AST101 - Chapter 3.docx

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University of Toronto St. George
Astronomy & Astrophysics
Michael Reid

3.1 The Ancient Roots of Science -Science is a way of learning about nature through careful observation and trial-and-error experiments -the Moon begins its monthly cycle as a crescent in the western sky just after sunset -Modern measures of time come directly from ancient observations of motion in the sky -the 7 days of the week were named after the seven naked-eye objects that appear to move among the constellations, the Sun, the Moon, and five planets Lunar cycle - 29 ½ days - About 11 days fewer than a calendar based on the Sun Metonic cycle - 19 year cycle on which the dates of lunar phases repeat o Lunar phases repeat with the Metonic cycle because 19 solar years is almost precisely 235 lunar months 3.3 The Copernican Revolution How did Copernicus, Tycho, and Kepler challenge the Earth-centred model? Copernicus - Copernican revolution: spurred the development of virtually all modern science and technology - recognized the much simpler explanation for apparent retrograde motion offered by a Sun-Centered system - discovered simple geometric relationships that allowed him to calculate each planet’s orbital period around the Sun and its relative distance from the Sun in terms of the Earth-Sun distance - model’s success in providing a geometric layout for the solar system convinced him that the Sun- centered idea must be correct o his model didn’t work that well, and was hesitant to publish his work, fearing that his suggestion that Earth moved would be considered absurd o the primary problem was that while he was willing to overturn Earth’s central place in the cosmos, he had held fast to the ancient belief that heavenly motion occur in perfect circles - In the end, his complete model was no more accurate and no less complex than the Ptolemaic model Tycho - proved that the nova was much farther away than the Moon - observed comets were not a phenomena of Earth’s atmosphere - never succeeded in coming up with a satisfying explanation for planetary motion - was convinced that the planets must orbit the Sun, o his inability to detect stellar parallax led him to conclude that Earth must remain stationary - advocated a model in which the Sun orbits the Earth while all other planets orbit the Sun o few people took this model seriously Kepler - believed that planetary orbits should be perfect circles, like Copernicus - Kepler sought a physically realistic orbit for Mars, he could not (as Ptolemy and Copernicus had done) tolerate one model for the east-west positions and another for the north-south positions - discovered that planetary orbits are not circles but instead are a special type of oval called an ellipse - The locations of the two tacks are called the foci (singular, focus) of the ellipse - The long axis of the ellipse is called its major axis, each half of which is called a semimajor axis, the length of the semimajor axis is particularly important in astronomy - The short axis is called the minor axis - Eccentricity: describes how much an ellipse deviates from a perfect circle - By altering the distance between the two foci while keeping the length of string the same, you can draw ellipse of varying eccentricity, a quantity that describes how much an ellipse is stretched out compared to a perfect circle - A circle is an ellipse with zero eccentricity, and greater eccentricity means a more elongated ellipse - Kepler’s decision to trust the data over his preconceived beliefs marked an important transition point in the history of science o he abandoned perfect circles in favour of ellipses - soon came up with a model that could predict planetary positions with far greater accuracy than Ptolemy’s Earth-centered model - Kepler’s model withstood the test of time and became accepted not only as a model of nature but also as a deep underlying truth about planetary motion Kepler’s three laws of planetary motion 1. Kepler’s First Law –the orbit of each planet around the Sun is an ellipse with the Sun at one focus. (Nothing is at the other focus). In essence, this law tells us that a planet’s distance from the Sun varies during its orbit. It is closest at the point called perihelion (from the Greek for near the Sun) and farthest at the point called aphelion (from Greek for away from the Sun). The average of a planet’s perihelion and aphelion distances is the length of its semimajor axis. We will refer to this simply as the planet’s average distance from the Sun. 2. Kepler’s Second Law –as a planet moves around its orbit, it sweeps out equal areas in equal times. This means the planet moves a greater distance when it is near perihelion than it does in the same amount of time near aphelion. That is, the planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. 3. Kepler’s Third Law –more distant planets orbit the Sun a slower average speeds, obeying p^2=a^3, where p is the planet’s orbital period in years and a is its average distance from the Sun in astronomical units. Notice that the square of each planet’s orbital period (p^2) is indeed equal to the cube of its average distance from the Sun (a^3). Because Kepler’s third law relates a planet’s orbital distance to its orbital time (period), we can use the law to calculate a planet’s average orbital speed. The fact that more distant planets move more slowly led Kepler to suggest that planetary motion might be the result of a force from the Sun. He even speculated about the nature of this force, guessing that it might be related to magnetism, Kepler was right about the existence of a force but wrong in his guess of magnetism, A half century later, Isaac Newton finally explained planetary motion as a consequence of gravity. How did Galileo solidify the Copernican revolution? Three basic objections to Copernican view: 1. Aristotle had held that Earth could not be moving because, if it were, objects such
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