. Sunrise is framed by the ancient stone pillars of Stonehenge in southern England. This monument was used to find midsummer and midwinter four thousand years ago Ė before the invention of writing and the calendar. The Sun rises at different points on the horizon during the year, reaching its most northerly rising on Midsummer Day (summer solstice on June 21). After this, the rising point of the Sun moves south along the horizon until it reaches its most southerly rising on Midwinter Day (winter solstice on December 22). An observer located at the center of the main circle of stones at Stonehenge watched midsummer sunrise over a marker stone located outside the circle; midwinter sunrise and sunset were framed by other stones within the circle. (Courtesy of Owen Gingerich.)
. The Sunís motion across the sky looking south. The maximum height of the Sun in the sky, and its rising and setting points on the horizon, change with the seasons. In the summer, the Sun rises in the northeast, reaches its highest maximum height, and stays up longest. The Sun rises southeast and remains low in the winter when the days are shortest. The length of day and night are equal on the Vernal, or Spring, Equinox (March 20) and on the Autumnal Equinox (September 23) when the Sun rises exactly east and sets exactly west.
. During the monthly cycle, the Moon waxes (grows) from crescent to gibbous, and then after full Moon, it wanes (decreases) to a crescent again. The term crescent is applied to the Moonís shape when it appears less than half-lit; it is called gibbous when it is more than half-lit but not yet fully illuminated. The reason for the Moonís changing shape is described in Figure 1.8 (Lick Observatory Photographs).
. This photograph shows the apparent movements of the planets against the background stars. Mars, Jupiter and Saturn appear to stop in their orbits, then reverse direction before continuing on Ė a phenomenon called retrograde motion by modern astronomers. Ancient and modern explanations for this temporary backward motion are illustrated in Figures 1.6 and 1.9, respectively. (Courtesy of Erich Lessing/Magnum).
. This multiple-exposure photograph of a total lunar eclipse reveals the curved shape of the Earthís shadow, regarded by ancient Greek astronomers as evidence that the Earth is a sphere. Only a spherical body will cast the same circular shadow on the Moon when viewed from different locations on Earth or during different lunar eclipses. This photograph was taken by Akira Fujii during the lunar eclipse of 30 December 1982.
. To explain the occasional retrograde loops in the apparent motions of Mars, Jupiter and Saturn, astronomers in ancient times imagined that each planet travels with uniform speed around a small circle, known as the epicycle. The epicycleís center moves uniformly on a larger circle, the deferent. A similar scheme was used by Ptolemy to explain the wayward motions of the planets in his Almagest. In the Ptolemaic system, the Earth was displaced from the center of the large circle, and each planet traveled with uniform motion with respect to another imaginary point, the equant, appearing to move with variable speed when viewed from the Earth.
. The Earth rotates with respect to the Sun once every 24 hours, causing the sequence of night and day. Each point on the Earthís surface moves in a circular track parallel to the equator, and each track spends a different time in the Sun depending on the season. This drawing depicts summer in the Northern Hemisphere and winter in the Southern Hemisphere. Because the northern part of the Earthís rotational axis is tipped toward the Sun, circular tracks in the Northern Hemisphere spend a longer time in the Sun than southern ones.
. Light from the Sun illuminates one half of the Moon, while the other half is dark. As the Moon orbits the Earth, we see varying amounts of its illuminated surface. The phases seen by an observer on Earth (bottom) correspond to the numbered points along the lunar orbit. The period from new Moon to new Moon is 29.53 days, the length of the month. As the Earth completes its daily rotation, all night-time observers see the same phase of the Moon.
. A Sun-centered model of the solar system explains the looping path of Mars in terms of the relative speeds of the Earth and Mars. The Earth travels around the Sun more rapidly than Mars does. As Earth overtakes and passes the slower moving planet (points 2 to 4), Mars appears to move backward (points B to D) for a few months.
. As the Earth orbits the Sun, the Earthís rotational axis in a given hemisphere is tilted toward or away from the Sun. This variable tilt produces the seasons by changing the angle at which the Sunís rays strike different parts of the Earthís surface. The greatest sunward tilt occurs in the summer when the Sunís rays strike the surface most directly. In the winter, the relevant hemisphere is tilted away from the Sun and the Sunís rays obliquely strike the surface. When it is summer in the northern hemisphere, it is winter in the southern hemisphere and vice versa. (Notice that the radius of the Earth and Sun and the Earthís orbit are not drawn to scale.)
. Each planet moves in an ellipse with the Sun at one focus. The length of a line drawn from the Sun, to a planet and then to the empty focus, denoted by the dashed line, is always 2a, or twice the semi-major axis, a. The eccentricity, or elongation, of the planetary ellipse has been greatly overdone in this figure; planetary orbits look much more like a circle.
