Gravity, a force of attraction that exists between every pair of objects in the universe, is proportional to the mass of each object in each pair, and inversely proportional to the square of the distance between the two. Thus, F = Gm1m2/r2, where m1 is the mass of the first object, m2 is the mass of the second object, r is the distance between their centers, and G is a fixed number termed the gravitational constant. (If m1 and m2 are given in kilograms and r in meters, then G = 6.673 × 10-1N m2/kg2.)
Background and scientific foundations
Greek philosopher Aristotle (384–322 BC) posed, following earlier traditions, that the material world consisted of four elements: Earth, water, air, and fire. Each element had a natural or proper place in the universe to which it spontaneously inclined. For example, Earth belonged at the very center, water in a layer covering Earth, air above the water, and fire above the air. Each element had a natural tendency to return to its proper place. Rocks fell toward the center and fire rose above the air. This was one of the earliest explanations of gravity; that it was the natural tendency for the heavier elements, Earth and water, to return to their proper positions near the center of the universe.
Aristotle's model of the universe also included the moon, sun, the visible planets, and the fixed stars. He assumed that these were outside the layer of fire and were made of a fifth element, the ether or quintessence (a term derived from the Latin expression quinta essentia, or fifth essence, used by Aristotle's medieval translators). The celestial bodies circled Earth attached to nested ethereal spheres centered on Earth. No forces were required to maintain these motions. Everything was considered perfect and unchanging, having been set in motion by a God.
Later, Polish astronomer Nicolaus Copernicus (1473–1543) developed a heliocentric (sun-centered) model to replace the geocentric (Earth-centered) one, which had been dominant in Europe and the Near East since Aristotle's time. (Non-European astronomers unfamiliar with Aristotle, such as the Chinese and Aztecs, developed their own geocentric models.) Copernicus's model placed the sun in the center of the universe with the planets orbiting the sun in perfect circles. It signaled a dramatic change, prompting the name Copernican Revolution.
As scientists sought to explain these celestial motions, some sought to understand terrestrial mechanics. They were guided by the idea that heavier objects would fall faster than lighter ones (a rock vs. a feather). The fault in this experiment is that air resistance affects the rate at which objects fall although it actually plays a lesser role when a large rock and a small rock are dropped. Eventually, Italian physicist Galileo Galilei (1564–1642) formulated his law of falling bodies. It stated that disregarding air resistance, bodies in free fall speed up with a constant acceleration (rate of change of velocity) that is independent of their weight or composition. Galileo also determined a formula to describe the distance that a body falls in a given time. Ultimately, Galileo described the effect of gravity on objects on Earth. However, it was English physicist Isaac Newton (1642–1727) who discovered just how universal gravity is. Legend says that Newton understood gravity after an apple fell out of a tree and hit him on the head. Yet this story may be fiction. Newton did acknowledge a falling apple helped him develop his theory of gravity though.
According to Newton's universal law of gravitation, all objects in the universe attract all other objects. Thus, the sun attracts Earth, Earth attracts the sun, Earth attracts a book, a book attracts Earth, and so on. The gravitational pull between small objects, such as molecules and books, is generally negligible. The gravitational pull exerted by larger objects, such as stars and planets, organizes the universe. Gravity keeps us on the Earth, the moon in orbit around the Earth, and the Earth in orbit around the sun. Newton's law of gravitation explains that the strength of the force of attraction depends on the masses of the two objects. The mass of an object is a measure of how much material it has. However, it is not the same as its weight, which is a measure of how much force a given mass experiences in a given gravitational field. A given rock, for example, will have the same mass anywhere in the universe but will weigh more on Earth than on the moon.
We do not feel the gravitational forces from objects other than the Earth because they are weak. The gravitational force between two objects becomes weaker if the two objects are moved apart and stronger if they are brought closer together. The force depends on the distance between the objects. If we take two objects and double the distance between them, the force of attraction decreases to one fourth of its former value. If we triple the distance, the force decreases to one ninth of its former value. The force depends on the inverse square of the distance.
Newton explained how bodies respond to forces (including gravitational forces) that act on them. His second law of motion states that a net force (i.e., force not canceled by a contrary force) causes a body to accelerate and the amount of this acceleration is inversely proportional to the mass of the object. This means that under the influence of a given force, more massive objects accelerate more slowly than less massive objects. Alternatively, to experience the same acceleration, more massive objects require more force. Consider the gravitational force exerted by Earth on two rocks, the first with a mass of 2 lb (1 kg) and a second with a mass of 22 lb (10 kg). Since the mass of the second is 10 times the mass of the first, the gravitational force on the second will be 10 times the force on the first. However, a 22-lb (10-kg) mass requires 10 times more force to accelerate it. As such, both masses accelerate Earthward at the same rate. Ignoring Earth's own acceleration toward the rocks (which is extremely small), it follows that equal falling rates for small objects are a natural consequence of Newton's law of gravity and second law of motion.
