Early development of astronomy First astronomers

The rhythmic motions of the stars, the planets, and the sun in the sky have fascinated humankind from the earliest of times. The motions were given religious significance

Figure 1.1. Stonehenge, an early astronomical observatory used for tracking the sun and moon in their seasonal excursions. [(g) Crown copyright, NMR]

and were useful agricultural indicators. The sun's motion from south to north and back again marked the times of planting and harvesting. The annual motion of the sun against the background of the much more distant stars could also be followed and recorded, as could the motions of the moon and planets. This made possible predictions of the future motions of the sun and moon. Successful forecasters of the dramatic eclipses of the sun seemed to be in touch with the deities.

The periodic motions of the sun and moon were noted and described with calendars as early as the thirteenth century BCE in China. Surviving physical structures appear to be related to the motions of celestial bodies. Notable are an eighth century BCE sundial in Egypt and the assemblage of large stones at Stonehenge in England dating from about 2000 BCE (Fig. 1)1. The Babylonians and Assyrians in the Middle East are known to have been active astronomers in the several centuries BCE (The designations BCE "before common era" and CE "common era" are equivalent to BC and AD respectively.)

1 In an attempt to minimize redundant numbers in the text, we omit the chapter designation in references to figures within the chapter in which the figure occurs, e.g. "Fig. 2". For references to figures in another chapter, say, Chapter 3, the reference is the conventional format "Fig. 3.2". Problem, equation, and section references are treated similarly. Equations are usually referenced in the text as a number within parentheses without the prefix "Eq.", for example: "as shown in (10)" for equations within the chapter, or "given in (5.10)" for Eq. 10 of Chapter 5.

Figure 1.2. Ptolemaic system, not drawn to scale. The earth is at the center, the moon and sun follow circular paths and the planets follow (small) circular orbits (epicycles) the centers of which move regularly along large circular orbits known as deferents. Elliptical orbits are taken into account by offsetting slightly the centers of the deferents and also the earth itself from a geometrical "center".

Figure 1.2. Ptolemaic system, not drawn to scale. The earth is at the center, the moon and sun follow circular paths and the planets follow (small) circular orbits (epicycles) the centers of which move regularly along large circular orbits known as deferents. Elliptical orbits are taken into account by offsetting slightly the centers of the deferents and also the earth itself from a geometrical "center".

Astronomy flourished under Greek culture (~600 BCE to ~400 CE) with important contributions by Aristotle, Aristarchus of Samos, Hipparchus, Ptolemy, and others. The Greek astronomers deduced important characteristics of the solar system. For example, Aristotle (384-322 BCE) argued from observations that the earth is spherical, and Aristarchus (310-230 BCE) made measurements to obtain the sizes and distances of the sun and moon relative to the size of the earth. Ptolemy (~ 140 CE) developed a complicated earth-centered model (Fig. 2) for the solar system which predicted fairly well the complicated motions of the planets as viewed from the earth.

The advance of astronomy in Europe faltered during the following 13 centuries. Nevertheless the sky continued to be observed in many cultures, e.g., the Hindu, Arabian, and Oriental. The sudden appearances of bright new and temporary "guest" stars in the sky were noted by the Chinese, Japanese, Koreans, Arabs, and Europeans. The most famous of all such objects, the Crab supernova, was recorded in 1054 by Chinese and Japanese astronomers. It is now a beautiful diffuse nebula in the sky (Fig. 3). The Mayan culture of Central America independently developed

Figure 1.3. Crab nebula, the remnant of a supernova explosion observed in 1054 CE. The neutron-star pulsar is indicated (arrow). The filters used for the two photos stress (a) the blue diffuse synchrotron radiation and the pulsar and (b) the strong filamentary structure that glows red from hydrogen transitions. The scales of the two photos are slightly different. The Crab is about 4' in extent and ~6000 LY distant. The orientation is north up and east to the left - as if you were looking at the sky while lying on your back with your head to the north; this is the standard astronomical convention. [(a) Jay Gallagher (U. Wisconsin)/WIYN/NOAO/NSF.; (b) FORS Team, VLT, ESO]

Figure 1.3. Crab nebula, the remnant of a supernova explosion observed in 1054 CE. The neutron-star pulsar is indicated (arrow). The filters used for the two photos stress (a) the blue diffuse synchrotron radiation and the pulsar and (b) the strong filamentary structure that glows red from hydrogen transitions. The scales of the two photos are slightly different. The Crab is about 4' in extent and ~6000 LY distant. The orientation is north up and east to the left - as if you were looking at the sky while lying on your back with your head to the north; this is the standard astronomical convention. [(a) Jay Gallagher (U. Wisconsin)/WIYN/NOAO/NSF.; (b) FORS Team, VLT, ESO]

strong astronomical traditions, including the creation of a sophisticated calendar that could be used, for example, to predict the positions of Venus.