. Keplerís first law states that the orbit of a planet about the Sun is an ellipse with the Sun at one focus. The other focus of the ellipse is empty. According to Keplerís second law, the line joining a planet to the Sun sweeps out equal areas in equal times. This is also known as the law of equal areas. It is represented by the equality of the three shaded areas ABS, CDS and EFS. It takes as long to travel from A to B as from C to D and from E to F. A planet moves most rapidly when it is nearest the Sun (at perihelion); a planetís slowest motion occurs when it is farthest from the Sun (at aphelion).
. The orbital periods of the planets are plotted against their semi-major axes, using a logarithmic scale. The straight line that connects the points has a slope of 3/2, thereby verifying Keplerís third law that states that the square of the orbital periods increase with the cubes of the planetary distances. This type of relation applies to any set of bodies in elliptical orbits, including Jupiterís four largest satellites shown in the inset.
. Among Galileoís most compelling arguments in favor of a Sun-centered solar system, previously advocated by Copernicus, was the fact that Venus displays phases like those of the Moon. In the long-held, Earth-centered Ptolemaic system (left) Venus always lies between the Earth and Sun, so it can never appear fully illuminated when viewed from the Earth. But in the Copernican system (right), Venus can show the whole range of illuminated phases.
. Light waves that fall on the Earth from a distant object are parallel to one another, and are focused to a point by the lens or mirror of a telescope. The earliest telescopes were refractors (left). The curved surfaces of the convex objective lens bend the incoming parallel light rays by refraction, and bring them to a focus at the center of the focal plane, where the light rays meet and an image is created. A second, smaller lens, called the eyepiece, was used to magnify the image in the early refractors; later versions placed photographic or electronic detectors at the focal plane. The reflecting telescope (right) uses a large, concave, or parabolic, primary mirror to collect and focus light. A small, flat secondary mirror, inclined at an angle of 45 degrees to the telescope axis, reflects the light sideways, at a place now known as the Newtonian focus. Other light-deflecting mirror arrangements can be used to obtain any desired focal length, which varies with the curvature and position of small convex mirrors.
. This picture was made by using crystals to liberate the spectral colors in visible sunlight, refracting them directly onto a photographic plate, more than three hundred years after Isaac Newton used a prism, in 1672, to disperse sunlight into a spectrum of rainbow-like colors. The beautiful display shown in this picture was obtained in the rarefied atmosphere atop Hawaiiís Mauna Kea volcano, where many of the worldís best telescopes are located. (Courtesy of Eric J. Pittman, Victoria, British Columbia.)
. The exact locations of five thousand flying rocks, called asteroids or minor planets, whose orbits are accurately known. The vast majority of the asteroids orbit the Sun in the main belt located between the orbits of Mars and Jupiter. A few of them pass inside the orbit of Earth, while others move about 60 degrees ahead of and behind Jupiter in similar orbits. (Courtesy of Jeff Bytof, University of California at San Diego.)
. The number of asteroids at different distances from the Sun. Most of the asteroids are found in the asteroid belt that lies between 2.2 and 3.3 AU from the Sun. Repeated gravitational interactions with Jupiter seem to have tossed asteroids out of the Kirkwood gaps with orbital periods of 1/4, 2/7, 1/3, 2/5, 3/7 and 1/2 of Jupiterís orbital period. These fractions are placed above the relevant gap in the figure. In addition, there are several peaks corresponding to groups of asteroids with nearly the same orbital distance, such as the Trojan asteroids that have orbits that are identical in size to the orbit of Jupiter.
. Values of the solar parallax obtained from measurements of the parallaxes of Venus, Mars, and the asteroid Eros between 1850 and 1970. Here the error bars denote the probable errors in the determination, whereas the points for 1941, 1950 and 1965 all have errors smaller than the plotted points. In the 1960s, the newly developed radar (radio detection and ranging) technology enabled the determination of the Sunís distance with an accuracy of about 1000 meters. The radar value of the solar parallax is 8.79405 seconds of arc.
. Accurate distances to the nearby planets have been determined by sending radio pulses from Earth to the planet, and timing their return several minutes later. The figure shows the emission of a pulse toward Venus; when it bounces from Venus the radiation spreads over the sky and we receive only a small fraction of the original signal, delayed by the round-trip travel time. If T is the round-trip time and c is the speed of light, the total distance traveled is cT and the distance to Venus is cT/2. For Venus, the round-trip time is 4.6 minutes when the planet is nearest Earth and increases to 28.7 minutes when it is furthest away from us.
