Heliocentrism is, strictly speaking, the view that the sun is at the center of the universe, though it is now generally understood to mean only that the sun is the center of the solar system.
Heliocentrism was proposed by some ancient Greeks, but it never gained wide support because its proponents could not explain why the relative positions of the stars seemed to remain the same despite the Earth’s changing angles of perspective as it revolved about the Sun. It became the dominant view in the 1700s and 1800s. The idea that the sun is at the center of the universe was abandoned by the mid 20th century. It is now accepted that the real controversy is whether the sun or the Earth is the center of the solar system, or, in simpler terms, whether the sun goes around the Earth or the Earth goes around the sun. The Copernican revolution established the latter; the former is often attributed to Ptolemy.
Some people, perhaps in an attempt to make Ptolemaic system seem acceptable, or perhaps to show that it wasn't wrong after all, have pointed out that the two are in a sense equivalent, such as this statement from an earlier version of this page:
- Since the advent of relativity theory in the early 1900s, the laws of physics have been written in covariant equations, meaning that they are equally valid in any frame.
- (The use of the word "covariant" in the scientific literature generally refers to Einsteinian relativity.)
While they are equivalent in an abstract sense of Newtonian/Galilean relativity, that fact is useless in practice. One generally uses a coordinate system that is inertial, or nearly so, for the calculations that one is making.
- For ordinary activities on Earth, such as walking or driving one's car, a co-rotating geocentric system is the one to use. It doesn't matter which of the sun or the Earth goes around the other. But the Coriolis force does figure into very accurate calculations for airplanes, missiles, and artillery guns. It may also have been involved in the outcome of a football game.
- For calculations involving artificial Earth satellites, a non-rotating Earth-based coordinate system is the one to use.
- For calculations of planetary motions and interplanetary spacecraft, a non-rotating sun-based coordinate system (that is, Copernican heliocentric) is the one to use. Calculation of planetary motions was what led to the Copernican formulation.
- For galactic calculations, it doesn't really matter.
- Aristarchus of Samos (ca. 310-230 BC) proposed it, Archimedes discussed it, and the idea was well-known in Europe when Copernicus proposed a heliocentric model.