lander Payload Service Sites Nov 10 at 8:30