Copernicus and the Heliocentric Model

Nicolaus Copernicus portrait from Town Hall in Thorn/Toruń - 1580. Click here for original source URL.

Nicolaus Copernicus started the drive to visualize the Sun, not the Earth, as the center of the solar system. He was born on February 14, 1473, the son of a Polish merchant. While being educated at university in Italy, he became excited by the burgeoning scientific thought in that country. At age 24 he made his first astronomical observations. A few years later, He obtained a position as a clerical official in the Catholic Church. This post gave him the time and economic security to continue his astronomical studies. At age 31 he observed a rare conjunction, or passage of planets close to each other as seen in the sky. The conjunction brought all five known planets as well as the Moon into the constellation of Cancer. He found that their positions departed by several degrees from an earlier set of Ptolemaic predictions.

Copernicus made few new observations. However, he spent a long time studying different models for the arrangement of the solar system. He concluded that the prediction of planetary positions would be simpler if we imagined that the Sun is at the center and Earth is one of the Sun's orbiting planets. In 1512 Copernicus circulated a short commentary containing the essence of his new hypothesis: the Sun is the center of the solar system, the planets move around it, and the stars are immeasurably more distant. This commentary was only distributed in handwritten form to a few of Copernicus’ acquaintances. Copernicus continued his studies but, fearing controversy with the Catholic Church, delayed publication for many years. Finally, encouraged by visiting colleagues, including some in the clergy, he allowed the written commentary to be more widely circulated. News of Copernicus’ work spread rapidly.

Late in his life, in 1543, Copernicus prepared a synthesis of all his work, called On the Revolutions of the Celestial Spheres. In this book he laid out and explained his evidence for the solar system's arrangement: planet positions in the sky could be explained if one assumed that Earth and other planets move around the Sun. Only 400 copies of this book were printed and only a small part of it deals with the heliocentric hypothesis. Yet the modern meaning of the word "revolution" — sudden political and social upheaval — originates with the title of Copernicus’ book.

When Copernicus published his revolutionary book, turmoil was ensured because Church officials and most intellectuals held that Earth was at the center. The printer of the book, a Lutheran minister, had tried to defuse the situation by inserting a preface stating that the new theory need not be accepted as physical reality but could be seen merely as a convenient model for calculating planetary positions. This was philosophically a valid way of looking at the situation. Already Copernicus had come under fire from Protestant fundamentalists: in 1539 Martin Luther had called him "that fool [who would] reverse the entire art of astronomy. Joshua bade the Sun and not the Earth to stand still." In a world of strong dogmas, tampering with established ideas is dangerous. In the 1530s Michael Servetus had been criticized for his writings on astrology and astronomy; in 1553 he was burned at the stake as a heretic for professing a mysterious theology that offended both Protestants and Catholics. Both Protestants and Catholics suppressed heretical ideas. John Calvin masterminded Servetus’ execution, although, in a fit of moderation, he recommended beheading instead of burning. Servetus, a man of wide learning and varied interests, had improved geographic data on the Holy Land and also discovered blood circulation in the lungs. Copernicus was aware that he too had rattled the hornet’s nest.

Despite the furor over his book, Copernicus was not able to prove that the heliocentric model was correct. He followed Greek tradition in assuming that the planet orbits must be perfect circles. Because of this his model did not predict the positions of the planets any more accurately than Ptolemy’s. Yet the hallmark of a good theory is its ability to accurately explain observations. So why then did scientists come to favor the heliocentric idea?

Copernican Planisphere. Click here for original source URL.

Schematic of a geocentric solar system. Click here for original source URL.
Placing the Sun at the center brings a certain symmetry and simplicity to the model of the solar system. In Ptolemy's model Mercury and Venus are special because they revolve around empty points between the Earth and Sun. Copernicus has all the planets orbiting the Sun in the same sense. He simply explains the fact that Mercury and Venus always appear close to the Sun. In Ptolemy's model the retrograde motions of some planets are explained with the artificial device of epicyclical motion. The Copernican model accounts for this naturally with the different speeds of planets in their orbits. Earth "overtakes" Mars on its interior orbit, Mars appears to temporarily reverse its motion with respect to the distant stars.

