Variations in Gravity

The Variations in Gravity are the supposed variations to gravity due to either the variations in strength of the gravitational field of the earth or due to the presence of masses such as hills or celestial bodies. It is often stated that the strength of gravity decreases with altitude or that the gravity of the Sun and Moon pulls upon the earth's surface.

A number of tests have been conducted in search of these variations. It has been found that in experiments on medium and long ranges, "gravity" does not deviate from the Universality of Free Fall or the Equivalence Principle. The Equivalence Principle is a principle of nature which says that 'gravity' behaves as if the experiment were conducted on an Earth or in a container which was accelerating upwards. Supposedly only a 'local' concept, experimenters have tested this concept at various vertical distances without violation of this principle.

External gravity sources, such as from the Sun, are also unable be felt. Gravity appears to behave as if the earth is accelerating upwards, that the strength of gravity is uniform, and there are no other gravitating sources around us.

Also see Weight Variation by Latitude for discussion on the weight variation by latitude experiments.

Celestial Variations in G
The Equivalence Principle Torsion Balance tests are incredibly reliable precision machines which are used to measure the Equivalence Principal to increasing sensitivity. Experimenters have redesigned the Equivalence Principle's Torsion Balance tests to try and detect the gravity variations caused by the sun, moon, and the tidal forces. It was found that the gravitational influence of the sun, moon, or the tidal forces could not be measured as manifest of the attraction of the bodies in the experiments. Variations to "gravity" did not appear.

Princeton Experiment
From 'The Pendulum Paradigm: Variations on a Theme and the Measure of Heaven and Earth', by Professor Martin Beech, we read the following on p.176:



Essentially, the experiment is summarized as follows:

The masses were not attracted to the sun in the experiment, to an accuracy of one part in one hundred billion.

Moscow State University Experiment
The experiment was repeated and improved by researchers at Moscow State University. The title of the paper states the conclusion:

Verification of the Equivalence of Inertial and Gravitational Mass V. B. Branginsky and V. I. Panov Full Text Link (Archive)

Repetitions
Additional experiments of this class are described (Archive). The first two experiments in this list are the Princeton and Moscow State experiments above:

The Eöt-Wash experiments were repeated by others:

https://plato.stanford.edu/entries/physics-experiment/app4.html (Archive)

Universality of Free Fall
The Newtonian gravitational constant: recent measurements and related studies By George T Gillies

Full Text Link (Archive)

p.200

'''5. Searches for variations in G 5.1. Spatial dependence of G'''

The above says that searches for departures from the inverse square bahavior of Newtonian gravity would be a violation of the Equivalence Principle which says that gravity is indistinguishable from an experiment which takes place on an upwardly accelerating Earth or compartment.

p.202

It should be noted that 500 meters is 1640.42 feet, and about as high as the Shanghai World Financial Center, a skyscraper in China.

Inverse Squared Law
The 'inverse squared law', the 'Universality of Free Fall,' and the 'Weak Equivalence Principle' refers to the 9.8 meters per second squared rate of acceleration. From Foundations of Modern Cosmology we see a description of the inverse square law and how Newton interpreted the phenomenon in coming up with his theory of gravity:

Eöt-Wash Hill Experiments
From No Easy Answers: Science and the Pursuit of Knowledge by Professor Allan Franklin (bio), on p.70 we read a summary of the Eöt-Wash hillside experiments with the rotating torsion balance:

Study Link

An Eöt-Wash presentation explains (Archive) that the influence of an external source mass on these type of experiments would be a violation of the Equivalence Principle (EP).



One will notice from the graphic above that any horizontal pulling phenomenon would violate the Equivalence Principle which states that gravity operates exactly like a rocket ship accelerating upwards at 1G with no other gravitating bodies around.

Short Range Variations in G
Over shorter ranges, such as with the Cavendish Experiment, it has been seen that an attraction was found, but the attraction is not consistent. The strength of "gravity" in the universe changes by over ten fold when tested at different times. This inconsistency suggests that there are other more dominant effects at that range creating or modifying those results and that the experiment has not yet been properly refined to remove all sources of error.

