The gravitational force is one of fundamental forces in nature discovered to govern the interaction of material objects. The other three fundamental forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force (which is now usually combined with the electromatic force as the electroweak force). The two nuclear forces are effective only at the subatomic scale. In contrast, the gravitational and electromagnetic forces act on objects from the atomic to extragalactic scales. Progress is also being made to treat gravitation as a side effect of string forces.
Johannes Kepler discovered (circa 1609) that the planets describe ellipses in their circuits about the Sun, with the Sun occupying a focal point of the ellipse. From this discovery scientists like Edmond Halley, Robert Hooke, and others, speculated that the force exerted by the Sun on the planets varied as the inverse square of the distance between the two bodies. In his Principia Sir Isaac Newton confirmed this suspicion with his law of universal gravitation as described in the following equation: F = GMm/r2 , where F is the magnitude of the gravitational forces between two bodies M and m separated by distance r. G is Newton's universal gravitational constant, defined as 6.67 x 10-11 Nm2 kg-2 .
Encapsulated in this equation are the following important features: (1) the gravitational force between two particles is a "central" force: that is, the force acts along the (straight) line drawn from one particle to the other; (2) the gravitational force is a force of attraction, unlike the electrostatic force, which can be either attractive or repulsive; (3) the size of the force is proportional to the masses of each of the two particles. Mass must not be confused with weight. In Newton's system, the mass of a particle is an intrinsic property of that particle that remains unaltered when moved from point to point in space. By definition, weight is the gravitational force that one object applies to another. The weight of the same object on different planets, for instance, varies, but its mass is the same at each locale; (4) the gravitational force between two particles varies as the inverse square of the distance between them. Many phenomena in nature exhibit this "1/r2 " dependence. The gravitational force decreases with distance in the same way that the intensity of light decreases from an emitting object; and (5) the gravitational constant G is used to convert the term on the right side of the equation into units of force. The first person to determine a relatively accurate value of G was Henry Cavendish, when in 1798 he used a very sensitive torsion balance for that purpose. In addition to the previous points it must be noted that the total force on a particle due to many masses (the so-called n-body problem) is just the summation of the forces exerted by each mass upon the particle according to the equation above.
Newton's law of universal gravitation stood the test of time for over 200 years, until the appearance of the general theory of relativity in 1915 (constructed by Albert Einstein). In Newton's theory only particles possessing mass were influenced by gravitation. But in the general theory of relativity, both mass and energy are influenced by gravity. Through numerous experimental confirmations, the general theory of relativity has superseded Newton's laws of motion as being the best theoretical model for explaining the interactions of matter and energy. However, for most problems (such as stellar and planetary motion, or the ballistic flight of rockets and projectiles) Newton's laws, including his law of universal gravitation, are still adequate.
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