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To develop his theory of gravitation, Newton first had to develop the science of forces and motion called mechanics. Newton proposed that the natural motion of an object is motion at a constant speed on a straight line, and that it takes a force to slow down, speed up, or change the path of an object. Newton also invented calculus, a new branch of mathematics that became an important tool in the calculations of his theory of gravitation.
Newton proposed his law of gravitation in 1687 and stated that every particle in the universe attracts every other particle in the universe with a force that depends on the product of the two particles' masses divided by the square of the distance between them. The gravitational force between two objects can be expressed by the following equation: F= GMm/d2 where F is the gravitational force, G is a constant known as the universal constant of gravitation, M and m are the masses of each object, and d is the distance between them. Newton considered a particle to be an object with a mass that was concentrated in a small point. If the mass of one or both particles increases, then the attraction between the two particles increases. For instance, if the mass of one particle is doubled, the force of attraction between the two particles is doubled. If the distance between the particles increases, then the attraction decreases as the square of the distance between them. Doubling the distance between two particles, for instance, will make the force of attraction one quarter as great as it was.
According to Newton, the force acts along a line between the two particles. In the case of two spheres, it acts along the line between their centers. The attraction between objects with irregular shapes is more complicated. Every bit of matter in the irregular object attracts every bit of matter in the other object. A simpler description is possible near the surface of the earth where the pull of gravity is approximately uniform in strength and direction. In this case there is a point in an object (even an irregular object) called the center of gravity, at which all the force of gravity can be considered to be acting.
Newton's law affects all objects in the universe, from raindrops in the sky to the planets in the solar system. It is therefore known as the universal law of gravitation. In order to know the strength of gravitational forces in general, however, it became necessary to find the value of G, the universal constant of gravitation. Scientists needed to perform an experiment, but gravitational forces are very weak between objects found in a common laboratory and thus hard to observe. In 1798 the English chemist and physicist Henry Cavendish finally measured G with a very sensitive experiment in which he nearly eliminated the effects of friction and other forces. The value he found was 6.754 x 10-11 N-m2/kg2óclose to the currently accepted value of 6.670 x 10-11 N-m2/kg2 (a decimal point followed by 10 zeros and then the number 6670). This value is so small that the force of gravitation between two objects with a mass of 1 metric ton each, 1 meter from each other, is about 67 millionths of a newton, or about 15 millionths of a pound.
Gravitation may also be described in a completely different way. A massive object, such as the earth, may be thought of as producing a condition in space around it called a gravitational field. This field causes objects in space to experience a force. The gravitational field around the earth, for instance, produces a downward force on objects near the earth surface. The field viewpoint is an alternative to the viewpoint that objects can affect each other across distance. This way of thinking about interactions has proved to be very important in the development of modern physics.