Gravitational Constant

The gravitational constant is fundamental quantity of the universe. The gravitational constant, G, was the first great universal constant of physics (the others subsequently being the speed of light and Planck's constant) and modern physicists still argue its importance and relationships to cosmology. Regardless, almost all the major theoretical frameworks dictate that the value for the gravitational constant (G) is in some regard related to the large-scale structure of the cosmos. Ironically, despite centuries of research, the gravitational constant, G, is—by a substantial margin—the least understood, most difficult to determine, and least precisely known fundamental constant value. The quest for "G" provides a continuing challenge to the experimental ingenuity of physicists, and often spurs new generations of physicists to recapture the inventiveness and delicacy of measurement first embodied in the elegant experiments conducted by English physicist Henry Cavendish (1731–1810).

The Cavendish constant "G" must not be confused with the "g" (designated in lowercase) that geophysicists use to designate gravitational acceleration (i.e., a change in the velocity of an object due to the gravitational field (commonly referred to as the gravitational force) of the earth that is due to the mass of the earth. Although the gravitational field of the earth fluctuates with the mass underneath the area in question, the overall average "g" is 9.80665 m/s2.

In 1798, Cavendish performed an ingenious experiment that led to the determination of the gravitational constant (G). Cavendish used a carefully constructed experiment that utilized a torsion balance to measure the very small gravitational attraction between two masses suspended by a thin fiber support. (Cavendish actually measured the restoring torque of the fiber support). Cavendish's experimental methodology and device design was not novel. Similar equipment had been designed by English physicist John Mitchell (1724–1793), and a similar apparatus had been designed by French physicist Charles Coulomb and others for electrical measurements and calibrations. Cavendish's use, however, of the torsional balance to measure the gravitational constant of Earth, was a triumph of empirical skill.

Cavendish balanced his apparatus by placing balls of identical mass at both ends of a crossbar suspended by a thin wire. By lead balls of known mass, Cavendish was able to account for both the masses in the Newtonian calculation and thereby allowing a determination of the gravitational constant (G). The Cavendish experiment worked because not much force was required to twist the wire suspending the balance. In addition, Cavendish brought relatively large masses close to the smaller weights—actually on symmetrically opposite sides of the weights—so as to double the actual force and make the small effects more readily observable. Over time, due to the mutual gravitational attraction of the weights the smaller balls moved toward the larger masses. The smaller balls moved because of their smaller mass and inertia (resistance to movement). Cavendish was able to measure the force of the gravitational attraction as a function of the time it took to produce any given amount of twist in the suspending wire. The value of the gravitational constant determined by this method was not precise by modern standards (only a 7% precision but with 1% accuracy) but was an exceptional value for the eighteenth century given the small forces being measured. Because all objects exert a gravitational "pull," precision in Cavendish type experiments is often hampered by a number of factors, including underlying geology or factors as subtle as movements of furniture or objects near the experiment.

The Cavendish experiment was, therefore, a milestone in the advancement of scientific empiricism. In fact, accuracy of the Cavendish determination remained unimproved for almost another century until Charles Vernon Boys (1855–1944) used the Cavendish Balance to make a more accurate determination of the gravitational constant. More importantly, the Cavendish experiment proved that scientists could construct experiments that were able to measure very small forces. Cavendish's work spurred analysis of the fundamental force of electromagnetism (a fundamental force far stronger than gravity) and gave confidence to the scientific community that Newton's laws were not only valid, they were also testable on exceedingly small scales.

In modern physics, the speed of light, Planck's constant, and the gravitational constant are among the most important of fundamental constants. According to relativity theory, G is related to the amount of space-time curvature caused by a given mass. Modern concepts of gravity and of the ramifications of the value of the gravitational constant are subject to seemingly constant revision as scientists aim to extend the linkage between the gravitational constant (G) and other fundamental constants. Although profoundly influential and powerful on the cosmic scale, the force of gravity is weak in terms of human dimensions. Accordingly, the masses must be very large before gravitational effects can be easily measured. Even using modern methods, different laboratories often report significantly different values for G.

See also Gravity and the gravitational field