Newton Formulates the Theory of Universal Gravitation

Newton’s theory of universal gravitation provided the physical basis for the Copernican revolution, establishing a mechanical universe governed by universal natural laws and thus forming the foundation for the Enlightenment.

Summary of Event

The publication of Sir Isaac Newton’s theory of universal gravitation in his monumental treatise Philosophiae naturalis principia mathematica (1687; The Mathematical Principles of Natural Philosophy, 1729; better known as the Principia
Principia (Newton) ) marked the culmination of the scientific revolution. This revolution began with the 1543 publication by Nicolaus Copernicus of his heliocentric (Sun-centered) system of the planets (De revolutionibus orbium coelestium; On the Revolutions of the Heavenly Spheres, 1939; better known as De revolutionibus). Copernicus was unable to explain how Earth could rotate on its axis and move around the Sun, however, and his system contradicted the philosophical and theological ideas of his time. Only a few astronomers began to develop his ideas, most notable of whom were Galileo and Johannes Kepler Kepler, Johannes . [kw]Newton Formulates the Theory of Universal Gravitation (Summer, 1687)
[kw]Gravitation, Newton Formulates the Theory of Universal (Summer, 1687)
[kw]Universal Gravitation, Newton Formulates the Theory of (Summer, 1687)
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Physics;universal gravitation
Newton, Sir Isaac[Newton, Isaac];gravitation
Newton, Sir Isaac
Kepler, Johannes
Hooke, Robert
Halley, Edmond
Locke, John

In 1609, Galileo Galileo;astronomy began to use the telescope for astronomy and discovered four moons that orbit Jupiter in much the same way that Copernicus described planetary motion around the Sun. He also introduced the concept of inertia, which proposed that motion is the natural state of an object, and described the constant acceleration of gravity. By 1619, Kepler had completed his laws of the planets, which described and correlated the speeds, sizes, and shapes of their elliptical orbits around the Sun. He made an unsuccessful attempt to explain how the Sun could cause the motion of the planets.

The mechanical concepts of Galileo and Kepler were further developed by French philosopher and mathematician René Descartes Descartes, René (1596-1650) and Dutch scientist Christiaan Huygens Huygens, Christiaan (1629-1695), but neither was able to successfully account for planetary motion. In the latter half of the seventeenth century, Newton was able to correct and correlate these new mechanical ideas within a unified heliocentric system, but the emergence of this Newtonian synthesis involved many other scientists, and it is difficult if not impossible to assign credit properly.

Sir Isaac Newton.

(Library of Congress)

Newton was born on Christmas Day of 1642 at the farm of his mother’s parents near Grantham in Lincolnshire, after his father had died. He was raised by his maternal grandparents and then enrolled in Trinity College, Cambridge, in 1661, to study mathematics under Isaac Barrow Barrow, Isaac (1630-1677). After completing his degree in 1665, he returned home for nearly two years to escape the plague. During this isolation, he began to formulate his ideas about universal gravitation after making a connection between the fall of an apple and the motion of the Moon. His calculations revealed that the Moon in its orbit, which is sixty times farther from the center of Earth than the apple, accelerates toward Earth about 602 times slower than the falling apple. Thus, if gravity extends to the Moon, it diminishes according to an inverse-square law. After returning to Cambridge, Newton received his master’s degree in 1668 and became Lucasian professor of mathematics a year later on the recommendation of Barrow. For nearly two decades, much of his work remained unknown beyond Cambridge.

In the meantime, Robert Hooke Hooke, Robert was trying to develop the idea that gravity was similar to magnetic attraction. In discussing the comet of 1664 with Christopher Wren, Wren, Sir Christopher[Wren, Christopher] Hooke suggested that the gravitational attraction of the Sun caused the greater curvature of the comet’s orbit near the Sun. After Huygens’s formula for centrifugal force appeared in 1673, several scientists, including Hooke, Wren, and Edmond Halley, Halley, Edmond showed that circular orbits could be explained by a force that varied inversely as the square of the distance from the Sun. They were unable to show, however, that such an inverse-square law could account for elliptical orbits.

In 1684, Halley visited Newton at Cambridge and posed the problem to him. Newton immediately replied that he had solved the problem, but he was unable to find his calculations. Three months later, he sent Halley a paper that successfully derived all three of Kepler’s laws. Recognizing the importance of Newton’s achievement, Halley returned to Cambridge and urged him to write a book on his new dynamics of the solar system. For nearly two years, Newton concentrated on writing his Principia, perhaps the single most important scientific treatise in the history of science.

When book 1 of three projected volumes reached the Royal Society in 1685, Hooke claimed that Newton had plagiarized his ideas. Newton was furious and proceeded to delete all references to Hooke. Although the society at first planned to publish the Principia, it was short of funds, so Halley agreed to pay the expenses himself. He received the completed manuscript in April, 1686, and it was published in the summer of 1687. In an introductory section entitled “Axioms or Laws of Motion,” the three laws of Newton appear as the basis for his study of motion. The first two laws define inertia and force, based on the earlier work of Galileo and Descartes, while the third law introduces the idea that every force has an equal and opposite reaction.

