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Newton's law of universal gravitation

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Newton's law of universal gravitation says that every particle in the universe attracts every other particle. The force pulls along the line joining them, it grows with the product of their masses, and it becomes weaker with the square of the distance between them.[1] The law was set out by Isaac Newton in his book the Principia, published in 1687.[2] It was the first exact description of the gravitational force, and it showed that the same force explains both falling objects on Earth and the motions of the Moon and planets.[3]

The law

Gravity is a simple force. It always attracts and never repels, and its strength depends only on the masses involved and the distance between them.[4] In symbols the law is written F = G'mM/r2, where F is the size of the force, m and M are the two masses, r is the distance between them, and G is the gravitational constant.[5] Measurements give G a value of about 6.674 × 10−11 N·m2/kg2 in SI units.[6] Because the force falls off with the square of the distance, it is called an inverse square law. Laws of this shape appear in many parts of nature, because the strength of a source spreads out over the surface of a sphere that grows as the distance increases.[7]

History

Newton was not the first person to think that one force might cause both the weight of things on Earth and the motion of the planets.[8] Galileo Galilei had argued that falling bodies and planetary motions had the same cause, and Robert Hooke, Christopher Wren and Edmund Halley had also made some progress.[9] Newton went further. He gave the force an exact mathematical form and used it to show that moons, planets and comets should travel along paths called conic sections, such as circles, ellipses and parabolas.[10] He reasoned that objects near the Earth's surface and the much more distant Moon could both be explained by a force between any two objects equal to the product of their masses divided by the square of the distance between them.[11] A well-known story says Newton was inspired by seeing an apple fall from a tree. According to the textbook College Physics, this story is part of worldwide folklore and may even be based in fact.[12]

The Principia had three editions in Newton's lifetime: London in 1687, Cambridge in 1713 and London in 1726.[13] The Stanford Encyclopedia of Philosophy calls it the single most important work in the change from early modern natural philosophy to modern physical science.[14]

Acceptance

Like many revolutionary ideas, the law was not accepted straight away. The French scientist and philosopher Émilie du Châtelet helped to establish Newton's theory in France and the rest of mainland Europe.[15] She translated and added to Newton's key work, and used calculus to explain gravity, which helped the theory to be accepted.[16] According to the Stanford Encyclopedia of Philosophy, the leading thinkers Christiaan Huygens and Gottfried Wilhelm Leibniz strongly opposed the theory. They saw it as calling on a mysterious power that acted at a distance, because Newton had not proposed any contact mechanism through which gravity could act.[17]

Measuring G

About a century after Newton published his law, Henry Cavendish measured the constant G in a careful experiment.[18] He hung small masses from a wire and placed larger masses near them. The gravitational pull twisted the wire by an amount that could be measured.[19]

Limits

Since Albert Einstein's special and general theories of relativity, Newton's theory has been seen as holding only to a very close approximation, and only in limited circumstances.[20] Modern experiments of the Cavendish type continue to test how the law works, including over distances smaller than a millimetre.[21]

See also

References

  1. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. Stated in modern language, Newton's universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
  2. ↑ "Isaac Newton". Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 18 October 2026. He became a dominant figure in Britain almost immediately following publication of his Principia in 1687
  3. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. Sir Isaac Newton was the first scientist to precisely define the gravitational force, and to show that it could explain both falling bodies and astronomical motions.
  4. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. The gravitational force is relatively simple. It is always attractive, and it depends only on the masses involved and the distance between them.
  5. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. G G is a universal gravitational constant—that is, it is thought to be the same everywhere in the universe.
  6. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. It has been measured experimentally to be G = 6 . 674 × 10 − 11 N ⋅ m 2 kg 2
  7. ↑ Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). "13.1 Newton's Law of Universal Gravitation". University Physics Volume 1. OpenStax. Retrieved 18 October 2026. We now know that this inverse square law is ubiquitous in nature, a function of geometry for point sources. The strength of any source at a distance r is spread over the surface of a sphere centered about the mass.
  8. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. But Newton was not the first to suspect that the same force caused both our weight and the motion of planets.
  9. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. His forerunner Galileo Galilei had contended that falling bodies and planetary motions had the same cause. Some of Newton's contemporaries, such as Robert Hooke, Christopher Wren, and Edmund Halley, had also made some progress toward understanding gravitation.
  10. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. But Newton was the first to propose an exact mathematical form and to use that form to show that the motion of heavenly bodies should be conic sections—circles, ellipses, parabolas, and hyperbolas.
  11. ↑ Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). "13.1 Newton's Law of Universal Gravitation". University Physics Volume 1. OpenStax. Retrieved 18 October 2026. He could explain this by postulating that a force exists between any two objects, whose magnitude is given by the product of the two masses divided by the square of the distance between them.
  12. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. The inspiration of Newton's apple is a part of worldwide folklore and may even be based in fact.
  13. ↑ "Newton's Philosophiae Naturalis Principia Mathematica". Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 18 October 2026. London, 1687; Cambridge, 1713; London, 1726.
  14. ↑ "Isaac Newton". Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 18 October 2026. for having formulated the theory of universal gravity — the latter in his Principia , the single most important work in the transformation of early modern natural philosophy into modern physical science.
  15. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. Like many revolutionary discoveries, it was not immediately accepted. Prominent French scientist and philosopher Émilie du Châtelet helped establish Newton's theory in France and mainland Europe.
  16. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. translated and augmented Newton's key work. She also utilized calculus to explain gravity, which helped lead to its acceptance.
  17. ↑ "Isaac Newton". Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 18 October 2026. His influence on the continent, however, was delayed by the strong opposition to his theory of gravity expressed by such leading figures as Christiaan Huygens and Leibniz, both of whom saw the theory as invoking an occult power of action at a distance in the absence of Newton's having proposed a contact mechanism by means of which forces of gravity could act
  18. ↑ Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). "13.1 Newton's Law of Universal Gravitation". University Physics Volume 1. OpenStax. Retrieved 18 October 2026. A century after Newton published his law of universal gravitation, Henry Cavendish determined the proportionality constant G by performing a painstaking experiment.
  19. ↑ Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). "13.1 Newton's Law of Universal Gravitation". University Physics Volume 1. OpenStax. Retrieved 18 October 2026. He constructed a device similar to that shown in Figure 13.3 , in which small masses are suspended from a wire. Once in equilibrium, two fixed, larger masses are placed symmetrically near the smaller ones. The gravitational attraction creates a torsion (twisting) in the supporting wire that can be measured.
  20. ↑ "Newton's Philosophiae Naturalis Principia Mathematica". Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 18 October 2026. The retrospective view of the Principia has been different in the aftermath of Einstein's special and general theories of relativity from what it was throughout the nineteenth century. Newtonian theory is now seen to hold only to high approximation in limited circumstances
  21. ↑ Urone, Paul Peter; Hinrichs, Roger (2022). "6.5 Newton's Universal Law of Gravitation". College Physics 2e. OpenStax. Retrieved 18 October 2026. Ongoing measurements there use a torsion balance and a parallel plate (not spheres, as Cavendish used) to examine how Newton's law of gravitation works over sub-millimeter distances.
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