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The Cosmos, 4th ed. by Pasachoff & Filippenko Chapter 5 Concept Review » The Solar System has been largely explored with spacecraft over the last five decades (Sec. 5.1). Long before that, and even before the telescope was invented, it was known that planets somehow undergo retrograde motion (slowly drifting east to west among the stars) besides their generally prograde motion (drifting west to east among the stars). Aristotle’s cosmological model, a description of reality, had the Sun, Moon, and planets orbiting the Earth (Sec. 5.2). Ptolemy enlarged on Aristotle’s geocentric (Earth‐centered) theory and explained retrograde motion by having the planets orbit the Earth on epicycles, small circles whose centers move along larger circles called deferents at a constant angular rate relative to a point called the equant (Sec. 5.2). As a calculational tool, Ptolemy’s model could be used to predict the positions of planets with reasonable accuracy. » Copernicus, in 1543, advanced a heliocentric (Sun‐centered) theory that explained retrograde motion as a projection effect (Sec. 5.3). Copernicus still used circular orbits and a few epicycles, and so had not completely broken with the past, but his idea was nevertheless revolutionary and had lasting consequences. However, Copernicus did not have clear observational evidence favoring his model over that of Ptolemy; instead, the appeal was largely philosophical. See Fig. 5–26. » Tycho Brahe made unprecedentedly accurate observations of planetary positions (Sec. 5.4), which Johannes Kepler interpreted quantitatively in terms of ellipses (Sec. 5.5a). An ellipse is a closed curve, all of whose points have the same summed distance from two interior points, each of which is called a focus (plural foci). The major axis of an ellipse is the longest line that can be drawn within the ellipse, or the length of that line; it passes through the two foci. The semimajor axis is half this length. The minor axis is perpendicular to the center of the major axis, or the length of this line; the semiminor axis is half of the minor axis. The eccentricity of an ellipse, a measure of how far it is out of round, is equal to the distance between the foci divided by the major axis. » Kepler formulated three empirical laws of planetary motion (Sec. 5.5a–c): (1) The orbits are ellipses with the Sun at one focus. (2) (The law of equal areas.) The line joining the Sun and a planet sweeps out equal areas in equal times. Thus, a planet moves fastest when it is at perihelion, the point on the orbit closest to the Sun. (3) The orbital period squared is proportional to the semimajor axis cubed. When measured in Astronomical Units (au; the semimajor axis of the Earth’s orbit, or Earth’s average distance from the Sun) and Earth years, Kepler’s third law has a particularly simple form. » Galileo first systematically turned a telescope on the sky and discovered features on the Moon, moons of Jupiter, and a full set of phases of Venus (Sec. 5.6). His observational discoveries strongly endorsed the Copernican heliocentric theory and provided evidence against the Ptolemaic geocentric model. Near the end of his life, Galileo published his much earlier studies of the motions of falling bodies, providing the foundation for Newton’s subsequent work. © Cambridge University Press, 2013 Page 1 The Cosmos, 4th ed. by Pasachoff & Filippenko » Newton developed three basic laws of motion (Sec. 5.7): (1) If no external forces act on an object, its speed and direction of motion stay constant. (2) The force on an object is equal to the object’s mass times its acceleration (F = ma). (3) When two bodies interact, they exert equal and opposite forces on each other. Newton also discovered the law of gravity, namely, that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them (Sec. 5.7). He derived Kepler’s laws mathematically and invented calculus, which he needed for these studies. » A planet revolves around the Sun and rotates on its axis (Sec. 5.8). Its orbit is generally inclined by only a few degrees to the plane of the Earth’s orbit. Spinning or rotating objects have angular momentum, roughly a product of an object’s mass, physical size, and rotation rate. The total angular momentum of a system can change only if the system interacts with something from the outside. The angular momentum associated with planetary orbits probably came from the material that formed the planets. © Cambridge University Press, 2013 Page 2