GRAVITATION

in mechanics, the universal force of attraction that affects all matter. It is the weakest of the four basic physical forces, but, on the scale of everyday objects near the Earth or that of astronomical bodies, it is the dominant one. The fall of bodies released from a height to the surface of the Earth and the weight of resting bodies at or near the surface are the most familiar manifestations of gravitation, but the rotation of the Earth about the Sun, the motion of the Sun around the centre of the Milky Way Galaxy, and the geometric structure of the universe itself are equally the results of the force of gravitation. Building on the work of Galileo (Galilei) and Johannes Kepler, Isaac Newton developed the first quantitative theory of gravitation, which he published in his Principia in 1687. Newton held that every particle of matter in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically this is expressed by the classical formula where F is the force of attraction, m1 and m2 are the masses, d is the distance, and G is a universal gravitational constant whose value depends on the units chosen to express it. Newton was able to show that Kepler's three empirical laws of planetary motion followed from his own three general laws of motion and the above law of gravitation. The power of the law to explain and predict phenomena was triumphantly confirmed when two astronomers, J.C. Adams and U.-J.-J. Le Verrier, working independently, used data on perturbations in the orbit of the planet Uranus to predict the existence and location of an undiscovered planet whose gravitational attraction was held to be responsible for the observed anomalies. The planet subsequently named Neptune was discovered in 1846 almost precisely where it had been predicted to be. The value of the universal constant of gravitation G has been measured a number of times. The first reliable measurement was made by Henry Cavendish in 1798, using two large lead balls to attract two smaller balls that were attached to a torsion balance. Cavendish's value was 6.754 10-11 newton-square metre per square kilogram; the presently accepted value is 6.67259 10-11Nm2 kg-2. Some cosmological theories suggest that G may be changing by about one part in 1011 per year or that it may vary somewhat in different regions of space. Measurements indicate that G cannot vary by more than four parts in 1010 per year. (See also Cavendish experiment.) Newton's conception and quantification of gravitation held firm until the beginning of the 20th century, when the notion of instantaneous action at a distance, which it entailed, was recognized generally as unintelligible, particularly from the viewpoint of relativity. In his general theory of relativity, Albert Einstein developed a wholly new conception of gravitation. Einstein proposed that the four-dimensional space-time continuum is curved by the presence of matter, producing a universe in which bodies travel in geodesics (shortest paths) that are the curved orbits interpreted by Newton as the result of some attractive force. (See also space-time.) Einstein also showed that there is no way in principle to distinguish between a body undergoing uniform acceleration and one that is stationary in a gravitational field. The relativistic view of gravitation yielded predictions of several phenomena that violate Newtonian theory and that, to the limits of observational accuracy, have been confirmed; these include the bending of a ray of light passing near a very massive object such as the Sun, the reddening of light emitted by a very massive object, and the speeding up of a clock raised above the Earth relative to one remaining on the surface. The new theory was also able to explain a long-known phenomenon, the precession of the orbit of Mercury about the Sun, which had defied Newtonian analysis. Another prediction of relativistic gravitation theory is the existence of gravity waves propagated by objects moving in a gravitational field. Some experimenters have claimed to have detected such waves, but their results remain so far unconfirmed. Yet another apparent implication of relativistic gravitational fields is the existence of particles, called gravitons, as carriers of the field. They are postulated to be massless, uncharged particles moving at the speed of light; they, too, are as yet undetected. in mechanics, the universal force of attraction acting between all matter. It is by far the weakest known force in nature and thus plays no role in determining the internal properties of everyday matter. Due to its long reach and universality, however, gravity shapes the structure and evolution of stars, galaxies, and