Newton's Law of Universal Gravitation

views updated

Newton's Law of Universal Gravitation

Overview

In 1687 English physicist Sir Isaac Newton (1642-1727) published a law of universal gravitation in his important and influential work Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). In its simplest form, Newton's law of universal gravitation states that bodies 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 them. This mathematically elegant law, however, offered a remarkably reasoned and profound insight into the mechanics of the natural world because it revealed a cosmos bound together by the mutual gravitational attraction of its constituent particles. Moreover, along with Newton's laws of motion, the law of universal gravitation became the guiding model for the future development of physical law.

Background

Newton's law of universal gravitation was derived from German mathematician and astronomer Johannes Kepler's (1571-1630) laws of planetary motion, the concept of "action-at-a-distance," and Newton's own laws of motion. Building on Galileo's observations of falling bodies, Newton asserted that gravity is a universal property of all matter. Although the force of gravity can become infinitesimally small at increasing distances between bodies, all bodies of mass exert gravitational force on each other. Newton extrapolated that the force of gravity (later characterized by the gravitational field) extended to infinity and, in so doing, bound the universe together.

The impact of Newton's law of gravity was initially more qualitative than quantitative. Newton's law of gravitation, mathematically expressed as F = (G)(m₁m₂) /r², stated that the gravitational attraction between two bodies with masses m₁ and m₂ was directly proportional to the masses of the bodies, and inversely proportional to the square of the distance (r) between the centers of the masses. Accordingly, a doubling of one mass resulted in a doubling of the gravitational attraction, while a doubling of the distance between masses resulted in a reduction of the gravitational force to a fourth of its former value. Nearly a century passed, however, before English physicist Henry Cavendish (1731-1810) was to determine the missing gravitational constant (G) that allowed a reasonably accurate determination of the actual gravitational force. Regardless, the parsimony of Newton's law made its quantitative application easy to translate to problems in astronomy and mechanics.

Newton admitted having no fundamental explanation for the mechanism of gravity itself. In Principia Newton stated, "...I have been unable to discover the cause of those properties of gravity from phenomena, and I feign no hypotheses (regarding its mechanism)." Moreover, Newton asserted, "To us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for the motions of the celestial bodies and our seas." In his later work, Opticks, Newton raised the possibility that the gravitational force might be conveyed through a medium or "ether."

Regardless, that the force of gravity had calculable and measurable effect on the universe proved vastly important to astronomers and scientists. It was useful enough to explain that gravity was the force accelerating planets in their orbits (i.e. keeping the direction of orbital motion forever changing toward the Sun). Paradoxically, the widespread acceptance of Newton's law was enhanced by being detached from an underlying mechanism. Accordingly, Newton's law became a powerful descriptive and predictive tool that could be used as a confirmation of the existence of God or, in the alternative, as proof that no divine intervention was needed to move the heavens.

Impact

Newton's law of gravitation proved to be a precise and effective tool wherever applied. A truly universal law, it could be verified by the simplest fall of an apple or measured against the most detailed observations of celestial movements. In the twentieth century Newtonian mechanics, based in part on Newton's laws of universal gravitation, still proved accurate enough to guide the navigation of spacecraft.

Although Newton's law of gravitation offered no fundamental explanatory mechanism for gravity, its usefulness of explanation lay in a higher level of cause and effect. Using the law allowed physicists and astronomers to bridge the relationship between cause and effect with regard to falling bodies and orbiting planets.

In addition, Newton's law found widespread acceptance and usage because it was a universal law that related information about bodies far removed from direct experimentation. Observation and induction based upon Newton's law yielded rich insight into the workings of the natural world, and Newton's law of universal gravitation became a powerful impetus to further the generalizations of natural laws gleaned from the rise of experimentalism during the Scientific Revolution. Newton's law became a powerful and testable verification that the cosmos could yield to inductive reasoning (i.e. where a more general case is used to reason to a more specific case).

Providing proof of the universality of Newton's law provided an impetus to eighteenth-century astronomers, including German-born English astronomer William Herschel (1738-1822). Although Herschel is most famous for his discovery of the planet Uranus in 1781, his celestial surveys not only provided an extensive star catalogue, they also provided abundant and unwavering validation of the universality of Newton's law.

