An Assessment of the Gravity Data Collected at the Mohe Observation Center in China during the March 9, 1997 Total Solar Eclipse
| Scientific Paper | |
|---|---|
| Title | An Assessment of the Gravity Data Collected at the Mohe Observation Center in China during the March 9, 1997 Total Solar Eclipse |
| Read in full | Link to paper |
| Author(s) | Bill Stubbs |
| Keywords | gravity, wang eclipse, gravity anomalies, speed of gravity |
| Published | 2013 |
| No. of pages | 12 |
Read the full paper here
Abstract
An assessment was done of the gravity data collected at the Mohe Observation Center in China during the March 9, 1997 total solar eclipse. After a search for the original tabulated measured data proved unsuccessful, the data was reconstituted by extracting values from a graph of the data found in a report. The reconstituted measured gravity values were processed by removing an approximation of what the gravity would have been had no eclipse occurred, leaving values of the gravity caused by the eclipse. These values were plotted and analyzed. The plot shows that, contrary to previous claims, there does not appear to be any anomalies in the data. The graph also suggests that the gravimeter collecting the data sensed the eclipse about eight minutes before it was visually noticeable. Based on the gravity profile of the eclipse, it appears to have behaved as expected.
Overview
William L. Stubbs re-examines one of the best-known modern claims of an eclipse gravity anomaly. During the total solar eclipse of 9 March 1997 a high-precision LaCoste-Romberg D gravimeter at the Mohe Observation Center (MOC) in northern China recorded gravity through the morning; the published analysis reported two large dips, one just before first contact and one just after fourth contact, which "fueled a plethora of speculation" about gravitational shielding by the Moon. Stubbs' verdict runs against both the original claim and, in a different direction, against the sceptics: he concludes there is no anomaly in the data at all, but that the record does show the gravimeter responding to the eclipse roughly eight minutes ahead of its visual appearance.
The paper is as much a data-forensics exercise as a physics argument. Stubbs could not obtain the 1,760 tabulated readings said to have been taken between 6:00 AM and noon; an exhaustive search of journals and an unsuccessful attempt to reach the World Data Center geophysical database left only two published figures. He therefore reconstituted the dataset by digitising a printed graph by hand, then re-processed it with a different baseline from the one the original authors used. The two conclusions — no anomaly, and an eight-minute lead — both follow from that re-processing rather than from any new measurement.
The argument
Recovering the data from a graph
The eclipse ran from 8:03:29 AM to 10:19:50 AM local time. With no tabular record available, Stubbs worked from Fig. 4 of Wang et al. (Chinese Science Bulletin 1999), which contains three things: a solid curve (labelled 1) of calculated gravitational-tide (GT) values, dots showing the measured gravity (MG), and a dotted curve (labelled 2) of the delta gravity (DG), the MG−GT difference. He laid a grid over the figure in a drawing program, magnified it six times, recorded window x–y coordinates and converted them to gravity values at one-minute intervals from 6:00 to 11:59 AM.
The extracted GT values were smoothed with a third-order polynomial, y = 0.9516x3 − 26.222x2 + 218.67x − 481.17 (x in hours, y in 10−8 m/s2), with R2 = 0.9999, "essentially perfect". Adding the extracted DG back to GT regenerates a set of MG points, and Stubbs argues from side-by-side comparison that the reconstituted plot distributes its points essentially as the published one does.
Why the original baseline was wrong
The heart of the reanalysis is a claim about what was subtracted. The original workers subtracted a calculated gravitational tide from the measurement on the assumption that "the GT calculation does not model the effects of the eclipse, just what would normally factor into the tidal gravity when no eclipse is occurring." Stubbs says the figure refutes this: the theoretical curve "lies practically on top of the measured values during the eclipse", so the gravitational tide model (GTM) was in fact "very successful at modeling the gravity caused by the eclipse". The only places the GTM struggled were the transitions into and out of eclipse configuration, where it over-predicted the gravity — and those over-predictions, in his reading, are exactly the two dips that were mistaken for an anomaly.
A new no-eclipse baseline
To isolate a genuine eclipse signal, Stubbs constructs what the gravity would have been with no eclipse at all. He deletes the measured points between 7:30 and 10:30 AM and fits a fourth-order polynomial to what remains: y = −1.6204516×10−1x4 + 6.8303972x3 − 1.0383281×102x2 + 6.5926227×102x − 1.3892815×103, with R2 = 0.9992. Restoring the eclipse-interval points then leaves a visible separation from this new theoretical gravity (NGT) curve, and the new delta-gravity curve is what he takes to be the true profile of the event.
