Lesson plans, interactive activities, and other resources to help students learn about and explore our solar system
Motions of Sun, Moon, and Planets
From the dawn of civilization until the time of Copernicus astronomy was dominated by the study of the motions of celestial bodies. Such work was essential for astrology, for the determination of the calendar, and for the prediction of eclipses, and it was also fueled by the desire to reduce irregularity to order and to predict positions of celestial bodies with ever-increasing accuracy. The connection between the calendar and the motions of the celestial bodies is especially important, because it meant that astronomy was essential to determining the times for the most basic functions of early societies, including the planting and harvesting of crops and the celebration of religious feasts.
The celestial phenomena observed by the ancients were the same as those of today. The Sun progressed steadily westward in the course of a day, and the stars and the five visible planets did the same at night. The Sun could be observed at sunset to have moved eastward about one degree a day against the background of the stars, until in the course of a year it had completely traversed the 360° path of constellations that came to be known as the zodiac. The planets generally also moved eastward along the zodiac, within 8° of the Sun's apparent annual path (the ecliptic), but at times they made puzzling reversals in the sky before resuming their normal eastward motion. By comparison, the Moon moved across the ecliptic in about 27 1/3 days and went through several phases. The earliest civilizations did not realize that these phenomena were in part a product of the motion of the Earth itself; they merely wanted to predict the apparent motions of the celestial bodies.
Although the Egyptians must have been familiar with these general phenomena, their systematic study of celestial motions was limited to the connection of the flooding of the Nile with the first visible rising of the star Sirius. An early attempt to develop a calendar based on the Moon's phases was abandoned as too complex, and as a result astronomy played a lesser role in Egyptian civilization than it otherwise might have. Similarly, the Chinese did not systematically attempt to determine celestial motions. Surprising evidence of a more substantial interest in astronomy is found in the presence of ancient stone alignments and stone circles found throughout Europe and Great Britain, the most notable of which is Stonehenge in England. As early as 3000 B.C., the collection of massive stones at Stonehenge functioned as an ancient observatory, where priests followed the annual motion of the Sun each morning along the horizon in order to determine the beginning of the seasons. By about 2500 B.C., Stonehenge may have been used to predict eclipses of the Moon. Not until 1000 A.D. were similar activities undertaken by New World cultures.
Babylonian Tables. Astronomy reached its first great heights among the Babylonians. In the period from about 1800 to 400 B.C., the Babylonians developed a calendar based on the motion of the Sun and the phases of the Moon. During the 400 years that followed, they focused their attention on the prediction of the precise time the new crescent Moon first became visible and defined the beginning of the month according to this event. Cuneiform tablets deciphered only within the last century demonstrate that the Babylonians solved the problem within an accuracy of a few minutes of time; this was achieved by compiling precise observational tables that revealed smaller variations in the velocity of the Sun and of the Moon than ever before measured. These variations - and others such as changes in the Moon's latitude - were analyzed numerically by noting how the variations fluctuated with time in a regular way. They used the same numerical method, utilizing the same variations, to predict lunar and solar eclipses.
Greek Spheres and Circles. The Greeks used a geometrical rather than a numerical approach to understand the same celestial motions. Influenced by Plato's metaphysical concept of the perfection of circular motion, the Greeks sought to represent the motion of the divine celestial bodies by using spheres and circles. This explanatory method was not upset until Kepler replaced the circle with the ellipse in 1609.
Plato's student Eudoxus of Cnidus, c.408-c.355 B.C., was the first to offer a solution along these lines. He assumed that each planet is attached to one of a group of connected concentric spheres centered on the Earth, and that each planet rotates on differently oriented axes to produce the observed motion. With this scheme of crystalline spheres he failed to account for the variation in brightness of the planets; the scheme was incorporated, however, into Aristotle's cosmology during the 4th century B.C.. Thus the Hellenic civilization that culminated with Aristotle attempted to describe a physical cosmology. In contrast, the Hellenistic civilization that followed the conquests of Alexander the Great developed over the next four centuries soon predominant mathematical mechanisms to explain celestial phenomena. The basis for this approach was a variety of circles known as eccentrics, deferents, and epicycles. The Hellenistic mathematician Apollonius of Perga, c.262-c.190 B.C., noted that the annual motion of the Sun can be approximated by a circle with the Earth slightly off-center, or eccentric, thus accounting for the observed variation in speed over a year. Similarly, the Moon traces an eccentric circle in a period of 27 1/3 days. The periodic reverse, or retrograde, motion of the planets across the sky required a new theoretical device. Each planet was assumed to move with uniform velocity around a small circle (the epicycle) that moved around a larger circle (the deferent), with a uniform velocity appropriate for each particular planet. Hipparchus, c.190-120 B.C., the most outstanding astronomer of ancient times, made refinements to the theory of the Sun and Moon based on observations from Nicaea and the island of Rhodes, and he gave solar theory essentially its final form. It was left for Ptolemy, c.100-c.165, to compile all the knowledge of Greek astronomy in the Almagest and to develop the final lunar and planetary theories.
