# The Law of Universal Gravitation

Gravity is so well established it has been considered a law for a long time.

In this video from 1964 Richard Feynman gives a lecture on the proof of the Law of Universal Gravitation. Notice that he doesn’t call it a “theory”, he calls it a “law”.

Gravity has been proven many times in many ways. One amazingly awesome example is the LIGO experiment where they measure gravitational waves from supernovas. The LIGO experiment is very similar to the Michelson-Morley experiment where they were trying to measure the effect of Luminiferous aether and concluded there was no aether. This experimenters at LIGO have authored over 170 papers. Below is a list of the papers that have come out of the LIGO experiment:

https://www.lsc-group.phys.uwm.edu/ppcomm/Papers.html

Cavendish style experiments have been done many times since Mr. Cavendish initially performed his experiment. This experiment confirms gravity as two masses attracting each other, and it can also be used to measure the Universal Gravitational Constant.

Anyone can purchase their own pre-made instrument to perform the experiment for about $1000. There are many of these in universities and students regularly perform this experiment as a regular part of physics classes

# See gravity in action

# Measuring “G”

Big G, called the “Universal Gravitational Constant”, also called the “Newtonian Constant of Gravitation”. The Universal Gravitational Constant is difficult to measure because gravity is the weakest of the 4 fundamental forces. It’s made more difficult since measuring it cannot easily be performed outside the gravitational influence of the earth. The Cavendish Experiment is specifically designed to neutralize this force but is it still very sensitive.

In 2000 a very thorough experiment was done by Jens H. Gundlach, and Stephen M. Merkowitz to measure G.

The published paper is called “Measurement of Newton’s Constant Using a Torsion Balance with Angular Acceleration Feedback”. You can look at the overview here: https://arxiv.org/abs/gr-qc/0006043 and you can directly download and read the full published paper here: https://arxiv.org/pdf/gr-qc/0006043.pdf. This experiment was so well controlled that they measured the constant with an uncertainty of just 14 parts per million. The value the measured is 6.674215 × 10^{-11 }± 0.000092

In 2018 another experiment was performed that measured the Universal Gravitational Constant even better using two different methods. The values measured are 6.674184 × 10^{-11} and 6.674484 × 10^{-11}. The uncertainty is 11.64 and 11.61 parts per million respectively. You can download the PDF and read it, it’s very detailed and has nice pictures.

# Measuring “g”

Little “g” is the strength of the gravitational attraction between two objects, like the earth and and any object on the surface of the earth. This can be directly measured with a Gravimeter. These can be extremely accurate. The FG5-x Absolute Gravity Meter pictured is one high precision example.

The Law of Universal Gravitation is expressed in a function:

Fg = G (m_{1} * m_{2} / r^{2})

Where:

m_{1}, m_{2} = the masses of the different objects

r = distance between the object

G = gravitational constant: 6.674215×10^{−11} N × kg^{–2} * m^{2}

This formula can be used to confirm the observations and predict future observations.

Little “g” varies based on the distance between the objects. If an object on the earth is at a higher altitude it should experience less gravity.

This prediction has been confirmed. See this paper where the force of gravity was measured at 10 locations in Malysia at high altitudes, the lowest measured value was 9.7793997m/s^{2} at an elevation of 575.3 meters. Oslo, Norway has one of the cities with the highest measured gravity value. This is predicted as it is about 60 degrees North latitude so the oblateness of the earth means the surface of the ground is slightly closer to the center of mass of the earth. There is a gravity station in the Oslo Airport, The value measured is 9.8191767m/s^{2}.

If you’re interested, you can even have a look at all the gravity stations in Denmark.

The lowest measured gravitational acceleration has been measured at Mount Nevado Huascarán in Peru, at 9.7639m/s^{2. }The surface of the Arctic Ocean has the highest, at 9.8337m/s^{2}.

# How did we get that Formula?

This formula wasn’t invented out of thin air, it was derived using observations. There are many ways to do this and get the same formula. One such example is a concise video by AB Science using the measured movement of Jupiter’s moons.

Other videos:

# It does exist

Surprisingly there are people that doubt the existence of gravity today. There have been small efforts to attempt to offer an alternative explanation for the approximate 9.8 m/s^{2} acceleration that is consistently measured on the surface of the earth.

One of the humorous alternatives is “density and buoyancy”. It’s funny because the buoyant force requires gravity to function.

Since gravity has been thoroughly proved in many ways, some listed in this article, the burden of proof rests heavily on the people making the claim that the Law of Universal Gravitation isn’t a law. A replacement for the Law of Universal Gravitation must be presented that offers a better solution.

Should someone attempt to do this a good place to start would be offering a replacement for the gravitation formula mentioned above. The acceleration consistently measured all over the earth matches the current formula, a different formula will need to, at the very least, output the same 9.8m/s^{2} measured on earths surface. Then something to account for the confirmed variations at different locations will need to be confirmed.

Once a formula has been provided some experimental evidence showing that masses ** do not** attract each other would be helpful.

Later in this process many of the other research papers and experiments related to gravity would need to be disproved or otherwise explained away. For example, all the publications that have come out of the LIGO experiment, listed above, would need to be addressed.

Having a keen interest in this topic, should someone make any progress in the area, I would be happy to assist in reviewing or co-authoring these papers. Send me an email with your current progress and I’ll be happy to assist. Something successfully replacing gravity would undoubtedly merit the Nobel Prize. I look forward to sharing this prestigious honor.

# List of publications on gravity

- Publications of the LIGO Scientific Collaboration and Virgo Collaboration
- Measurement of Newton’s Constant Using a Torsion Balance with Angular Acceleration Feedback
- Jens H. Gundlach, Stephen M. Merkowitz
- (Submitted on 13 Jun 2000 (v1), last revised 8 Aug 2000 (this version, v2))
- https://arxiv.org/abs/gr-qc/0006043
- Direct PDF Download

- Measurements of the gravitational constant using two independent methods
- Li, Qing & Xue, et al, Jun. (2018). Nature. 560. 10.1038/s41586-018-0431-5.
- https://www.nature.com/articles/s41586-018-0431-5
- Direct PDF download

- Improved Determination of G Using Two Methods
- Terry Quinn, Harold Parks, Clive Speake, and Richard Davis

Phys. Rev. Lett. 111, 101102 – Published 5 September 2013 - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.101102
- Direct PDF Download

- Terry Quinn, Harold Parks, Clive Speake, and Richard Davis
- Determination of the Gravitational Constant with a Beam Balance
- St. Schlamminger, E. Holzschuh, and W. Kündig

Phys. Rev. Lett. 89, 161102 – Published 30 September 2002 - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.89.161102
- Direct PDF Download

- St. Schlamminger, E. Holzschuh, and W. Kündig
- Reflections on a Measurement of the Gravitational Constant Using a Beam Balance and 13 Tons of Mercury
- S. Schlamminger, R.E. Pixley, F. Nolting, J. Schurr4 and U. Straumann
- https://arxiv.org/abs/1407.5214
- Direct PDF Download

- An Account of Observations Made on the Mountain Schiehallion for Finding Its Attraction
- Nevil Maskelyne, 1775
- https://royalsocietypublishing.org/doi/10.1098/rstl.1775.0050
- Direct PDF Download

- An Account of the Calculations Made from the Survey and Measures Taken at Schehallien
- Charles Hutton, 1778
- https://royalsocietypublishing.org/doi/abs/10.1098/rstl.1778.0034
- Direct PDF Download