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Newtonian gravity is the classical theory of gravitation formulated by Isaac Newton and published in his Philosophiæ Naturalis Principia Mathematica (1687). The theory describes gravity as a force acting instantaneously at a distance between any two bodies with mass, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them. For roughly two centuries, Newtonian gravity served as the foundational framework for celestial mechanics and terrestrial physics, and it remains the standard model for most engineering and applied physics contexts where relativistic effects are negligible.

The central expression of Newtonian gravity is the law of universal gravitation:

F = G(m₁m₂)/r²

where F is the gravitational force between two point masses, m₁ and m₂ are the masses of the two bodies, r is the distance between their centers of mass, and G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N·m²·kg⁻²). The force acts along the line connecting the two bodies and is attractive. Paired with Newton's second law of motion (F = ma), the law of universal gravitation enables precise calculation of planetary orbits, tidal forces, projectile trajectories, and a wide range of gravitational phenomena.

Newton described gravity operationally - as a mathematical law governing observable behavior - while explicitly declining to speculate on its underlying mechanism. His phrase hypotheses non fingo (“I feign no hypotheses”) marked a deliberate separation between predictive formalism and physical explanation, a distinction that shaped subsequent debates about the theory's foundations.

The law of universal gravitation synthesized earlier work by Johannes Kepler on planetary motion and Galileo Galilei on terrestrial acceleration. Newton demonstrated that Kepler's three empirical laws of planetary motion follow mathematically from the inverse-square law. Subsequent developments extended the framework to predict the return of Halley's Comet, the existence and position of Neptune (predicted mathematically before telescopic confirmation in 1846), and the shape of the Earth. Newtonian gravity dominated physics until the early twentieth century, when anomalies - most notably the precession of Mercury's perihelion - pointed toward its limits. For a full account, see Newtonian Gravity - History.

Newtonian gravity produces highly accurate predictions in conditions where gravitational fields are weak and velocities are small relative to the speed of light. It breaks down in strong-field regimes and at high velocities, where general relativity - Einstein's 1915 theory of gravitation - supersedes it. General relativity recovers Newtonian gravity as a limiting case under weak-field, low-velocity conditions. Practical applications including satellite navigation, ballistic trajectories, and orbital mechanics routinely use Newtonian equations, sometimes with small relativistic correction terms. The theory does not account for gravitational waves, frame-dragging, or the gravitational lensing of light, all of which require the full relativistic treatment.

There is broad consensus in physics and astronomy that Newtonian gravity is an accurate and sufficient model within its domain of applicability, and that it is superseded by general relativity outside that domain. See Newtonian Gravity - Physics Consensus for a structured account of where agreement exists and where open questions remain.

Newtonian gravity is not contested as an empirical model within its established domain. Philosophical and foundational questions, however, have generated sustained debate.

• Action at a distance - Newton's formulation requires that gravity acts instantaneously across arbitrary distances with no specified medium or mechanism. This was criticized in Newton's own time, notably by Leibniz and Huygens, and remained philosophically contentious until field theories replaced action-at-a-distance as the standard framework. See Action at a Distance - Viewpoint.

• Absolute space and time - Newtonian mechanics presupposes absolute space and absolute time as the framework within which forces and motions are defined. This was challenged by Leibniz, later by Ernst Mach, and ultimately replaced in physics by the relational spacetime of special and general relativity. See Absolute Space and Time - Viewpoint.

• Instrumentalism vs. realism - Newton's deliberate agnosticism about gravity's underlying nature raised the question of whether physical theories need to describe real mechanisms or only predict observations accurately. This debate extends beyond gravity into the philosophy of science generally. See Instrumentalism vs. Realism - Viewpoint.

• Modified Newtonian dynamics (MOND) - Some researchers have proposed modifications to the inverse-square law at low accelerations as an alternative to dark matter explanations for galactic rotation curves. MOND and its variants remain minority positions within physics but are actively debated. See Modified Newtonian Dynamics - Viewpoint.

• Newtonian Gravity - History
• Newtonian Gravity - Debate
• Newtonian Gravity - Physics Consensus
• General Relativity
• Gravitational Constant
• Classical Mechanics
• Dark Matter
• Philosophy of Science

1. Newton, Isaac. Philosophiæ Naturalis Principia Mathematica. London: Royal Society, 15 July 1687 [N.S.].
2. Cohen, I. Bernard, and Anne Whitman, trans. The Principia: Mathematical Principles of Natural Philosophy. Berkeley: University of California Press, 1999.
3. Le Verrier, Urbain. “Recherches sur les mouvements de la planète Herschel (dite Uranus).” Connaissance des Temps (1846).
4. Einstein, Albert. “Die Grundlage der allgemeinen Relativitätstheorie.” Annalen der Physik 49 (1916): 769-822.
5. Milgrom, Mordehai. “A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis.” Astrophysical Journal 270 (1983): 365-370.
6. Jammer, Max. Concepts of Force: A Study in the Foundations of Dynamics. Cambridge: Harvard University Press, 1957.