The gravitation of the Moon is a Vector Force, which passes through the Earth. At the moment of Moonrise for a given location, the gravitational attraction of the Moon on the bob of a long pendulum inside a deep borehole will pull the pendulum eastward, probably exactly 3.38561456 millimeters. A few hours later, at the moment of Moonset, the Moon's Gravitational Vector Force necessarily pulls the pendulum bob that same distance (but now westward). We have laser interferometry equipment that can monitor that movement to better than a wavelength of light. Such an experiment, which is relatively simple to do, should improve our accuracy of the Gravitational Constant by better than a factor of a thousand.
I am surprised that Isaac Newton himself did not think of the experiment described here. He probably could have performed it 300 years ago.
Graphic is of a heavy (metric tonne) pendulum hanging in a 24 hour 50 minute cycle in a kilometer deep borehole, beginning at the moment of Moonrise for that particular location. The Pendulum is gray. The Moon is momentarily in the direction indicated by the arrow. The bedrock surrounding the borehole is not shown in this graphic. At the bottom of the graphic, the centerline of the borehole is indicated as well as the instantaneous location of the centerline of the pendulum (indicated in red). The instantaneous horizontal offset of the pendulum in the borehole is given in millimeters, at the time in the 24 hour 50 minute tidal cycle of the Earth's rotation and the Moon's orbiting.
Modern scientists seem infatuated with gravitation but none of them seems to realize that the Moon exists. Newton's gravitation is a VECTOR equation, which seems to be overlooked.
Consider this very simple experiment. An extremely carefully vertical borehole is made, at the Equator or anywhere else, a little more than a kilometer deep and twenty centimeters or more in diameter. A solid steel rod of 5-cm diameter and 5 meters long is used as a metric tonne pendulum weight, suspended on a cable one kilometer long, which does not rub against any walls. The steel rod has two first-surface mirrors on opposite sides, toward the west and the east. Mounted on both proximate walls of the borehole are two more first-surface mirrors, which are tilted exactly 45 degrees. This is essentially the entire experimental apparatus.
Two laser interferometry light beams are sent down both sides of the borehole to reflect off the angled mirrors, to then reflect off the fixed mirror on the steel rod, then back to the angled mirror and back up to the surface. This will constantly (doubly) monitor the precise lateral position of the pendulum rod to a fraction of a wavelength of light.
At the moment of Moonrise for that location, the gravitational Vector force due to the Moon will be horizontal, toward the east, with an amplitude of 0.03317902 newton (per Newton's gravitational Vector equation). At this moment, the Moon will pull the pendulum around 3.38561456 millimeters toward the east from its natural location. Six hours later when the Moon is nearest its Zenith, that effect will be vertical and the lateral position will revert to its standard borehole centerline location. Six hours later yet, the Moon will be at Moonset, and that gravitational attraction of the Moon will pull the pendulum about 3.38561456 millimeters toward the west. This interferometry method of measuring the position is good (for visible light) to about 1/100,000 millimeter. Data that are even more accurate might be possible with an ultraviolet laser or maser. The graph of the results will be a sinusoidal graph with a precision of about 1/700,000 part or better. The borehole will be sealed so that no wind currents could occur. No temperature effects would occur in this very deep borehole. Since this same graph will be repeated every 24 hours and 50 minutes, we will statistically obtain an extremely precise value for the gravitational Vector force due to the Moon. Using Newton's equation will provide us with a value for Newton's Gravitational Constant that is many thousands of times more accurate than previous experimental results.
The exact experimental data will vary due to variations in the orbit of the Moon and the exact azimuthal direction of the Moonrise on that day for that location on Earth, but all that data is very precisely known.
Such an experiment could be set up in a few days and for minimal cost. Forever after that, we will have continuous monitoring of the Moon's gravitational effect, and therefore also the Earth's gravitational effect to wonderfully more accurate precision.
We are NOT using our pendulum AS a pendulum. There is no source of the necessary power involved, so, except for the Moon's daily Gravitational attraction force, the pendulum would hang motionless inside the borehole. In fact, for a pendulum of the dimensions described, IF we actually did provide any power it to swing, as a pendulum, it would swing around each 63 seconds. These facts are important in ensuring that the Gravitational attraction of the Moon on the pendulum bob is the only action which occurs. This ensures that the data collected is as precise as we have achieve it. There are some mathematical adjustments which must be made to this data. At every day at the moment of Moonrise, the orbit of the Moon is such that the Moon will not be precisely eastward. A simple cosine factor must be applied for the final precise result. This "due east" result will repeat almost twice every day, so in a month of data, we would collect more than 50 precise values. Another mathematical adjustment is required regarding the instantaneous orbital radius of the Moon at the moment of the measurement.
During the past forty years, thirteen very careful experiments have been performed, but their results have been dreadfully different from each other. I believe that those previous values might now be greatly improved. None of those experimenters had given any thought to where the Moon was in the sky for the location of their apparatus on Earth and for the exact time when their experiment was performed. Since we know where and when each of those earlier experiments were performed, it would be simple to calculate the gravitational effect of the Moon on the Barycenter at that instant. The previous results might be corrected for the Vector Addition effect of the Moon on our Barycenter, and those previous results might be more compatible with each other. However, even then, such previous experiments can not compete regarding precision with the apparatus described here. If the borehole is not made at the Equator, then some additional space angles would need to be included, along with the Moon's orbital path.
The same borehole described above might also be used for a confirmational experiment. Rather than monitoring the lateral motions of the pendulum, this experiment monitors the vertical effects of the Vector Addition of the gravitation of the Earth and Moon. A low-friction but strong pulley would be mounted with its shaft horizontal near the very top of the borehole. A second, identical, steel rod weight is used as a second pendulum, where the two share a mutual supporting cable, over the pulley. The second pendulum would be near the very top of the borehole. The two identical pendulums would then have a gravitational radius of exactly one vertical kilometer difference. A "strain gauge" is attached to the longer supporting cable near the top, and to the sidewall of the borehole, as otherwise, the difference in the vertical force would cause the pendulums to move vertically. The strain gauge would constantly monitor and resist a strain of 313.590 grams (plus the weight of the longer supporting cable. This value would be measured when the Moon was at either Moonrise or Moonset, when only the Earth's gravitational Vector Force is acting on the apparatus. When the Moon was nearest its Zenith, the strain gauge reading would reduce by around 3.4 grams. When the Moon was nearest its Nadir, the strain gauge reading would increase by about 3.4 grams. This experiment again would provided repeated results every day, where the vertical Vector Addition effect would provide a value for Newton's Gravitational Constant that is far better than previous experimental apparatus have provided. No one seems to be interested in monitoring the precise location of the Barycenter within the Earth, but the results of both these experiments could also provide that continuous data.
There is yet another experimental benefit of this apparatus. Imagine that a hundred such boreholes were made around the Equator of the Earth. If some external cause affected the precise value measured (at that instant), such as a Gravity Wave, it might then also be possible to confirm or deny that gravitation occurs at the speed of light or whatever other speed it uses, as the data from the hundred boreholes might show a pattern of change. If such results were detected, it might even suggest an exact direction that the gravitational aberration had come from.
Carl W. JohnsonE-mail to: firstname.lastname@example.org
Carl W. Johnson, Theoretical Physicist, Physics Degree from University of Chicago