History of gravitational theory

• 1. Introduction

  ›

  The history of gravitational theory stretches back more than two thousand years, from pre-Socratic Greek philosophers puzzling over why things fall to physicists today searching for a unified theory of everything. In 1585, Flemish polymath Simon Stevin dropped two lead balls from the Nieuwe Kerk in Delft and listened for the sound of their impact. Both hit at the same time. That single experiment overturned a belief Aristotle had set in motion nearly two thousand years earlier.

  How did humans move from explaining falling objects through cosmic "Love" and "Strife" to encoding gravity in ten simultaneous non-linear differential equations? Why did Newton's theory face immediate resistance from continental philosophers, and what planetary crisis nearly broke it a century after publication? How did a thought Einstein described as "the happiest thought of my life" eventually replace Newton's entire framework? And what remains unresolved, even now, about the force that holds the universe together?

• 2. Ancient Roots

  ›

  Empedocles, writing in the 5th century BC, described the cosmos as governed by two opposing forces he named Philotes and Neikos, meaning Love and Strife. These were not metaphors for him. They were fundamental physical agents, one pulling matter together and the other driving it apart. His framework was the earliest recorded attempt to explain gravitational attraction as a universal principle rather than a property of specific objects.

  Aristotle, writing in the 4th century BC, gave the subject its first systematic treatment. He taught that heavy bodies, those composed of earth and water, moved downward by their very nature toward the center of the geocentric universe. Light bodies, composed of fire and air, moved upward by levity. Objects near the fixed stars were made of aether, whose natural motion was circular. Aristotle correctly observed that objects falling through a medium slow down as the medium grows denser, but he drew the wrong conclusion: that weight alone determined fall speed.

  Strato of Lampsacus challenged this directly. He argued that the greater impact of a falling body was not due to weight but to increasing speed. Epicurus, writing around 270 BC, offered a competing model in which atoms fall at equal speed in a vacuum regardless of mass, with upward motion arising only from atomic collisions. Aristarchus of Samos went further still, proposing Earth's rotation and its orbit around the Sun, while Seleucus of Seleucia described the Moon's gravitational influence on tidal range.

  Archimedes, working in the 3rd century BC, gave the study of gravity its first mathematical precision. He located the center of mass of a triangle, proved the law of the lever by reasoning about equal weights, and in On Floating Bodies described the upward buoyant force exactly equal to the weight of displaced fluid. His fluids, notably, were not self-gravitating; he assumed all fluid surfaces were spherical with the Earth's center as their center.

• 3. Medieval Transmissions

  ›

  John Philoponus, a Byzantine Alexandrian scholar writing in the 6th century AD, made a specific empirical claim that would echo through the centuries. He wrote that if two bodies differing greatly in weight are dropped from the same height simultaneously, "the difference in time is a very small one" rather than proportional to the weight difference, directly contradicting Aristotle.

  Philoponus also proposed the theory of impetus, a causative force imparted to a moving object that diminishes over time. This was not a small revision to Aristotle; it replaced the idea that continued motion requires continued force with something closer to what we now call momentum. Ibn Sina, the 11th-century Persian polymath known in Europe as Avicenna, refined this theory in The Book of Healing. Where Philoponus thought impetus would fade even in a vacuum, Ibn Sina argued it was persistent and required external forces such as air resistance to dissipate it. He also distinguished between force and inclination, foreshadowing the concept of inertia.

  Brahmagupta, the 7th-century Indian astronomer working in Ujjain, described gravity in terms that were strikingly modern. He wrote that "it is the nature of the earth to attract and to keep things" and that seeds thrown in any direction always return to it, never rising upward from it. Al-Biruni, another 11th-century Persian scholar, extended this idea to heavenly bodies: he proposed that the Moon, the Sun, and other celestial objects possess mass, weight, and gravity just as Earth does, and criticized both Aristotle and Ibn Sina for restricting these properties to Earth alone.

  Abu'l-Barakat al-Baghdadi, writing in the 12th century, took Ibn Sina's impetus theory and pushed it toward acceleration. He argued that a continuous force produces not uniform motion but acceleration, a claim that scholar Shlomo Pines later called "the oldest negation of Aristotle's fundamental dynamic law" and an anticipation of classical mechanics.

• 4. The Renaissance Crucible

  ›

  Nicole Oresme proved the mean speed theorem in 1382. A uniformly accelerated body starting from rest covers the same distance as a body moving at a constant speed equal to half the final velocity of the accelerated body. Oresme's proof would feed directly into the equations Galileo developed more than two centuries later, but in 1382 there was no way to measure small time intervals accurately enough to test it against falling objects.

  By 1544, according to Benedetto Varchi, two Italians had already run experiments that discredited Aristotle's weight-speed claim. Francesco Beato, a Dominican philosopher at Pisa, and Luca Ghini, a physician and botanist from Bologna, found empirically that objects fall at equal speeds regardless of mass. Domingo de Soto formalized the idea in 1551, theorizing in his book Physicorum Aristotelis quaestiones that objects in free fall accelerate uniformly.

  Galileo, who derived his kinematics from the 14th-century Merton College tradition and from Buridan, and possibly from de Soto as well, put this on rigorous mathematical footing. In a 1604 letter to Paolo Sarpi, he correctly stated that the distance a falling object travels is proportional to the square of the elapsed time. The result appeared in Two New Sciences in 1638. Italian Jesuits Grimaldi and Riccioli confirmed this relationship experimentally between 1640 and 1650, and also calculated the gravitational constant of Earth by timing pendulum oscillations.