Another example would be what happens when a ball is thrown horizontally. If thrown slowly, it will hit the ground a short distance away. If thrown faster, it will land farther away. Since the Earth is round, the Earth will curve slightly away from the ball before it lands so the farther the throw, the greater the amount of curve. If one could throw or launch the ball at 18,000 mi/h (28,800 km/h), the Earth would curve away from the ball by the same amount that the ball falls. Thus, the ball would never get any closer to the ground and would be in orbit around the Earth. Gravity still accelerates the ball at 9.8 m/s2 toward the Earth's center, but the ball never approaches the ground (this is exactly what the moon does). In addition, the orbits of Earth and other planets around the sun and all the motions of the stars and galaxies follow Newton's laws. His law of gravitation is considered "universal" because it describes the effect of gravity on all objects in the universe. Newton's laws of motion and gravity were published in 1687 in his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).
German-born American physicist Albert Einstein (1879–1955) worked to rectify some issues in Newton's theory of gravity, especially pertaining to the concept that the force between two objects depends on the distance between them. If one object moves closer, the other object will feel a change in the gravitational force. Newton thought this change would be immediate even if the objects were millions of miles apart. Einstein assumed that nothing could travel instantaneously, not even a change in force. Einstein sought to change the way people thought about space, time, and the structure of the universe—something he did via his general theory of relativity.
Einstein asserted that a mass bends space like a heavy ball, making a dent on a rubber sheet. He contended that space and time are intimately related to each other. Einstein asserted that we do not live in three spatial dimensions and time, but rather in a four-dimensional space-time continuum, a seamless blending of the four. It is not "space," naively conceived, but space-time that warps in reaction to a mass. This, in turn, explains why objects attract each other. Einstein's general relativity makes predictions that Newton's theory of gravitation does not. Since particles of light (photons) have no mass, Newtonian theory predicts that they will not be affected by gravity. However, if gravity is due to the curvature of space-time, then light should be affected in the same way as matter. This proposition was tested as follows. During the day, the sun is too bright to see any stars but during a total solar eclipse the sun's disk is blocked by the moon, making it possible to see stars that appear in the sky near the sun. During the total solar eclipse of 1919, astronomers measured the positions of several stars close to the sun and determined that the measured positions were altered as predicted by general relativity. The sun's gravity bent the starlight so that the stars appeared to shift their locations when they were near the sun. The detection of the bending of starlight by the sun was one of the great early experimental verifications of general relativity.
General relativity also theorizes that waves can travel in gravitational forces just as waves travel through air or other media. These gravitational waves are formed when masses move back and forth in space-time, much as sound waves are created by the oscillations of a speaker cone. In 1974, scientists discovered two stars orbiting around each other that were losing energy at the exact rate required to generate the predicted gravity waves. That is, they were steadily radiating energy away in the form gravitational waves. Scientists have already verified that changes in gravitation do propagate at the speed of light, as predicted by Einstein's theory.
The predictions of general relativity include the existence of black holes. When a very massive star runs out of fuel, the gravitational self-attraction of the star makes it shrink. If the star is massive enough, it will collapse to a point having finite mass but infinite density. Space-time will be so distorted in the vicinity of this "singularity," that not even light will be able to escape; hence the term "black hole."
Issues and Developments
In 2017, American physicists Rainer Weiss, Barry C. Barish, and Kip S. Thorne received the Nobel prize in physics for their detection of gravitational waves that provided "an entirely new way of observing the most violent events in space and testing the limits of our knowledge."
The greatest remaining challenge for gravity theory is unification with quantum mechanics. Quantum theory describes the physics of phenomena at the atomic and subatomic scale but does not account for gravitation. General relativity, which employs continuous variables, does not describe the behavior of objects at the quantum scale. Physicists therefore seek a theory of "quantum gravity," a unified set of equations that described the whole range of known phenomena. Some theorists believe the highly mathematical field of string theory will be able to reconcile gravity and quantum mechanics. Results from experiments at the Large Hadron Collider further complicate this goal as they place significant constraints on prevalent string theory models.