Gravity

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Gravity

Gravity is the force of attraction between any two objects in the universe with mass. Although it is much weaker than any of the other fundamental forces (electromagnetism, the weak force, and the strong force) and is neglected in the interactions of elementary particles, which occur at short distances, the effects of gravity manifest themselves at larger length scales, most notably at astronomical distances.

Historically, gravity is the first of the fundamental forces of nature whose behavior was extensively studied and elucidated. Aristotle maintained the rate at which objects fell depended upon their masses. If two objects are dropped, the heavier one falls faster. Galileo showed that Aristotle's conclusion was false. Any two objects fall towards the center of Earth with the same rate of acceleration. This observation is an empirical one. It does not provide an explanation for why gravity acts as it does.

Isaac Newton offered an explanation through his law of universal gravitation, F = Gmm/r2 , which holds that the force of gravity between any pair of masses is directly proportional to the product of their masses and inversely proportional to the square of their separation. The factor G in this relation is a fundamental constant called the universal gravitational constant or Newton's constant. It is the same irrespective of whether one is talking about an apple that is dropped or a star that orbits the center of a galaxy.

An apple and a cannonball fall at the same rate because Newton's law tells us that they have the same acceleration, g = GM/R2 where M is the mass and R is the radius of Earth. The Moon and Earth rotate about a common center of mass. Because Earth is roughly a hundred times heavier than the Moon, the center of mass of Earth-Moon system resides within Earth. The force of attraction between the two bodies is centripetal. This fact, together with Kepler's third law and a knowledge of the distance between Earth and the Moon, the period of the Moon's orbit, and the radius of Earth, is sufficient to deduce that the ratio of Earth's and the Moon's masses M/M = 81.3 and g = 9.8 m/s2 . Similarly, it can be shown that Earth revolves around the Sun, which is roughly a million times more massive. Universal gravitation therefore vindicates the heliocentric models of Aristarchus (310-c.230 B.C.) and Nicholas Copernicus.

The constant G is typically determined using a torsion balance. Henry Cavendish performed the first such experiment by using a pair of solid lead spheres 5 cm in diameter attached to the ends of a light rod suspended by a thin fiber. When heavier 30 cm lead spheres were brought in proximity to this system, the gravitational attraction of the small balls to the larger ones produced a torque that twisted the fiber. Measuring this force allows G to be determined as 6.67 x 10-11 m3 /s2 -kg. A similar experiment also allowed Cavendish to measure the mass of Earth as 5.98 x 1024 kg.

The French astronomer Jean Leverrier (1811-1877) noticed that Mercury's perihelion, the radial point in its orbit nearest the Sun, precessed too rapidly by about 40 seconds of arc per century. This phenomenon suggested that Newton's theory of gravitation was wrong. A better model for gravity was provided by Albert Einstein in his general theory of relativity.

Newton's law of universal gravitation assumes that force acts at distance (i.e., without a medium that transmits the force) and does work instantaneously in that every object in the universe knows how far away and how massive any other object in the universe is and immediately responds accordingly. Newtonian physics also invokes the existence of privileged inertial reference frames. Einstein's special theory of relativity contradicts these long-held beliefs by positing that the laws of physics are the same in every inertial reference frame and that the maximum speed at which the information about a particle's properties can travel is the speed of light. The general theory of relativity takes this argument one step further. Its starting point is the assumption that on a local scale, the physical consequences of an accelerated reference frame and the force of gravity cannot be distinguished. This is a restatement of the principle of equivalence, which maintains that the inertial mass, which determines how a body resists changes to its inertia, and the gravitational mass, which is used in the law of universal gravitation, are the same. In Einstein's theory, the gravitational force results from the curvature of space-time in the presence of matter (or energy). The measured deflection of starlight by the Sun, the delay of radar echoes when Venus passes behind the Sun, and the precession of Mercury's perihelion all provide spectacular evidence to support the general theory of relativity.

A technical problem remains. Unlike the other three fundamental forces, gravity cannot be treated as a renormalizable field theory. That is to say, it is inconsistent with quantum mechanics, and the short-distance physics of gravity leads to infinities that do not cancel. In order to treat all of the fundamental forces on an equal footing, it becomes necessary to spread the gravitational interaction out in space. String theory accomplishes this by treating the graviton, the particle that mediates gravity, as a loop of string. Such a theory is only consistent in 10 space-time dimensions. The details of string theory are still in the process of being worked out.