  Simon Stevin's 1585 Delft experiment with lead balls predated Galileo's published work and reached the same conclusion from sound alone. His result was published in 1586. In 1632, Galileo put forth the basic principle of relativity, a conceptual shift that would eventually underpin Einstein's entire program.

• 5. Newton's System and Its Troubles

  ›

  Robert Hooke wrote to Isaac Newton in 1679, proposing that orbital motion combined tangential inertial motion with a central force, and asking Newton to calculate the trajectory implied by an inverse-square force. Newton later denied that Hooke had given him the idea. In January 1684, Hooke told Edmond Halley and Christopher Wren that he had proven the inverse-square law but refused to show his proof. That summer, Halley visited Newton directly. Newton said the trajectory would be an ellipse, and by November 1684 he sent Halley a paper mathematically deriving Kepler's laws from an inverse-square force.

  Newton published Philosophiae Naturalis Principia Mathematica in 1687, with Halley's support. The Principia sold out quickly enough that Newton published a second edition in 1713. Yet acceptance was slow. German philosopher Gottfried Wilhelm Leibniz objected that Newton's gravity relied on action at a distance, calling the mechanism "invisible, intangible, and not mechanical." Voltaire eventually wrote a book in 1738 to explain Newton's theory to French readers.

  The bigger crisis was astronomical. Observations from the early 1700s compared to ancient records suggested Saturn's orbit was growing while Jupiter's was shrinking. If sustained, Saturn would exit the solar system and Jupiter would collide with other planets or the Sun. Leonhard Euler tackled the problem in 1748, Joseph-Louis Lagrange in 1763, and Pierre-Simon Laplace in 1773. Laplace finally resolved it in 1784, roughly a century after Newton's first publication on gravity, showing the changes were periodic variations with periods far too long to be detected in existing records.

  Newton's greatest empirical victory came in 1846. Calculations by John Couch Adams and Urbain Le Verrier independently predicted the position of an unseen planet based on anomalies in Uranus's orbit. Le Verrier sent his prediction to Johann Gottfried Galle in Berlin. That same night, Galle spotted Neptune within one degree of the predicted location. Henry Cavendish had measured the gravitational constant precisely enough for these calculations in 1797, filling the gap Newton himself acknowledged in his formula.

• 6. Einstein's Revision

  ›

  In 1907, Albert Einstein described a realization he later called "the happiest thought of my life": a person in free fall experiences no gravitational field. Gravity and acceleration were exactly equivalent. Between 1911 and 1915 he developed this equivalence principle into general relativity, fusing three spatial dimensions and one dimension of time into the four-dimensional fabric of spacetime.

  General relativity replaced Newton's gravitational force with spacetime curvature. Einstein and David Hilbert discovered the field equations together; these are ten simultaneous, non-linear differential equations whose solutions describe the geometry of spacetime. Notable solutions include the Schwarzschild solution, describing spacetime around a non-rotating mass, which predicts black holes for objects smaller than a critical radius. The Kerr solution, for rotating masses, produces black holes with multiple horizons. The Robertson-Walker solution, dating to 1922 and 1924, predicts an expanding universe.

  Arthur Eddington confirmed the theory in 1919 by observing gravitational lensing of starlight around the Sun during a solar eclipse, matching Einstein's equations. Edwin Hubble then confirmed the expanding universe prediction in 1929. The Pound-Rebka experiment, the Hafele-Keating experiment, and the GPS system have all since confirmed that time runs slower at lower gravitational potentials. Irwin Shapiro identified the time delay of light passing near a massive object in 1964 using interplanetary spacecraft signals. In 2015, the LIGO experiments directly detected gravitational waves from two colliding black holes, the first direct observation of both phenomena simultaneously.

  Yet Einstein's own field equations contained a cosmological constant he added to account for what he assumed was a static universe. When Hubble showed the universe was expanding, that assumption collapsed. By the 1930s, Paul Dirac was hypothesizing that gravity slowly decreases over cosmic time. In 1980, Alan Guth and Alexei Starobinsky proposed that a negative pressure field drove cosmic inflation in the early universe. This concept, later named dark energy, was found in 2013 to have composed around 68.3% of the early universe.

• 7. Gravity's Open Edges

  ›

  Jacobus Kapteyn proposed the existence of dark matter in 1922, an unseen substance whose gravitational effects cause stars to orbit galaxies faster than visible matter alone could explain. Dark matter was found in 2013 to have comprised 26.8% of the early universe. Together with dark energy, it sits outside Einstein's relativity without an accepted explanation.

  General relativity itself breaks down at short distances of the order of the Planck length. In the framework of quantum field theory, gravity should arise from the exchange of virtual particles called gravitons, just as electromagnetism arises from virtual photons. This approach reproduces general relativity in the classical limit, but it fails at the smallest scales. Several decades of effort to reconcile general relativity with quantum mechanics have produced candidate frameworks, among them string theory, which requires additional spatial dimensions. In 1921, Swedish physicist Oskar Klein gave a physical interpretation to the idea of a fifth dimension that Theodor Kaluza had earlier attached to general relativity, forming a prototypical version of what would later be recognized as string theory.

  Hermann Bondi proposed in 1957 that negative gravitational mass paired with negative inertial mass would comply with general relativity and Newton's laws simultaneously, and found that this yielded singularity-free solutions to the relativity equations. The question of whether a complete theory of everything can encompass gravity alongside the other fundamental forces remains the central unsolved problem in theoretical physics, and dark matter's unexplained 26.8% share of the early universe is one of the sharpest constraints any such theory must satisfy.