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Top Comments: Measuring Newton's Gravitational Constant [1]
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Date: 2023-08-13
Newton’s universal law of gravitation.
According to Newton’s universal law of gravitation allows the calculation of the force of attraction between two massive object due to gravity. The form of the equation is shown below. F is the force, m 1 and m 2 are the masses of the two objects, r is the length of the separation between them, and G is the gravitational constant. This equation is used to calculate the orbits of planets and the dynamics of galaxy clusters, but it can also be used, in principle, to calculate the force of attraction between two ping pong balls, for example.
Of all the constants of nature (including such quantities as the charges and masses of elementary particles, the speed of light, Planck’s constant, etc), the precision of the measured value of the gravitational constant G is the worst. The current accepted value for G is 6.67430x10-11 m3 kg-1 s-2, with an uncertainty of about 1 part in 50,000. In contrast, the mass of the electron is known to about 1 part in 3 billion.
Why do we lack a more precise value for G? There are several reasons. First, of the four known fundamental forces in the universe (Electromagnetism, the strong nuclear force, the weak nuclear force, and gravity), gravity is the weakest, making precise measurements more difficult. Second, there is no theory (yet) that incorporates all four of these forces. Second, the Standard Model, the current best functioning theory in physics includes all of the forces except gravity; constants for the other three forces and the elementary particles can be made more precise and consistent within this framework, but gravity is excluded from that framework. Third, for practical calculations, a more precise value is not really necessary.
However, the fact that this one constant of physics is less precise than all others bu many orders of magnitude is a fact that some physicists and meteorologists find bothersome. Further, recent measurements of G, have shown a puzzlingly large lack of precision, despite efforts to improve that precision. Most commonly, such experiments follow the lead of Henry Cavendish, the 18th Century English physicist who first measured G. He did so using the apparatus shown in the title figure. Two lead balls on either end of a rod suspended by a wire are placed such that the balls are a measurable distance from two larger, fixed lead balls. gravitational attraction will cause the wire to twist; the amount of twist can be determined by the deflection of light from a mirror attached to the wire. If you know the torsion constant for the wire, it’s possible to calculate the force. Modern versions have increased the number of balls from 4 to 8, incorporate vacuum chambers, and locate the apparatus under mountains, but the rest is pretty much the same.
Scientists are trying hard to locate sources of systematic error in these measurements, but such a source is not apparent. Of course, the alternative is new physics! Is it possible that G is actually variable? If so, what does it depend on? Are there aspects of general relativity (Eistein’s more sophisticated theory of gravity) that could explain this? As yet, nobody knows, but physicists are working hard on these questions.
Comments are below the fold.
Top Comments (August 13, 2023):
No nominations tonight.
Top Mojo (August 12, 2023):
Top Mojo is courtesy of mik! Click here for more on how Top Mojo works.
Top Photos (August 12, 2023):
Thanks to jotter (RIP) for creating it and elfling for restoring it.
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