The new model of Copernicus was also elegant. In Ptolemy's model, there were many different combinations of epicycle size and motion that could roughly fit the planet motions. This seemed to Copernicus to be arbitrary and unsatisfactory — like a puzzle with no single solution. In the heliocentric model the relative spacing of the planets is fixed uniquely by their apparent motions. There is regularity of the motions in that the planets closest to the Sun orbit the fastest. Interior planets are always seen near the Sun. Exterior planets are seen at any angle to the Sun and can sometimes perform retrograde motion. Copernicus also knew of the work of Aristarchus. It made sense to put the largest object, the Sun, at the center of all motions.

Objections were raised to the heliocentric model. If the Earth is moving, why do we not feel the motion? Copernicus had no simple answer to this, but he pointed out that the annual movement of the Sun in the sky could equally well be explained by the Earth moving annually around the Sun with a tilted axis. The apparent motion of the celestial sphere could equally well be explained by the daily rotation of the Earth. While some critics complained that it was implausible for the equator of the Earth to rotate at a thousand miles per hour, the geocentric model required the celestial sphere to rotate a thousand times faster! The last major objection was the lack of any seasonal change in the angles and brightness of stars. In a geocentric model the stars orbit the Earth at a fixed distance and so never change their brightness or angular separation on the sky. However, in a heliocentric model the Earth must change its distance from each part of the celestial sphere as the seasons pass. Yet no star appeared to brighten and dim and no constellation appeared to change its size over the course of a year. Defenders of the heliocentric view were forced to hypothesize that the stars were so far away that these changes would be undetectable.

A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object appears to have moved in front of the red square. Click here for original source URL.

Stellar Parallax diagram: The apparent motion of a near by star is a small ellipse in the sky relative to background stars over the period of a year. The angle representing major axis radius of the elliptical path is the parallax angle. The minor axis radius angle is simply related to the direction of the star relative to the earth's orbital axis. Stars near the north and south poles will make perfect circles, while stars near the ecliptic will make flat ellipses. Click here for original source URL.
How far away did stars have to be in the Copernican model? To understand this we must introduce the idea of parallax. Parallax is the shift in angle that occurs when a nearby object is seen against a distant backdrop from two different perspectives. This is a familiar idea. Imagine driving in a car with a distant mountain range on the horizon. A nearby tree appears to shift more quickly than a distant one as seen against the horizon — this is a shift in parallax angle. Hold a finger out at arm's length and view it with one eye and then the other. The slight change in perspective from one eye to the other is a parallax shift. This is the way we get depth perception from our binocular vision. If you know the distance between the viewing points and the parallax angle, then simple geometry gives you the distance to the nearby object. If the angle a is small, you can use the small angle equation.

The same idea applies to stars. In the geocentric model, we might expect to see a difference in the angle between two stars on the celestial sphere when observations are made at different times or from different positions on the Earth's surface. But no difference is seen which means that the stars must be very far away compared to the size of the Earth. By the time the Copernican idea was accepted, astronomers believed that stars were scattered through space rather than fixed to a crystalline sphere. In the heliocentric model, a nearby star should show a parallax shift with respect to more distant stars as the Earth moves in its orbit of the Sun. No shift had ever been observed. We can use the small angle equation to show how far away the stars had to be. The limit of angular observation was about 1 arc minute (1') or 60 arc seconds (60"). So d/D < (a / 206,265) < 0.003 and therefore D / d < 3300. The stars had to be at least 3300 times further way than the diameter of the Earth-Sun orbit for parallax to be unobservable! Many people were uncomfortable with the idea of such an immense universe.

Copernicus himself missed the height of the violent debate over a Sun-centered universe. The first copies of his book were reportedly delivered to him on the day of his death in 1543, at age 70. Aided by the invention of the printing press one hundred years earlier, the heliocentric idea was soon being discussed in centers of learning all over Europe. The Copernican revolution was underway and our way of thinking about the universe would never be the same again.

Author: Chris Impey