Renaissance

The Renaissance period in Europe brought about great advances in many intellectual fields including astronomy. The Polish monk Nicholaus Copernicus (1473-1543) proposed the solar-centered model of the planetary system. The Dane Tycho Brahe (1546-1601, Fig. 4) used elegant mechanical devices to measure planetary positions to a precision of ~1' (1 arcminute)1 and, over many years, recorded the daily positions of the sun, moon, and planets.

The German Johannes Kepler (1571-1630, Fig. 4), Brahe's assistant for a time, had substantial mathematical skills and attempted to find a mathematical model that would match Brahe's data. After much effort, he found that the apparent motions of Mars in the sky could be described simply if Mars' orbit about the sun is taken to be an ellipse. He summarized his work with the three laws now known as Kepler's laws of planetary motion. They are: (i) each planet moves along an elliptical path with the sun at one focus of the ellipse, (ii) the line joining the sun and a planet sweeps out equal areas in equal intervals of time, and (iii) the squares of the periods P (of rotation about the sun) of the several planets are proportional to the cubes of the semimajor axes a of their respective elliptical tracks,

This formulation laid the foundation for the gravitational interpretation of the motions by Newton in the next century.

Galileo Galilei (1564-1642, Fig. 4), a contemporary of Kepler and an Italian, carried out mechanical experiments and articulated the law of inertia which holds that the state of constant motion is as natural as that of a body at rest. He adopted the Copernican theory of the planets, and ran afoul of the church authorities who declared the theory to be "false and absurd". His book, Dialog on the Two Great World Systems published in 1632, played a significant role in the acceptance of the Copernican view of the solar system. Galileo was the first to make extensive use of the telescope, beginning in 1609.

The telescope was an epic technical advance in astronomy because, in effect, it enlarged the eye; it could collect all the light impinging on the objective lens and direct it into the observer's eye. Since the objective lens was much larger than the lens of the eye, more light could be collected in a given time and fainter objects could be seen. The associated magnification allowed fine details to be resolved. Galileo was the first to detect the satellites (moons) of Jupiter and to determine

1 The measures of angle are degree (°), arcmin ('), and arcsec (") where 60" = 1' and 60' = 1°.

(a) Tycho Brahe (1546-1601) (b) Galileo Galilei (1564-1642)

(a) Tycho Brahe (1546-1601) (b) Galileo Galilei (1564-1642)

ft) Johannes Kepler (1571-1630)

Figure 1.4. The three astronomers who pioneered modern astronomy. [(a) Tycho Brahe's Glada Vanner; (b) portrait by Justus Sustermans; (c) Johannes Kepler Gesammelte Werke, C. H. Beck, 1937. All are on internet: "Astronomy Picture of the Day", NASA/GSFC and Michigan Tech U.]

their orbital periods. He showed that the heavens were not perfect and immutable; the earth's moon was found to have a very irregular surface and the sun was found to have dark "imperfections", now known as sunspots.

The Englishman Isaac Newton (1643-1727; Gregorian calendar) was born 13 years after the death of Kepler and almost exactly one year after Galileo died.

His study of mechanics led to three laws, Newton's laws, which are stated here in contemporary terms: (i) the vector momentum p = mv of a body of mass m moving with velocity v is conserved in the absence of an applied force1 (this is a restatement of Galileo's law of inertia), (ii) a force applied to a body brings about a change of momentum, dp

dt and (iii) the force F12 on one body due to second body is matched by an opposing force of equal magnitude F2, i on the second body due to the first,

These laws are the bases of Newtonian mechanics which remains the essence of much modern mechanical theory and practice. It fails when the speeds of the bodies approach the speed of light and on atomic scales.

Newton was able to show that a gravitational force of a particular kind described perfectly the planetary motions described by Kepler. This force is an attractive gravitational force F between two bodies that depends proportionally upon the masses (m 1, m2) and inversely with the squared distance r2 between them, m 1m 2

where r is the unit vector along the line connecting the two bodies. Such a force leads directly to the elliptical orbits, to the speeds of motion in the planetary orbit, and to the variation of period with semimajor axis described by Kepler's three laws. Thus, all the celestial motions of the earth, moon, and sun could be explained with a single underlying force. This understanding of the role of gravity together with the invention of the telescope set astronomy solidly on a path of quantitative measurements and physical interpretation, i.e., astrophysics.

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