What the new curve shows
Before the eclipse the residual "flickers between ±3 × 10−8 m/s2", which Stubbs identifies as the precision of the gravimeter. From about 8:00 AM it rises smoothly to a peak near 8 × 10−8 m/s2 around 9:00 AM — close to mid-eclipse — then declines and returns to the noise band shortly after 10:00 AM. There are no dips, no discontinuities: "there does not appear to be any anomalies."
Enlarging the 7:00–11:00 AM window, however, he marks two points. The rise begins at point A, 7:55 AM, whereas visual first contact was 8:03 AM. The drop back into the noise band occurs at point B, 10:11 AM, whereas fourth contact was 10:19 AM. Both offsets are eight minutes, and both are early. Stubbs reasons that since sunlight takes a little over eight minutes to reach the Earth, "what the Sun appears to be doing now really happened eight minutes earlier": the contacts physically occurred at 7:55 and 10:11, and the gravimeter registered them then, while the eye had to wait for the light. His five listed findings end with the conclusion that "the effects of gravity are felt instantly regardless of distance", which he offers in support of the "instantly" camp in the speed-of-gravity debate associated with Tom Van Flandern.
Assessment
The paper's strongest contribution is its scepticism about the original processing, and that scepticism is well founded. A tidal model computed for a given place and time necessarily contains the positions of both Sun and Moon, and a total solar eclipse is by definition a syzygy — so the alignment that produces the eclipse is already inside the model. Residuals taken against such a model are therefore not "the gravity caused by the eclipse" in any interesting sense, and Stubbs is right to say so. His willingness to publish a null result on a subject where an anomaly would be more welcome is also to his credit, as is his frankness about the provenance of the data.
That same point, however, cuts against his own procedure. Having correctly identified that the tidal model contains the eclipse alignment, he replaces it with a fourth-order polynomial in time — a baseline that contains no tidal physics whatsoever. Whatever the real lunisolar tide was doing between 7:30 and 10:30 AM is thereby swept into his "eclipse" signal. The size of the effect confirms this. Evaluating his two published fits at 9:00 AM gives GT ≈ 56.5 × 10−8 m/s2 and NGT ≈ 49.8 × 10−8 m/s2, a difference of about 7 × 10−8 — which reproduces his quoted peak of "about 8 × 10−8" and shows that the peak is nothing but the gap between the tidal model and the polynomial. His result is arithmetically consistent, but it measures the inadequacy of a quartic as a tide predictor, not a property of the eclipse.
The eight-minute inference is the more serious difficulty, and it fails on the paper's own geometry. Light-travel time from the Sun is irrelevant to when an occultation begins. First contact is the moment the Moon's limb crosses the line of sight from the observer to the solar limb, and the Moon is about 1.3 light-seconds away, not eight light-minutes. The sunlight arriving at contact did leave the Sun eight minutes earlier, but it is intercepted at the Moon's present position; there is no eight-minute discrepancy between an "actual" and an "apparent" contact to be detected. Nor should a gravimeter register a contact at all: contacts are line-of-sight events determined by the apparent angular radii of Sun and Moon, whereas the gravitational field at Mohe varies smoothly with the Sun–Moon angle and has no shadow edge to cross. A sharp feature at contact is what one would not expect on any theory of gravitation, instantaneous or otherwise.
There is also a mundane explanation Stubbs does not consider. Points A and B are displaced by the same amount in the same direction, which is precisely the signature of a constant offset in the time axis — exactly what a hand digitisation of a printed figure spanning six hours can be expected to introduce. Eight minutes is about 2 per cent of that span, a fraction of a millimetre on the original page; the author's own six-times magnification cannot remove a registration error present in the source. Given that the entire dataset was recovered by eye from a graph rather than from the 1,760 recorded values, a two-per-cent horizontal shift is not a demanding hypothesis.
Finally, the conclusion drawn from the offset conflicts with direct measurement. The orbital decay of the binary pulsar PSR B1913+16 tracks the quadrupole radiation formula, which presupposes a finite propagation speed; and the coincidence of GW170817 with GRB 170817A constrains the speed of gravitational-wave propagation to within roughly one part in 1015 of the speed of light over some 130 million light years. An eight-minute-per-astronomical-unit advance is not a small correction to those results; it is incompatible with them. Stubbs is careful to write "if this finding stands", and on the evidence presented it does not. What the paper does establish, and establishes usefully, is the negative half of its case: on this record there is no dip, no shielding signature, and nothing at Mohe that requires new physics.