Gravitational constant
According to the law of universal gravitation, the attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. The constant of proportionality is called G, the gravitational constant or universal gravitational constant. The gravitational constant is a fundamental physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of general relativity.In SI units, the 2002 CODATA recommended value of the gravitational constant is
- G = 6.6742 × 10^{−11} N·m^{2}/kg^{2}
The gravitational force is relatively weak. As an example, two SUVs, each with a mass of 3000 kilograms and placed with their centers of gravity 3 meters apart, will attract each other with a force of about 67 micronewtons. This force is approximately equal to the weight of a large grain of sand.
Table of contents |
2 The GM product 3 Planck units 4 References 5 External links |
Measurement of the gravitational constant
G was first measured by Henry Cavendish (Philosophical Transactions 1798). 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. See torsion bar experiment.
The accuracy of the measured value of G has increased only modestly since the original experiment of Cavendish. G is quite difficult to measure, as gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies. Furthermore, gravity has no established relation to other fundamental forces, so it does not appear possible to measure it indirectly. A recent review (Gillies, 1997) shows that published values of G have varied rather broadly, and some recent measurements of high precision are, in fact, mutually exclusive.
The GM product
As with G, the mass of the Sun is not known to a high degree of accuracy. However, the product of G and the mass of the Sun is known more accurately than either quantity alone. In calculations of gravitational force in the solar system, it is the product which appears. Therefore calculations in celestial mechanics are carried out using the unit of solar mass rather than the standard SI unit kilogram. In this case we use the Gaussian gravitational constant which is the square of k, and k is:
- k = 0.01720209895 A^{3/2}D^{-1}S^{-1/2}
Planck units
By combining the gravitational constant with Planck's constant and the speed of light in vacuum, it is possible to create a system of units known as Planck units. The gravitational constant, Planck's constant and the speed of light all take the numerical value 1 in this system.
References
- George T. Gillies. "The Newtonian gravitational constant: recent measurements and related studies". Reports on Progress in Physics, 60:151-225, 1997. (A lengthy, detailed review. See Figure 1 and Table 2 in particular. Available online: PDF)
- E. Myles Standish. "Report of the IAU WGAS Sub-group on Numerical Standards". In Highlights of Astronomy, I. Appenzeller, ed. Dordrecht: Kluwer Academic Publishers, 1995. (Complete report available online: PostScript. Tables from the report also available: Astrodynamic Constants and Parameters)
- Jens H. Gundlach and Stephen M. Merkowitz. "Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback". Physical Review Letters, 85(14):2869-2872, 2000. (Also available online: PDF)
External links
- CODATA Internationally recommended values of the Fundamental Physical Constants (at The NIST References on Constants, Units, and Uncertainty)
- The Controversy over Newton's Gravitational Constant (additional commentary on measurement problems)