. A spectrograph has spread out the visible portion of the Sunís radiation into its spectral components, displaying radiation intensity as a function of wavelength. When we pass from short wavelengths to longer ones (left to right and top to bottom), the spectrum ranges from violet through blue, green, yellow, orange and red. Dark gaps in the spectrum, called Fraunhofer absorption lines, represent absorption by atoms or ions in the Sun. The wavelengths of these absorption lines can be used to identify the elements in the Sun, and the relative darkness of the lines helps establish the relative abundance of these elements. (Courtesy of the National Solar Observatory/Sacramento Peak, NOAO).
. The radiation spectra of the giant planets at visible wavelengths photographed by Vesto M. Slipher at the Lowell Observatory in 1907. Slipher's work was discussed by Rupert Wildt in 1931, who interpreted some of the bands of Jupiter as absorption by ammonia and methane, the natural gas we use for cooking and heating. Multiples of methane's vibration frequency, n3, are given along the bottom of this figure. The Moon's spectrum is also shown to illustrate the dark Fraunhofer lines found in reflected sunlight and those introduced by the terrestrial atmosphere. The wavelength scale at the top of the figure is in the Angstrom units that were in common use when Slipher took his observations; just divide these numbers by ten to get the wavelength in nanometers.
. Six of Saturnís large moons are shown in this one-minute exposure made with the United States Naval Observatoryís 0.66-meter (26-inch) refractor. From left to right, the satellites are Titan, Dione, Enceladus, Tethys, Mimas and Rhea (on the other side). The faint image below the planet is that of a star. A partially transparent metallic film was used to weaken the light from Saturn and its rings. (Courtesy of Dan Pascu.)
. In 1659 Christiaan Huygens published this drawing of Saturn and its ring in his monograph Systemia Saturnium. Huygens recognized that a detached ring would explain the planetís ever-changing appearance, and announced his discovery in the form of an anagram, a succession of scrambled letters. The drawing shown here was accompanied by the deciphered anagram "Saturn is girdled by a thin flat ring, nowhere touching it, and inclined to the ecliptic".
. Eight satellites of Jupiter have eccentric orbits that are inclined with respect to Jupiterís equatorial plane. The inner group of four moves around Jupiter in conventional direct orbits, in the same direction that the planet orbits the Sun, at distances between 11 and 12 billion (1.1 and 1.2 x 1010) meters. Their names all end in the letter "a" - Leda, Himalia, Lysithea, and Elara. The outer group of four has backward retrograde orbits that lie at distances between 20 and 24 billion (2.0 and 2.4 x 1010) meters from Jupiter. The outer group has names ending in "e" - Ananke, Carme, Pasiphae, and Sinope. In contrast, the four Galilean satellites, which are relatively near to the planet, move with direct orbits close to the planet's equatorial plane, as do four smaller satellites that are even closer to Jupiter.
. A region of the constellation Gemini, photographed by Clyde W. Tombaugh on 23 January 1930 (left), and the same region photographed six days later (right). When comparing the two plates on 18 February 1930 with a blink microscope, Tombaugh noticed an object (arrows) on the second plate that had changed its location with respect to the background stars since the first plate was taken. This was a previously unknown object that had to belong to the solar system. Because of its slow apparent motion across the sky, the planet images were separated by just 3.5 millimeters on the two photographs. (Courtesy of the Lowell Observatory.).
. The Hubble Space Telescope (HST) distinguishes between Pluto, the bright object at the middle of the central image, and its companion Charon, the fainter object in the lower left of the central image. Observations from telescopes on Earth (left) were unable to clearly resolve the pair because of atmospheric distortions. At the time of the HST photograph, Charonís orbit around Pluto (right) was seen nearly edge on, and Charon was near its maximum angular separation from Pluto, a mere 0.9 seconds of arc. Plutoís diameter is 2.32 million meters, Charon is half that size, and the two objects are just 19.64 million meters apart. The HSTís ability to distinguish Plutoís disk at its distance of 4.4 trillion (4.4 x 1012) meters is equivalent to seeing a baseball at a distance of about 100 thousand meters. (Courtesy of NASA.)
. When a comet travels close to the Sun, the solar heat vaporizes ice from the comet's surface, and solar forces bend the liberated material into comet tails that always point away from the Sun. The long tail of this comet stretches 120 billion (1.2 x 1011) meters, or nearly the mean distance between the Earth and the Sun, at 1 AU = 1.496 x 1011 meters. It is named Comet Ikeya-Seki (1965 VIII) after the last names of its discoverers, Kaoru Ikeya and Tsutomu Seki, and the year and order of its discovery. ( Courtesy of the Lick Observatory.)