views updated

# Heliocentric Theory

Copernican revival of the heliocentric theory

The triumph of the heliocentric theory

The heliocentric theory and the universe

Resources

The heliocentric theory argues that the sun is the central body of the solar system and perhaps of the universe. Everything else (planets and their satellites, asteroids, comets, etc.) revolves around it.

The first evidence of the theory is found in the writings of ancient Greek philosopher-scientists. By the sixth century BC they had deduced that Earth is round (nearly spherical) from observations that during lunar eclipses Earths shadow on the moon is always a circle of about the same radius wherever the moon is on the sky. Only a round body can always cast such a shadow.

Despite this discovery, the prevailing theory at that time was that of a geocentric (Earth-centered) universe, in which all celestial bodies were believed torevolve around Earth. This was seen as more plausible than the heliocentric theory because to a casual observer, all celestial bodies seem to move around a motionless Earth at the center of the universe.

Over 200 years later Aristarchus of Samos (310-230 BC) attempted to measure the suns distance from Earth in Earth-moon distance units by measuring lunar intervals. Observing the new moon to the first quarter and the first quarter to full moon, then using geometry and several assumptions, Aristarchus used the time-interval differences to calculate the suns distance from Earth. The smaller the difference between the intervals, the more distant the sun. From this value he determined the suns distance and the relative sizes of Earth, the moon (about 1/4 that of Earth), and the sun. Aristarchus concluded that the sun was several times larger than Earth, and thought it reasonable that the smaller Earth revolved around the larger sun.

Because the stars are all located on an enormous celestial sphere (the entire sky) centered on the sun, Earths yearly motion around the sun is reflected in the stars. Those most likely to show the effect of this yearly motion are those in Gemini, especially its brightest stars: Castor and Pollux, which are about 4.56° apart and close to the ecliptic, the suns yearly path among the stars. In heliocentric theory, the ecliptic is the projection of Earths orbit onto the sky. If one views the heliocentric model from the north ecliptic pole in Figure 1 we see the sun, Earth (E) in several positions in its orbit, Castor (C), and Pollux (P) on the celestial sphere. If Castor and Pollux are fixed on the celestial sphere, then the distance CP between them is a fixed length.

Because they are fixed objects, the distance CP in this case appears largest when closest, and smallest when most distant. This effect was not detected with even the best astronomical instruments during the time of the ancient Greeks.

## Copernican revival of the heliocentric theory

Nicholas Copernicus (1472-1543) revived the heliocentric theory in the sixteenth century, after hundreds of years of building on Claudius Ptolemys (c. AD 90-168) geocentric cosmological model (proving Earth is at the center of the universe). In his book, De revolutionibus orbium coelestium (On the revolutions of the celestial spheres), he placed the sun at the center of the universe with the planets revolving around it in epicycles (a circle around which a planet moves) and deferents (the imaginary circle around Earth in whose periphery the epicycle moves). He argued that the planets in order from the sun are Mercury, Venus, Earth (with the Moon orbiting it), Mars, Jupiter, and Saturn. The celestial sphere with the stars is far beyond Saturns orbit. The apparent daily westward rotation of the celestial sphere, the sun, moon, and of the planets is the result of Earths daily eastward rotation around its axis.

If one assumes that the orbital velocities decrease with increasing distance from the sun, then the apparent retrograde (backward) motion of the planets on the zodiac could be explained by Earth overtaking Mars, Jupiter, and Saturn near opposition (when they are 180° from the sun on the zodiac), and by it being overtaken by the faster-moving Mercury and Venus when they pass between the sun and Earth (inferior conjunction). Copernicuss heliocentric model achieved a simpler cosmology than did the modified (although not more accurate) Ptolemaic geocentric model that existed in the sixteenth century.

The major advantage of Copernicuss system was the aesthetic appearance of a system of concentric

orbits with ever-widening separations and, ironically, the return to some of the ancient Greek fundamentals, including purely circular motions. Copernicuss heliocentric model, however, did not accurately represent the observed planetary motions over many centuries. His model had many critics and was generally not accepted. An interesting variant of a geocentric model was developed at the end of the sixteenth century by the Danish astronomer Tycho Brahe (1546-1601), who placed Earth at the center of the solar system, except for Mercury and Venus, which revolved around the sun, which in turn revolved with them around Earth.

## The triumph of the heliocentric theory

Johannes Keplers (1571-1630) work enabled the heliocentric solar system model to match and predict planetary positions on the zodiac for many centuries. After trying many geometric curves and solids in Copernicuss 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 Keplers first of three laws of planetary motion, which 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 Keplers 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 showed that both Jupiter and Earth were centers of orbital motion for celestial bodiesrefuting geocentric theory, which assumed that celestial bodies revolve only around Earth.

2. Galileo observed the disks (visible surfaces of celestial objects) of at least several planets. His observations of Venuss disk were especially important

for determining whether the geocentric or heliocentric model was correct. Ptolemys geocentric model predicts that Venuss disk will show only the new moon (dark) and crescent phases as it orbits Earth on its epicycle(s) and deferent (see Figure 2). Keplers modified Copernican heliocentric model predicted that Venuss disk will show all the phases of the moon (including the half-moon, gibbous, and full moon phases; see Figure 3) as Venus and Earth both orbit the sun. galileo observed the second possibility for Venuss 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 observations, Galileo began to teach the modified Copernican heliocentric model of the solar system as the correct one. He even used Keplers laws to calculate parameters for the orbits of Jupiters moons. However, direct proof that Earth moves around the sun was still lacking. Furthermore, the Church considered Galileos heliocentric theory heretical. It placed Copernicuss book on its Index librorum prohibitorum (Index of forbidden 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 Catholic Church finally removed Copernicuss book from the Index in 1835.)