As a derivation of Kepler's second law, Newton's law mathematically fulfilled all of the requirements of a force propelling planetary motion. In accord with both Kepler's laws and Newton's laws of motion, the Sun was at the focus of the elliptical planetary orbits exerting a gravitational pull that, in specific accord with Kepler's third law, resulted in the proper relation of the planets' sidereal period to their mean distance from the Sun. Because the force of gravity directly depended upon the masses of the bodies, Newton's law of universal gravitation was also in accord with Newton's own third law of motion. More importantly, Newton used the law of universal gravitation to actually correct a defect in Kepler's third law. Kepler had failed to consider the gravitational influence of the smaller planetary body on the greatly more massive Sun. Newton's refinement and advancement of a mutual gravitational force proved important to the determination of subtleties in orbital mechanics that ultimately allowed the prediction of masses for the planets and other celestial objects. Ultimately, Newton's law of universal gravitation would, in the twentieth century, provide evidence of the existence of black holes.

The Newtonian methodology of simplifying mass to a point (i.e. with regard to gravitational fields, all of the mass of a body can be considered to lie in a center of mass without physical space) also proved a brilliant simplification that enabled the mathematical advancement of mechanics and electromagnetism.

Newton's law of universal gravitation also laid the template for the articulation of subsequent physical law. For a century after the publication of Principia, scientists tried to seize on Newton's law of universal gravitation to explain other at-a-distance phenomena (e.g. magnetism). Many failed in their attempts to characterize electrical and magnetic phenomena as forces analogous to gravitational force because they failed to properly integrate the effects of infinitesimal forces. By the start of the nineteenth century, however, it was discovered that electrostatic forces, the force between two charged particles, indeed was mathematically similar to Newton's law of universal gravitation.

The magnitude of the electrostatic force was found to be directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between the charges. Accordingly, both the electro-static force and the gravitational force obey Newton's third law, are characterized by magnitude and direction (i.e. forces can be added as vectors), act at a distance through seemingly empty space, and are inverse square law forces. Although there were important differences (e.g. although gravitational force is always attractive, electrostatic forces can be both attractive and repulsive), the formulation of the electrostatics force—a force much stronger than gravity, as articulated in Coulomb's law—was built on the Newtonian formulation of gravitational force.

The lack of a fundamental explanation for the actual mechanism of gravity, and Newton's own speculations, led to the assumption that there must be some universal or cosmic ether through which gravity acted. Although the need for such an ether was dispelled by Scottish physicist James Clerk Maxwell's (1831-1879) development of a set of equations that accurately described electromagnetic phenomena and subsequently by the late-nineteenth-century ingenious experiments of Albert Michelson (1852-1931) and Edward Morley (1838-1923), the quest for the discovery of a such an ether was to consume physicists until early in the twentieth century, when the need for its existence was rendered moot by the advancement of relativity theory.

Because Newton's law of universal gravitation was so mathematically simple and precise, it strengthened the idea that all the laws describing the universe should be mathematical. Correspondingly, Newton's law also fostered belief that the universe was governed in accord with mathematical laws. In turn this led to the reassertion of a Pythagorean concept of God as the ultimate mathematician.

For theologians the predictability of the law of gravity provided comforting reassurance that the universe was governed by regular laws that provided glimpses of divine revelation. For others, the mechanistic, mathematical, and predetermined influence of gravity left no need for a God to guide the heavens, and they too relied on the predictability of Newton's law to advance their arguments. For both camps, Newton's law was simply sufficient to explain a clockwork universe.

After Newton, the appearance of comets was not to be interpreted as a direct sign from God, but rather, in accord with Newton's law of universal gravity, a natural consequence of the attraction of the Sun for a body traveling through the solar system on a highly elliptical orbit. In essence, Newton's law of universal gravitation, a marvel of scientific reasoning, swept away the supernatural and made the expanse of the universe knowable and predictable.

K. LEE LERNER