With Ptolemy the immense power and versatility of these combinations of circles as explanatory mechanisms reached new heights. In the case of the Moon, Ptolemy not only accounted for the chief irregularity, called the equation of the center, which allowed for the prediction of eclipses. He also discovered and corrected another irregularity, evection, at other points of the Moon's orbit by using an epicycle on a movable eccentric deferent, whose center revolved around the Earth. When Ptolemy made a further refinement known as prosneusis, he was able to predict the place of the Moon within 10 min, or 1/6°, of arc in the sky; these predictions were in good agreement with the accuracy of observations made with the instruments used at that time. Similarly, Ptolemy described the motion of each planet in the Almagest, which passed, with a few notable elaborations, through Islamic civilization and on to the Renaissance European civilization that nurtured Nicolaus Copernicus.
The revolution associated with the name of Copernicus was not a revolution in the technical astronomy of explaining motions, but rather belongs to the realm of cosmology. Prodded especially by an intense dislike of one of Ptolemy's explanatory devices, known as the equant, which compromised the principle of uniform circular motions, Copernicus placed not the Earth but the Sun at the center of the universe; this view was put forth in his De revolutionibus orbium caelestium (On the Revolutions of the Heavenly Spheres, 1543). In that work, however, he merely adapted the Greek system of epicycles and eccentrics to the new arrangement. The result was an initial simplification and harmony as the diurnal and annual motions of the Earth assumed their true meaning, but no overall simplification in the numbers of epicycles needed to achieve the same accuracy of prediction as had Ptolemy. It was therefore not at all clear that this new cosmological system held the key to the true mathematical system that could accurately explain planetary motions.
Keplerian Ellipses and Newtonian Gravitation. The German astronomer Johannes Kepler provided a daring solution to the problem of planetary motions and demonstrated the validity of the heliocentric theory of Copernicus, directly associating the Sun with the physical cause of planetary motions. At issue for Kepler was a mere 8 ft discrepancy between theory and observation for the position of the planet Mars. This degree of accuracy would have delighted Ptolemy or Copernicus, but it was unacceptable in light of the observations of the Danish astronomer Tycho Brahe, made from Uraniborg Observatory with a variety of newly constructed sextants and quadrants and accurate to within 1 ft to 4 ft. This new scale of accuracy revolutionized astronomy, for in his Astronomia nova (New Astronomy, 1609), Kepler announced that Mars and the other planets must move in elliptical orbits, readily predictable by the laws of planetary motion that he proceeded to expound in this work and in the Harmonices mundi (Harmonies of the World, 1619). Only by abandoning the circle could the heavens be reduced to an order comparable to the most accurate observations.
Kepler's laws and the Copernican theory reached their ultimate verification with Sir Isaac Newton's enunciation of the laws of universal gravitation in the Principia (1687). In these laws, the Sun was assigned as the physical cause of planetary motion. The laws also served as the theoretical basis for deriving Kepler's laws. During the 18th century, the implications of gravitational astronomy were recognized and analyzed by able mathematicians, notably Jean d' Alembert, Alexis Clairaut, Leonhard Euler, Joseph Lagrange, and Pierre Laplace. The science of celestial mechanics was born and the goal of accurate prediction was finally realized.
During all of this discussion the stars had been regarded as fixed. While working on his catalog of 850 stars, however, Hipparchus had already recognized the phenomenon known as the precession of the equinoxes, an apparent slight change in the positions of stars over a period of hundreds of years caused by a wobble in the Earth's motion. In the 18th century, Edmond Halley, determined that the stars had their own motion, known as proper motion, that was detectable even over a period of a few years. The observations of stellar positions, made with transit instruments through the monumental labors of such scientists as John Flamsteed, laid the groundwork for solving a cosmological problem of another era: the distribution of the stars and the structure of the universe.