Heliocentric Theory

Johannes Kepler's (1571-1630) work enabled the heliocentric solar system model to accurately match and predict planetary positions on the zodiac for many centuries. After trying many geometric curves and solids in Copernicus's heliocentric model to match earlier observations of planetary positions, Kepler found that the model would match the observed planetary positions if the Sun is placed at one focus of elliptical planetary obits. This is Kepler's First Law of Planetary Motion. Kepler's three laws of planetary motion allow accurate matches and predictions of planetary positions.

Almost simultaneously, Galileo Galilei (1564-1642) built a small refracting telescope and began astronomical observations in 1609. Several of his observations lent support to Kepler's heliocentric theory:

1. Galileo discovered the four satellites of Jupiter (Io, Europa, Ganymede, and Callisto in order of increasing distance from Jupiter) in 1610. Their orbits around Jupiter showed that Jupiter and Earth were centers of orbital motion for celestial bodies (geocentric theory assumed that celestial bodies revolve only around Earth).
2. Galileo observed the disks of at least several planets. His observations of Venus's disk were especially important for determining whether the geocentric or heliocentric model was correct for the solar system. Ptolemy's geocentric model predicts that Venus's disk will show only the new Moon (dark) and crescent phases as it orbits Earth on its epicycle(s) and deferent (see Fig. 2). Kepler's modified Copernican heliocentric model predicts that Venus's disk will show all the phases of the Moon (including the half-moon, gibbous, and full Moon phases; see Fig. 3) as Venus and Earth both orbit the Sun. Galileo observed the second possibility for Venus's disk, which supported the heliocentric theory. The enormous variations in the angular size of Mars could not be explained by a circular orbit about Earth, but were easily understood if Mars orbits the Sun instead, thus varying its distance from Earth by a factor of five from the closest approach to the most distant retreat.

On the basis of these observational discoveries, Galileo began to teach the modified Copernican heliocentric model of the solar system as the correct one. He even used Kepler's laws to calculate orbital parameters for the orbits of the satellites revolving around Jupiter. However, direct proof that Earth moves around the Sun was still lacking. Furthermore, the Catholic Church considered Galileo's heliocentric theory to be heretical. It placed Copernicus's book on its Index of Restricted Books and tried Galileo before the Inquisition. Galileo was forced to recant the heliocentric theory and was placed under house arrest for the last eight years of his life.

The next major development was the generalization of Kepler's laws in 1687 by Isaac Newton (1642-1727). His generalized form of Kepler's laws showed that the Sun and planets all revolve around the solar system's center of mass. Telescopic observations of solar system objects gave indications of their size and when used in the generalized Kepler's laws, soon showed that the Sun is much larger and more massive than even Jupiter (the largest and most massive planet). Thus the center of the solar system, around which Earth revolves, is always in or near the Sun. Earth orbits the Sun much more than the Sun orbits Earth.

Another demonstration of Earth's orbital motion is the aberration of starlight. Astronomical observations and celestial mechanics indicate that Earth should have a 16-19 mi/sec (25-30 km/sec) orbital velocity around the solar system's center which continuously changes its direction due to the gravitational effect of the Sun. James Bradley's (1693-1762) attempt to determine the parallaxes Figure 1. Illustration of how the angle PEC "opens up" as Earth approaches Castor (C) and Pollux (P) as it moves from position E₁ in its orbit around the Sun in September to E₂ in January, then PEC "closes up" as the Earth moves from E₂ to its position E₃ in early June. The distance PC between Castor and Pollux is assumed to be fixed on the celestial sphere. Illustration by Hans & Cassidy. Courtesy of Gale Group.
of stars starting in 1725 with a telescope rigidly fixed in a chimney soon found that the apparent positions of the stars shifted along elliptical paths. These ellipses were 90° out of phase with the parallax ellipse for a nearby star on a distant background that is expected to be produced by Earth's motion around the Sun. Moreover the ellipses' semi-major axes were always 20.5", with no variation from the different distances of the stars. These same size ellipses were soon understood to be the yearly paths of the aberrations of the apparent positions of the stars caused by the addition of Earth's constantly changing orbital velocity to the vacuum velocity of the light arriving from the stars (whose true positions are at the centers of the aberrational ellipses). These ellipses show that Earth does indeed have the expected orbital velocity around the solar system's center of mass.

Final proof of the heliocentric theory for the solar system came in 1838, when F.W. Bessel (1784-1846) determined the first firm trigonometric parallax for the two stars of 61 Cygni (Gliese 820). Their parallax (difference in apparent direction of an object as seen from two different points) ellipses were consistent with orbital motion of Earth around the Sun.

In 1835 the Catholic Church removed Copernicus's book from its index of restricted books. It is fitting to mention Copernicus's book here. Bessel's successful measurement of a parallax ellipse established the Sun as the central body of the solar system, but it was not certain that the Sun was at or near the center of the universe.