On the topic of the Cavendish Experiment, the Encyclopedia Britannica article discussed below says:

For further information see the Cavendish Experiment

Encyclopedia Britannica
Encyclopedia Britannica has provided an article on the experimental study of gravity. Aside from the gravimeter devices which have been shown to be seismometers (See: Gravimetry) and the Cavendish Experiment, which is an inconsistent short range experiment, Encyclopedia Britannica agrees that there are no variations in gravity:

https://www.britannica.com/science/gravity-physics/Experimental-study-of-gravitation (Archive)

Torsion Balances
On the topic of the Torsion Balance tests discussed above which attempted to measure the gravitation of the sun, Encyclopedia Britannica says:

{{cite|Experiments with ordinary pendulums test the principle of equivalence to no better than about one part in 10{{sup|5}}. Eötvös obtained much better discrimination with a torsion balance. His tests depended on comparing gravitational forces with inertial forces for masses of different composition. Eötvös set up a torsion balance to compare, for each of two masses, the gravitational attraction of Earth with the inertial forces due to the rotation of Earth about its polar axis. His arrangement of the masses was not optimal, and he did not have the sensitive electronic means of control and reading that are now available. Nonetheless, Eötvös found that the weak equivalence principle (see above Gravitational fields and the theory of general relativity) was satisfied to within one part in 10{{sup|9}} for a number of very different chemicals, some of which were quite exotic. His results were later confirmed by the Hungarian physicist János Renner. Renner’s work has been analyzed recently in great detail because of the suggestion that it could provide evidence for a new force. It seems that the uncertainties of the experiments hardly allow such analyses.

Eötvös also suggested that the attraction of the Sun upon test masses could be compared with the inertial forces of Earth’s orbital motion about the Sun. He performed some experiments, verifying equivalence with an accuracy similar to that which he had obtained with his terrestrial experiments. The solar scheme has substantial experimental advantages, and the American physicist Robert H. Dicke and his colleagues, in a careful series of observations in the 1960s (employing up-to-date methods of servo control and observation), found that '''the weak equivalence principle held to about one part in 10{{sup|11}} for the attraction of the Sun on gold and aluminum. A later experiment by the Russian researcher Vladimir Braginski, with very different experimental arrangements, gave a limit of about one part in 10{{sup|12}} for platinum and aluminum.'''

Conclusion
The Britannica article concludes:

Searching for Extra Dimensions
From the introduction of Searching for Extra Dimensions and New String-Inspired Forces in the Casimir Regime (Archive), its authors Dr. Dennis E. Krause (bio) and Professor Ephraim Fischbach (bio) tell us:

The Weak Equivalence Principle is the principle of nature which states that the gravity behaves as if the observer were on a surface which was accelerating upwards. The Inverse Square Law is the law which says that bodies will fall at inverse proportion to the square of the distance from the Earth. The above states that experimentalists have searched for violations in the WEP and the Inverse Square Law on ranges from 10-3 m to 1015 m and that "no such violations have been observed".

History of the Torsion Balance
The history of the Torsion Balance experiments began in 1889, with Barron Rosland von Eötvös' attempt to detect the Coriolis force.

Foundations of Modern Cosmology By Professor John F. Hawley, and Katherine A. Holcomb

From p.219 of the above text we read:

Official Explanation: Selective Gravity
The paradox that external celestial gravity from the Sun and other effects cannot be felt by the test bodies in the torsion balance experiments of Dicke, Eötvös, and others, is acknowledged and addressed by mainstream science with the concept of selective gravity. In the book Gravitation by physicists Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, on the topic of the Dicke-Eötvös experiments, we read the following at the bottom of p.1055 (Archive):

The reader is left to decide whether this answer, which was invented for the purpose, is sufficient or valid.