The next major development was the generalization of Keplers laws in 1687 by Isaac Newton (1642-1727), who showed that the sun and planets all revolve around the solar systems center of mass. Telescopic observations of solar system objects gave indications of their size, and, when used in the generalized Keplers 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.

Another demonstration of Earths 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 systems center which continuously changes its direction due to the suns gravitational

effect. James Bradleys (1693-1762) attempt to determine the parallaxes of stars starting in 1725 using 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 Earths motion around the sun. Moreover the ellipses semi-major axes were always 20.5, with no variation from the stars different distances. 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 Earths 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 systems 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. While Bessels successful measurement of a parallax ellipse established the sun as the central body of the solar system, it was not certain that the sun was at or near the center of the universe.

## The heliocentric theory and the universe

Astronomers seem to have been of differing opinions on this aspect of the heliocentric theory. Thomas Wright (1711-86) and William Herschel (1738-1822) thought that the sun was at or near the center of the Milky Way, which most astronomers believed to comprise most or all of the universe. Herschel arrived at this conclusion by making star counts in different directions (parts of the sky) but he did not allow for the absorption of starlight by interstellar dust. J.H. Lambert (1728-77) concluded that the sun was somewhat away from its center on the basis of the Milky Ways geometry. As long as there seemed to be evidence that the sun was at or near the Milky Ways center and the Milky Way comprised most of the universe, a case could be made that the sun was at or near the center of the universe.

Immanuel Kant (1724-1804) suggested that some of the nebulae seen in deep space were other Milky Ways, or island universes, as he termed them. If his speculation proved correct, this would almost certainly mean that the sun is nowhere near the center of the universe.

Astrometry (measurement and position of celestial objects) also showed that the sun and other stars move

### KEY TERMS

Celestial sphere The entire sky on which are situated the Sun, Moon, planets, stars, and all other celestial bodies for a geocentric observer.

Constellation A region of the celestial sphere (sky). There are 88 officially recognized constellations over the entire celestial sphere.

Parallax (parallactic shift) The apparent shift of position of a relatively nearby object on a distant background as the observer changes position.

Semimajor axis The longest radii of an ellipse.

Zodiac The zone 9° on each side of the ecliptic where a geocentric observer always finds the Sun, Moon, and all the planets except Pluto.

relative to each other. The sun is not at rest relative to the average motions of the nearby stars, but is moving relative to them at about 12 mi/sec (20 km/sec) towards the constellations Lyra and Hercules, indicating that the sun is only one of perhaps billions of ordinary stars moving through the Milky Way.

Harlow Shapley (1887-1972) postulated the first fairly correct idea about the suns location in the Milky Way. He found that the system of the Milky Ways globular star clusters is arranged in a halo around the Milky Ways disk (within which the sun is located). These clusters are concentrated towards its nucleus and center, which are beyond the stars of the constellation Sagittarius. He found about 100 globular clusters in the hemisphere of the celestial sphere centered on the direction to the center of the Milky Way in Sagittarius, while there were only about a dozen globular clusters in the opposite hemisphere centered in the constellation Auriga. Shapley reported this research in 1918 and estimated that the sun is about 2/3 from the Milky Ways center to the edge of its diskwhich is very far from its center.

Edwin Hubble (1889-1953) confirmed Kants hypothesis that the spiral and elliptical nebulae are other galaxies similar to the Milky Way in 1924. He also discovered that all the distant galaxies have spectra whose spectral lines are Doppler shifted towards the red end of their visible spectra, indicating that all distant galaxies are moving away from the Milky Way and its neighboring galaxies. Furthermore, the more distant such a galaxy seems to be, the faster it seems to be receding. This indicates that our universe seems to be expanding. One result of this discovery has been to make the concept of a center questionable, perhaps meaningless, in a universe with three spatial dimensions.

Present estimates indicate that the sun is between 25,000 to 30,000 light years from the Milky Ways center. The sun revolves around this center with an orbital velocity of about 155 mi/sec (250 km/sec). One revolution around the Milky Ways center takes about 200,000,000 years. The sun is only one star among 100,000,000,000 or more other ordinary stars that revolve around the Milky Ways center.

Heliocentric theory is valid for our solar system, but its relevance extends only a few light-years from the sun to the vicinity of the three stars of the Alpha Centauri system (Gliese 551, Gliese 559A, and Gliese 559B).

## Resources

### BOOKS

Bacon, Dennis Henry, and Percy Seymour. A Mechanical History of the Universe. London: Philip Wilson Publishing, Ltd., 2003.

Morrison, David and Sidney C. Wolff. Frontiers of Astronomy. Philadelphia: Sanders College Publishing, 1990.

### OTHER

University of Michigan, Center for the Study of Complex Systems. A History of the Warfare of Science with Theology in Christendom. Chapter III: AstronomyThe Heliocentric Theory <http://www.cscs.umich.edu/~crshalizi/White/astronomy/heliocentric-theory.html> (October 7, 2006).

Frederick R. West