Newton's Law of Universal Gravitation
English physicist Sir Isaac Newton's (1642-1727) 1687 work, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) advanced a law of universal gravitation that had a profound impact on the scientific and philosophical world. Newton's law specifies that objects with mass attract each other with a force that varies directly as the product of their masses and inversely as the square of the distance between the objects. Along with Newton's laws of motion, his law of gravitation became one of the key components in the development of physical theory.
Perhaps the most famous contribution of Isaac Newton to science was his theory of gravitation. As reported by the French philosopher, Voltaire: "One day in the year 1666, Newton had gone to the country, and seeing the fall of an apple, as his niece told me, let himself be led into a deep meditation on the cause which thus draws every object along a line whose extension could pass almost through the center of the Earth."
In Aristotle' physics, objects simply returned to Earth because everything was thought to return to its natural state, and the natural state of objects was to be on the ground. Newton improved on Aristotle's explanation by providing a mathematical expression for the gravitational force between two objects and by identifying the force which causes apples to fall as the same force that keeps planets in their orbits. The latter is the more subtle and profound of Newton's contributions because until Newton, people believed that planets were kept in place by divine purpose. Newton's laws of universal gravitation provided a physical explanation for the patterns in planetary motion.
The content of Newton's theory is summarized by the force equation, F= Gmm/r2 . Further equation reveals that the force between two objects is proportional to the product of their masses, m and m. The law of universal gravitation also states that the gravitational force between two objects is inversely proportional to the square of the distance r between m and m. A gravitational constant, G = 6.67 x10 -11 Nm2 /kg 2 provides a measure value for the gravitational force. Moreover, Newton showed that the attraction between two masses depends only on the distance between their "centers of mass." (When people refer to the "center of gravity" in everyday speech, they mean its center of mass.) In effect, gravity acts as if all the mass of an object were concentrated at one point, regardless of the actual shape of the object. The gravitational force is always attractive, masses never repel each other through gravity as can occur between like-charged particles.
Newton's first law of motion states that objects stay in their state of motion unless acted upon by a force. The second law describes how an object's motion can be altered by a force in a way which depends on the object's mass. The mass referred to in the first and second laws is the same, and it is often called the "intertial mass." The mass that appears in the law of gravity is called the "gravitational mass" because it determines the strength of the gravitational force between two objects. In classical mechanics, there is no reason why these two masses should be equivalent, but they are. An experiment by Eötvös in 1909 showed that the two quantities differ by less than one part in a billion. An explanation for why this is true follows immediately from Einstein's principle of equivalence and was critically important to the development of the general theory of relativity.
One of the most significant aspects of Newton's theory is the conceptual leap in identifying the force which pulls objects to Earth with the force which keeps planets in their orbits. Newton demonstrated this identity by deriving Kepler's laws of planetary motion from his theory of gravity. This triumph encouraged seventeenth-and-eighteenth century European philosophers to think of the universe in mechanical terms. God was seen as a "watchmaker" who built the machine of the universe and set it to run according to Newton's laws. Although some argued that explanations of natural phenomena reveled the very nature of God and that God could only be understood within the laws of science. For other scientists, however, the revelation of a mechanistic universe left no place for a divine operator, and they abandoned or modified their religious views.
In the twentieth century, Einstein's general theory of relativity supplanted Newton's theory of gravity as the most accurate theory of gravitation, yet Newton's theory remains the more useful theory for most purposes. The corrections to most calculations arising from relativistic effects are so small that they are not worth the extra effort it takes to use Einstein's much more complicated theory. Accordingly, sending astronauts to the Moon required modern technology, but the basis of the calculations used to plot trajectories and orbital paths was centuries old.
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