Gravitational Constant - Discovery - History - Application

tahanson43206 · 2024-08-20 05:36:51

This topic is dedicated to collection and presentation of information about the gravitational constant "G"

The term most recently showed up in the Python program written by ChatGPT4o to support an attempt to animate the equations prepared by GW Johnson for his course on Basic Orbital Mechanics.

I first read about the discovery (measurement) of the Gravitational Constant years ago in a book about the history of physics, and this topic is available for NewMars members to contribute examples of that history.

No doubt Wikipedia will have a well written (and thoroughly edited) version of the history.

This topic is also available for presentation of examples of the use of G in calculations for navigation within the Solar System (or any such system).

To start things off, here is the Britannica version of the definition, per Google:

What is the G constant value?
In Newton's law of universal gravitation, the attractive force between two objects (F) is equal to G times the product of their masses (m1m2) divided by the square of the distance between them (r2); that is, F = Gm1m2/r2. The value of G is (6.6743 ± 0.00015) × 10−11 m3 kg−1 s−2.Jun 21, 2024
Gravitational constant | Definition, Value, Units, & Facts
Britannica
https://www.britannica.com › Science › Physics

My recollection is that the value of G was measured by an enterprising researcher who placed two masses next to each other and measured the movement of the masses toward each other due to gravitational attraction.

This topic will include discussion of Einstein's interpretation of gravity as the bending of spacetime.

(th)

tahanson43206 · 2024-08-20 05:37:55

This post is reserved for an index to posts that may be contributed by NewMars members over time.

(th)

tahanson43206 · 2024-08-20 05:41:53

The direct measurement of the value of G that I remember from a book about the history of physics, is reported in Wikipedia as follows:

https://en.wikipedia.org/wiki/Gravitational_constant

The first direct measurement of gravitational attraction between two bodies in the laboratory was performed in 1798, seventy-one years after Newton's death, by Henry Cavendish.[15] He determined a value for G implicitly, using a torsion balance invented by the geologist Rev. John Michell (1753). He used a horizontal torsion beam with lead balls whose inertia (in relation to the torsion constant) he could tell by timing the beam's oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused. In spite of the experimental design being due to Michell, the experiment is now known as the Cavendish experiment for its first successful execution by Cavendish.
Cavendish's stated aim was the "weighing of Earth", that is, determining the average density of Earth and the Earth's mass. His result, ρ? = 5.448(33) g⋅cm−3, corresponds to value of G = 6.74(4)×10−11 m3⋅kg−1⋅s−2. It is surprisingly accurate, about 1% above the modern value (comparable to the claimed relative standard uncertainty of 0.6%).[16]

The Wikipedia article included mention of reasons for uncertainty in the value of G that have been present ever since Cavendish. The most recent measurements have (apparently) involved experiments at the atomic scale, using advanced modern technology.

(th)

GW Johnson · 2024-08-20 13:49:28

The value I have been using for estimating orbits (quite accurately I might add) is G = 6.6732 x 10^-11. It came from a 1973-vintage edition of the CRC Handbook for Chemistry and Physics.

GW

tahanson43206 · 2024-08-20 14:45:28

For GW Johnson!

Thanks for showing the value of G from a 1973 reference.

The modern value seems only slightly different: The value of G is (6.6743 ± 0.00015) × 10−11 m3 kg−1 s−2.Jun 21, 2024

That value is quoted by Britannica ... I don't know the source.

The value you cited is very slightly lower: 6.6732 x 10^-11.

My question is: What difference might these two values make in a trajectory calculation?

James Miller refers to G (the gravitational constant) but does not explicitly state it in Planetary Spacecraft Navigation. I will keep looking for any more specific mention. Since his career spans 50 years, it would not be at all surprising to me if he used the value you quoted for most of that time.

In quickly scanning through the book, I get the impression that there are inputs for navigation that are far more significant than the small difference in G that we are talking about here. For example, the radio signals used for spacecraft location travel through media that varies over the distance travelled, so there is uncertainty about how long the electromagnetic waves took, and therefore how far away the object is.

Other inputs that influence trajectory planning include non-gravitational acceleration, such as outgassing of molecules from the spacecraft itself as it travels while under the "gaze" of sunlight.

Other inputs that influence trajectory planning are gravitational in nature, but which are difficult to evaluate when the spacecraft is far from the Sun and far from the Earth, but nearer to large objects not yet known to human astronomers, or more importantly, to flight planners.

For GW ... if you can run a quick ? check using the modern value for G vs the ancient 1973 value, I'd be interested to know if it makes any difference in the near-Earth context.

(th)

tahanson43206 · 2024-08-20 15:01:42

In an effort to try to ferret out the most accurate value of G that is currently known, I found this:

There is a precise ideal value of the universal gravitational constant which equals 6.674010551359 × 10−11.
Precise Ideal Value of the Universal Gravitational Constant G

Here is an extended discussion. It appears the paper is a theoretical study, which refers to experimental results that are greater or less than the theoretical value.

For the purposes of this topic, I will not show the greater part of this work...