In the first two books of the Principia, Newton derives a series of theorems from his three laws to describe motions for various kinds of forces. Using an inverse-square force of attraction, he derives all three of Kepler’s laws. In book 3, entitled The System of the World, he applies the hypothetical laws of the first two books to the universe as observed. The central concept is the law of universal gravitation, which generalizes the inverse-square law to give the mutual attraction (F) between any two bodies as being proportional to the product of their masses (m and M) and inversely as the distance (R) between them. This is usually written as F = G mM/R2 where G is the constant of universal gravitation.

Perhaps the single most important law in the history of science, the law of universal gravitation unifies terrestrial and celestial motions, assigning the same cause to the motion of projectiles and planets. Newton uses it to derive Galileo’s law for falling bodies, calculates the bulge of Earth’s equator due to rotation and its effect on the acceleration of gravity, gives the first satisfactory explanation of the tides, and shows the requirements for an Earth satellite. He also accounts for the motions of comets, the slow wobbling of the axis of Earth, and small deviations from Kepler’s laws in the motions of the planets and the Moon.

The collapse of the geocentric view of the universe had caused consternation and confusion, compounded by the idea of a moving Earth in infinite space. The Newtonian synthesis restored confidence in reason based on experience, giving birth to a new sense of optimism and progress in the eighteenth century that was later called the Enlightenment. It produced a new picture of the world as a great machine consisting of moving bodies subjected to universal laws in perfect order and harmony. Almost immediately it began to influence social theories.

Philosopher John Locke Locke, John began the task of translating Newtonian science into political and philosophical theory. He argued that individuals are the atomic units of the state, which should be structured by self-evident natural rights such as life, liberty, and property, and the democratic ideals of equality and tolerance. He also suggested that the human mind is a “blank tablet” at birth, in which simple atomic ideas gained by sensation are correlated by the laws of association and reason to form complex ideas. Since reason must be based on experience, human knowledge is limited to the natural world, and humans can know God only through God’s universal laws in nature, thus initiating deism as a system of natural religion in which a clockmaker God is revealed only in nature. Philosophy;England


The enlightened ideas of Newton and Locke were brought to France by Voltaire, who, with his mistress, wrote a popular account of Newtonian theory in 1738. In 1776, Locke’s ideas were used as the basis of the American Revolution as expressed by Thomas Jefferson in the Declaration of Independence. In the same year, Scottish philosopher Adam Smith published the natural laws that govern economics. In Smith’s theory of free enterprise, individuals are subject to market forces, requiring no interference because the market automatically adjusts to the forces of competition according to universal economic laws. Even the arts were affected by these mechanical ideas, giving rise to formalized literary forms and Baroque musical styles.

Further Reading

  • Alioto, Anthony. A History of Western Science. Englewood Cliffs, N.J.: Prentice Hall, 1993. Chapter 16, “Such a Wonderful Uniformity,” gives a succinct historical account.
  • Aughton, Peter. Newton’s Apple: Isaac Newton and the English Scientific Revolution. London: Weidenfeld & Nicolson, 2003. Describes Newton’s life and work as part of the scientific rebirth occurring after the English Civil Wars.
  • Boorstin, Daniel J. The Discoverers. New York: Random House, 1983. Chapter 52, “God Said, Let Newton Be!” provides a brief but authoritative historical account.
  • Chandrasekhar, S. Newton’s “Principia” for the Common Reader. New York: Oxford University Press, 1995. This work explains the scientific theories explored in Principia, including the law of gravitation, theory of the tides, and ideas about revolving orbits and comets.
  • Cohen, I. Bernard. The Newtonian Revolution. New York: Cambridge University Press, 1980. A more-extensive discussion of Newton’s work and its influence.
  • Cohen, I. Bernard, and George E. Smith, eds. The Cambridge Companion to Newton. New York: Cambridge University Press, 2002. A collection of essays, including explorations of the methodology of the Principia and Newton’s argument for universal gravitation.
  • Manuel, Frank. A Portrait of Isaac Newton. Cambridge, Mass.: Harvard University Press, 1968. A well-written scholarly biography of Newton.
  • Westfall, Richard S. Never at Rest: A Biography of Isaac Newton. New York: Cambridge University Press, 1980. Along with the work by Frank Manuel, this is one of the best biographies of Newton and his work.

Rise of Scientific Societies

Invention and Development of the Calculus

Bacon Publishes Novum Organum

Earliest Calculators Appear

Galileo Publishes Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican

Descartes Publishes His Discourse on Method

Torricelli Measures Atmospheric Pressure

Newton Builds His Reflecting Telescope

Rømer Calculates the Speed of Light

Related articles in <i>Great Lives from History: The Seventeenth Century</i><br />

Giovanni Alfonso Borelli; Pierre de Fermat; Galileo; James Gregory; Francesco Maria Grimaldi; Edmond Halley; Robert Hooke; Christiaan Huygens; Johannes Kepler; Gottfried Wilhelm Leibniz; John Locke; Sir Isaac Newton; John Wallis; Sir Christopher Wren. Physics;universal gravitation
Newton, Sir Isaac[Newton, Isaac];gravitation