The Law of Universal Gravitation

Since the gravitational force is experienced by all matter in the universe, from the largest galaxies down to the smallest particles, it is often called universal gravitation. (Based upon observations of distant supernovas around the turn of the 21st cent., a repulsive force, termed dark energy, that opposes the self-attraction of matter has been proposed to explain the accelerated expansion of the universe.) Sir Isaac Newton was the first to fully recognize that the force holding any object to the earth is the same as the force holding the moon, the planets, and other heavenly bodies in their orbits. According to Newton's law of universal gravitation, the force between any two bodies is directly proportional to the product of their masses (see mass) and inversely proportional to the square of the distance between them. The constant of proportionality in this law is known as the gravitational constant; it is usually represented by the symbol G and has the value 6.670 × 10^-11 N-m²/kg² in the meter-kilogram-second (mks) system of units. Very accurate early measurements of the value of G were made by Henry Cavendish.

Newton's theory of gravitation was long able to explain all observable gravitational phenomena, from the falling of objects on the earth to the motions of the planets. However, as centuries passed, very slight discrepancies were observed between the predictions of Newtonian theory and actual events, most notably in the motions of the planet Mercury. The general theory of relativity proposed in 1916 by Albert Einstein explained these differences and provided a geometric explanation for gravitational phenomena, holding that matter causes a curvature of the space-time framework in its immediate neighborhood.

Tantalizing evidence for the existence of gravity waves, which are predicted by Einstein's general theory of relativity and would be analogous to electromagnetic waves, comes from astronomical observations of a binary pulsar designated 1913 + 16. The rate at which the two neutron stars in the binary rotate around each other is changing in a manner that is consistent with the emission of gravity waves. A hypothetical particle, given the name graviton, has been suggested as the mediator of the gravitational force; it is analogous to the photon, the particle embodying the quantum properties of electromagnetic waves (see quantum theory). The search for gravity waves continues with the building of large interferometers that would be sensitive enough to detect the faint waves directly (see interference). Millions of dollars have already been spent on the Laser Interferometer Gravitational Wave Observatory (LIGO), supported by the National Science Foundation, and work is beginning on the even more ambitious Laser Interferometer Space Antenna (LISA).

The Force of Gravity

The term gravity is commonly used synonymously with gravitation, but in correct usage a definite distinction is made. Whereas gravitation is the attractive force acting to draw any bodies together, gravity indicates that force in operation between the earth and other bodies, i.e., the force acting to draw bodies toward the earth. The force tending to hold objects to the earth's surface depends not only on the earth's gravitational field but also on other factors, such as the earth's rotation. The measure of the force of gravity on a given body is the weight of that body; although the mass of a body does not vary with location, its weight does vary. It is found that at any given location, all objects are accelerated equally by the force of gravity, observed differences being due to differences in air resistance, etc. Thus, the acceleration due to gravity, symbolized as g, provides a convenient measure of the strength of the earth's gravitational field at different locations. The value of g varies from about 9.832 meters per second per second (m/sec²) at the poles to about 9.780 m/sec² at the equator. Its value generally decreases with increasing altitude. Because variations in the value of g are not large, for ordinary calculations a value of 9.8 m/sec², or 32 ft/sec², is commonly used.

Statement that any particle of matter in the universe attracts any other with a force (math.F) that is proportional to the product of their masses (math.m₁ and math.m₂) and inversely proportional to the square of the distance (math.R) between them. In symbols: math.F = math.G(math.m₁math.m₂)/math.R², where math.G is the gravitational constant. Isaac Newton put forth the law in 1687 and used it to explain the observed motions of the planets and their moons, which had been reduced to mathematical form by Johannes Kepler early in the 17th century.

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Universal force of attraction that acts between all bodies that have mass. Though it is the weakest of the four known forces, it shapes the structure and evolution of stars, galaxies, and the entire universe. The laws of gravity describe the trajectories of bodies in the solar system and the motion of objects on Earth, where all bodies experience a downward gravitational force exerted by Earth's mass, the force experienced as weight. Isaac Newton was the first to develop a quantitative theory of gravitation, holding that the force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Albert Einstein proposed a whole new concept of gravitation, involving the four-dimensional continuum of space-time which is curved by the presence of matter. In his general theory of relativity, he showed that a body undergoing uniform acceleration is indistinguishable from one that is stationary in a gravitational field.

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