Journal of High Energy Physics, Gravitation and Cosmology > Vol.3 No.2, April 2017
Precise Ideal Value of the Universal Gravitational Constant GAbed El Karim S. Abou Layla
Independent Researcher, Gaza City, Palestine.
DOI: 10.4236/jhepgc.2017.32020 PDF HTML XML 2,182 Downloads 6,476 Views Citations
Abstract
In this paper, we are going to rely on the first law in physics through which we can obtain a precise ideal value of the universal gravitational constant, a thing which has not happened so far. The significance of this law lies in the fact that, besides determining a precise ideal value of the gravitational constant, it connects three different physical disciplines together, which are mechanics, electromagnetism and thermodynamics. It is what distinguishes this from other law. Through this law, we have created the theoretical value of the gravitational constant Gi and we found it equivalent to 6.674010551359 × 10-11 m3·kg-1·s-2. In the discussion, the table of measurements of the gravitational constant was divided into three groups, and the average value of the first group G1 which is the best precision, equals the following sum 6.67401×10-11 m3·kg-1·s-2, and it’s the same equal value to the ideal value Gi that results from the law, as shown through our research that any other experimental values must not exceed the relative standard uncertainty which has a certain amount that is equivalent to a value of 5.325×10-5 and that’s a square value of the fine-structure constant.
Keywords
<snip>
Therefore, we conclude that all ideal values we have obtained through the theoretical equations are extremely close to their experimental counterparts which we had got from Table 2, which shows the recommended values of 2014 CODATA, except that the ideal values are more accurate, having been theoretically concluded, and as such, the data of Table 2 may be updated and substituted for the ideal values as illustrated below in Table 3.
5. Conclusions
There is a precise ideal value of the universal gravitational constant which equals 6.674010551359 × 10−11.
That may be calculated through a theoretically concluded equation of its own, and the cause of discrepancy of the gravitation value is attributable to the circumstances of the experiment as well as the sophistication of the nature and speed of particles used to measure the gravitational constant in such experiments.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1] AbouLayla, A.K. (2016) The Khromatic Theoary. Al Manra, Palestinian Territories, p. 95.
[2] Mohr, P.J., Taylor, B.N. and Newell, D.B. (2012) CODATA Recommended Values of the Fundamental Physical Constants: 2010.
https://arxiv.org/abs/1203.5425
[3] Netchitailo, V.S. (2016) 5D World-Universe Model. Gravitation. Journal of High Energy Physics, Gravitation and Cosmology, 2, 328-343.
https://doi.org/10.4236/jhepgc.2016.23031
[4] The CODATA Value, Newtonian Constant of Gravitation.
http://physics.nist.gov/cgi-bin/cuu/Value?bg
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(th)

GW Johnson · 2024-08-21 08:24:44

The value of G and the masses of the celestial bodies that I have been using came from the same 1973-vintage edition of the CRC Handbook. Those go together in the gravity equations as the GM product, sometimes given the symbol mu. The values they were using back then gave results for orbit sizes and speeds that generally matched observations.

I suspect the mass values today are also slightly different, and in such a way that the GM product values today and back then, are just about the same. Whether you are using older or newer values is very likely less important than getting your G and M values from the same source. The stuff published in the more reputable sources was checked to see if predictions using it matched observations. Mixing and matching data from different sources is the way to make the small changes in accepted values over the years to show up as errors in predictions.

GW

tahanson43206 · 2024-08-21 09:24:17

for GW Johnson....

The value of G accepted as current (ie, 2024 vs 1973) is very very close to the value you reported from the printed edition of the Handbook of
Chemistry an Physics.

The value of M is a physical property of a planet, and it has nothing to do with G, which is a universal constant.

The value of M will increase as material falls into a planet, and will decrease as atmosphere is lost to the solar wind and other forces.

Here is the pair of numbers as reported earlier:

The modern value seems only slightly different: The value of G is (6.6743 ± 0.00015) × 10−11 m3 kg−1 s−2.Jun 21, 2024
That value is quoted by Britannica ... I don't know the source.
The value you cited is very slightly lower: 6.6732 x 10^-11.

The question I will venture to repeat is:

What difference does the small difference in the value of G make?

If you use the same value of M for each calculation, then I would expect the result to differ some very small amount, but I'm not clear on how the result would manifest itself. Is the result expressed as a value of acceleration that would be experienced by an object at some distance from the center of the planet?

(th)

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#1 2024-08-20 05:36:51

Gravitational Constant - Discovery - History - Application

#2 2024-08-20 05:37:55

Re: Gravitational Constant - Discovery - History - Application

#3 2024-08-20 05:41:53

Re: Gravitational Constant - Discovery - History - Application

#4 2024-08-20 13:49:28

Re: Gravitational Constant - Discovery - History - Application

#5 2024-08-20 14:45:28

Re: Gravitational Constant - Discovery - History - Application

#6 2024-08-20 15:01:42

Re: Gravitational Constant - Discovery - History - Application

#7 2024-08-21 08:24:44

Re: Gravitational Constant - Discovery - History - Application

#8 2024-08-21 09:24:17

Re: Gravitational Constant - Discovery - History - Application

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