## Key Concepts

**The mutual attraction of all entities with mass or energy in the universe**. Gravity, also referred to as gravitation, is one of the four fundamental interactions in nature. We experience gravity in everyday life as the force that holds our feet to the ground and brings a thrown ball back toward the Earth (Fig. 1). More broadly, gravity holds our planet in orbit around the Sun, and our Sun in orbit around the center of the Milky Way Galaxy. At grander scales, gravity holds galaxy clusters together and is the force responsible for building up structure across the expanse of the cosmos. * See also: ***Cosmology**; **Earth**; **Earth's gravity field**; **Fundamental interactions**; **Galaxy**; **Milky Way Galaxy**; **Planet**; **Solar system**; **Sun**; **Universe**

The first successful description of universal gravitation was offered by English physicist and mathematician Isaac Newton in the seventeenth century. In the twentieth century, German-born U.S. theoretical physicist Albert Einstein proposed the general theory of relativity, which subsumed and superseded Newton's laws, although Newtonian mechanics are sufficient for accurately modeling nearly all practical instances in physics and engineering (except at high speeds, high energies, and small scales). General relativity describes gravity as a property emerging from the warping of a four-dimensional—three spatial dimensions plus time—construct of reality known as spacetime. Bodies with larger masses cause more curvature in spacetime, which manifests as a stronger gravitational field (Fig. 2). * See also: ***Relativity**; **Spacetime**

Einstein's equations predict gravitation's effects to an astonishing degree of accuracy. However, general relativity is inconsistent with quantum mechanics and the force of gravity is not unified with the three forces of the standard model of particle physics. A related mystery regarding gravity is its weakness compared to the other fundamental forces. The gravitational interaction between a proton and an electron in an atom is of the order of 10^{40} times weaker than the electromagnetic interaction between the two particles. Much work in theoretical physics is dedicated to developing frameworks of quantum gravitation that render gravity compatible with quantum mechanics. * See also: ***Atom**; **Electromagnetism**; **Electron**; **Proton**; **Quantum gravitation**; **Quantum mechanics**; **Standard model**

### Newton's law of gravitation

Newton's law of universal gravitation, first published in the *Principia* in 1686 CE, states that every two particles of matter in the universe attract each other with a force that acts in the line joining them, the intensity of which varies as the product of their masses and inversely as the square of the distance between them. Expressed mathematically, the gravitational force *F* exerted between two particles with masses *m*_{1} and *m*_{2} separated by a distance *d* is given by Eq. (1), where *G* is called the constant of gravitation.

Newton verified that the gravitational force between the Earth and the Moon, necessary to maintain the Moon in its orbit, and the gravitational attraction at the surface of the Earth were related by an inverse-square law of force. Let *E* be the mass of the Earth, assumed to be spherically symmetrical with radius *R*. Then the force exerted by the Earth on a small mass m near the Earth's surface is given by Eq. (2), and the acceleration of gravity on the Earth's surface, *g*, by Eq. (3).

In Newtonian gravitation, *G* is an absolute constant, independent of time, place, and the chemical composition of the masses involved. Partial confirmation of this was provided before Newton's time by the experiment attributed to Italian physicist and astronomer Galileo in which different weights released simultaneously from the top of the Tower of Pisa reached the ground at the same time. Newton found further confirmation, experimenting with pendulums made out of different materials.

In Newtonian gravitation, the mass of a body appears as inertial mass, a measure of resistance to acceleration, and as gravitational mass in the expression of the gravitational force. Whereas mass in Newtonian mechanics is an intrinsic property of a body, the weight of the body depends on certain forces acting on it. For example, the weight of a body on the Earth depends on the gravitational attraction of the Earth on the body and also on the centrifugal forces due to the Earth's rotation. The body would have lower weight on the Moon, even though its mass would remain the same. * See also: ***Centrifugal force**; **Classical mechanics**; **Free fall**; **Moon**; **Newton's laws of motion**; **Weight**; **Weightlessness**

### Relativistic theory

The theory of relativity developed in the nineteenth century from attempts to describe electromagnetic phenomena in moving systems. Einstein's general theory of relativity, which he proposed in 1916, states that the geometry of spacetime is affected by the presence of matter and radiation. The relationship between mass-energy and the spacetime curvature is therefore a relativistic generalization of the Newtonian law of gravitation. Newtonian mechanics considered gravity as a direct action-at-a-distance and in the early days did not properly account for the time delay between the action of gravity experienced by a body and the motion of the source. General relativity, on the other hand, considers gravitational effects as being geometric and time-related. * See also: ***Electromagnetism**; **Energy**; **Mass**; **Relativity**; **Spacetime**

Einstein's theory has since gone on to pass increasingly stringent tests. Initially, general relativity accounted for the full motion of the perihelion of the orbit of Mercury, which had emerged as a serious discrepancy in Newtonian mechanics. General relativity also rightly predicted that light passing a massive body is deflected, as a result of gravitational lensing (Fig. 3). Another of the many examples involves the prediction that clocks run more slowly in strong gravitational fields compared to weak ones. To maintain accuracy, the clocks in the Global Positioning System of satellites must make relativistic corrections for both their motions relative to the Earth and their gravitational potential relative to the Earth's surface. * See also: ***Atomic clock**; **Global Positioning System (GPS)**; **Gravitational lens**; **Mercury (planet)**; **Optical clocks and relativity**; **Satellite (astronomy)**; **Satellite navigation systems**

Gravitational waves, or gravitational radiation, is still another consequence of the general theory of relativity. Colloquially thought of as "ripples" in the curvature of space-time, gravitational waves are propagating gravitational fields, or propagating patterns of strain, traveling at the speed of light. They carry energy and can exert forces on matter in their path, producing, for instance, extremely small vibrations, of the order of thousandths of the diameter of a proton. The technological capability to detect such small vibrations experimentally was not available until the building of the Laser Interferometer Gravitational-wave Observatory (LIGO) in the early twentieth century. In 2015, about a century after Einstein's original prediction, the first direct detection of gravitational waves with LIGO occurred, further cementing general relativity's place as the established theory of gravitation. * See also: ***Gravitational radiation**; **LIGO (Laser Interferometer Gravitational-wave Observatory)**