the entire universe. The trajectories of bodies in the solar system are determined by the laws of gravity, while on Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which the Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects. At the Earth's surface, the acceleration of gravity is about 9.8 metres (32 feet) per second per second. Thus, for every second an object is in free fall, its speed increases by about 9.8 metres per second. The works of Isaac Newton and Albert Einstein dominate the development of gravitational theory. Newton's classical theory of gravitational force held sway from his Principia, published in 1687, until Einstein's work in the early 20th century. Even today, Newton's theory is of sufficient accuracy for all but the most precise applications. Einstein's modern field theory of general relativity predicts only minute quantitative differences from the Newtonian theory except in a few special cases. The major significance of Einstein's theory is its radical conceptual departure from classical theory and its implications for further growth in physical thought. Additional reading General: Isaac Newton, The Mathematical Principles of Natural Philosophy, 2 vol. (1729, reissued in 1 vol., 1975; originally published in Latin, 1 vol., 1687), often referred to as the Principia, is the origin of all fundamental work on gravity. Stephen W. Hawking and W. Israel (eds.), Three Hundred Years of Gravitation (1987), provides many authoritative review articles in commemoration of the tercentenary of the publication of Newton's Principia. Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation (1973), is a leading work on gravitational theory. Alan Cook, The Motion of the Moon (1988), discusses theories of the lunar orbit, with a chapter on applications that includes an account of gravitational studies. Gravity around the Earth, Moon, and planets: Alan Cook, Physics of the Earth and Planets (1973), includes a chapter on methods and results of gravity measurements. Wolfgang Torge, Geodesy: An Introduction (1980), contains a full and up-to-date chapter on gravity measurements. James A. Hammond and James E. Faller, "Results of Absolute Gravity Determinations at a Number of Sites," Journal of Geophysical Research, 76(32):7850-7854 (Nov. 10, 1971), gives an account of absolute measurements by free fall. C. Morelli et al., The International Gravity Standardization Net 1971 (I.G.S.N. 71) (1974), is the result of adjusting a large number of gravity measurements over the Earth. Alan Cook, Interiors of the Planets (1980), summarizes knowledge of the gravity fields of the planets and their interpretation. Theories of gravitation and astronomical aspects: Stephen W. Hawking, A Brief History of Time: From the Big Bang to Black Holes (1988), is a nonmathematical book by an outstanding author; see especially the chapter on black holes. Clifford M. Will, Theory and Experiment in Gravitational Physics (1981, reprinted 1985), is a thorough treatment. See also J.H. Taylor and P.M. Mcculloch, "Evidence for the Existence of Gravitational Radiation from Measurements of the Binary Pulsar PSR 1913+16," Annals of the New York Academy of Sciences, 336:442-446 (1980); and B.W. Petley, The Fundamental Physical Constants and the Frontier of Measurement (1985, reprinted 1988). Experiments on gravitation: Experiments on aspects of gravitation are treated in the following journal articles: Alan Cook, "Experiments on Gravitation," Reports on Progress in Physics, 51(5):707-757 (May 1988), a comprehensive review, with many references to early work, to the measurements of G in the table, and to recent studies of the inverse square law; P.G. Roll, R. Krotkov, and R.H. Dicke, "The Equivalence of Inertial and Passive Gravitational Mass," Annals of Physics, 26(3):442-517 (Feb. 20, 1964), a thorough account of a classical experiment; Henry Cavendish, "Experiments to Determine the Density of the Earth," Philosophical Transactions of the Royal Society of London, 88:469-526 (June 21, 1798), the first measurement of G; Gabriel G. Luther and William R. Towler, "Redetermination of the Newtonian Gravitational Constant G," Physical Review Letters, 48(3):121-123 (Jan. 8, 1982), probably the best measurement of G up to that time; F.D. Stacey et al., "Geophysics and the Law of Gravity," Reviews of Modern Physics, 59(1):157-174 ((Jan. 1987), a review of work on a possible difference between G as measured in the laboratory and estimated geophysically; and T.C. Van Flandern, "Is the Gravitational Constant Changing?" The Astrophysical Journal, 248(2):813-816 (Sept. 1, 1981), a discussion of relevant observations of the Moon. Sir Alan H. Cook