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Roots of Astronomy

Roots of Astronomy. 0. The Roots of Astronomy. Already in the stone and bronze ages , human cultures realized the cyclic nature of motions in the sky. Monuments dating back to ~ 3000 B.C . show alignments with astronomical significance .

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Roots of Astronomy

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  1. Roots of Astronomy www.assignmentpoint.com

  2. 0 The Roots of Astronomy • Already in the stone and bronze ages, human cultures realized the cyclic nature of motions in the sky. • Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance. • Those monuments were probably used as calendars or even to predict eclipses. www.assignmentpoint.com

  3. 0 Stonehenge www.assignmentpoint.com

  4. 0 Stonehenge • Constructed 3000 – 1800 B.C. in Great Britain • Alignments with locations of sunset, sunrise, moonset and moonrise at summer and winter solstices • Probably used as calendar. www.assignmentpoint.com

  5. 0 Other Examples around the World www.assignmentpoint.com Big Horn Medicine Wheel (Wyoming)

  6. 0 Other Examples around the World Caracol (Mexico); Maya culture, approx. A.D. 1000 www.assignmentpoint.com

  7. Why is it so difficult to find out about the state of astronomical knowledge of bronze-age civilizations? • Written documents from that time are in a language that we don’t understand. • There are no written documents documents from that time. • Different written documents about their astronomical knowledge often contradict each other. • Due to the Earth’s precession, they had a completely different view of the sky than we have today. • They didn’t have any astronomical knowledge at all. www.assignmentpoint.com

  8. 0 Ancient Greek Astronomers • Models were based on unproven“first principles”, believed to be “obvious” and were not questioned: 1. Geocentric “Universe”: The Earth is at the Center of the “Universe”. 2. “Perfect Heavens”: The motions of all celestial bodies can be described by motions involving objects of “perfect” shape, i.e., spheres or circles. www.assignmentpoint.com

  9. Ptolemy:Geocentric model, including epicycles 0 Central guiding principles: 1. Imperfect, changeable Earth, www.assignmentpoint.com 2. Perfect Heavens (described by spheres)

  10. What were the epicycles in Ptolemy’s model supposed to explain? • The fact that planets are moving against the background of the stars. • The fact that the sun is moving against the background of the stars. • The fact that planets are moving eastward for a short amount of time, while they are usually moving westward. • The fact that planets are moving westward for a short amount of time, while they are usually moving eastward. • The fact that planets seem to remain stationary for substantial amounts of time. www.assignmentpoint.com

  11. 0 Epicycles Introduced to explain retrograde (westward) motionof planets The ptolemaic system was considered the “standard model” of the Universe until the Copernican Revolution. www.assignmentpoint.com

  12. At the time of Ptolemy, the introduction of epicycles was considered a very elegant idea because … • it explained the motion of the planets to the accuracy observable at the time. • it was consistent with the prevailing geocentric world view. • it explained the apparently irregular motion of the planets in the sky with “perfect” circles. • because it did not openly contradict the teaching of the previous authorities. • All of the above. www.assignmentpoint.com

  13. 0 The Copernican Revolution Nicolaus Copernicus (1473 – 1543): Heliocentric Universe(Sun in the Center) www.assignmentpoint.com

  14. 0 New (and correct) explanation for retrograde motion of the planets: Retrograde (westward) motion of a planet occurswhen the Earth passes the planet. This made Ptolemy’sepicyclesunnecessary. Described in Copernicus’ famous book “De Revolutionibus Orbium Coelestium” (“About the revolutions of celestial objects”) www.assignmentpoint.com

  15. In the Copernikan “Universe”, the orbits of planets and moons were … • Perfect Circles • Ellipses • Spirals • Epicycles • None of the above. www.assignmentpoint.com

  16. Johannes Kepler (1571 – 1630) 0 • Used the precise observational tables of Tycho Brahe (1546 – 1601) to study planetary motion mathematically. • Found a consistent description by abandoning both • Circular motion and • Uniform motion. • Planets move around the sun on elliptical paths, with non-uniform velocities. www.assignmentpoint.com

  17. Kepler’s Laws of Planetary Motion 0 • The orbits of the planets are ellipses with the sun at one focus. c Eccentricity e = c/a www.assignmentpoint.com

  18. 0 Eccentricities of Ellipses 1) 2) 3) e = 0.1 e = 0.2 e = 0.02 5) 4) e = 0.4 e = 0.6 www.assignmentpoint.com

  19. 0 Eccentricities of planetary orbits Orbits of planets are virtually indistinguishable from circles: Most extreme example: Pluto: e = 0.248 Earth: e = 0.0167 www.assignmentpoint.com

  20. 0 • A line from a planet to the sun sweeps over equal areas in equal intervals of time. Fast Slow www.assignmentpoint.com Animation

  21. Are all four seasons equally long? • Yes. • No, summer is the longest; winter is the shortest. • No, fall is the longest; spring is the shortest. • No, winter is the longest; summer is the shortest. • No, spring is the longest; fall is the shortest. www.assignmentpoint.com

  22. Why is the summer longer than winter? • Because of the precession of the Earth’s axis of rotation. • Because of the moon’s 5o inclination with respect to the Ecliptic. • Because the Earth is rotating around its axis more slowly in the summer (→ longer days!). • Because the Earth is closest to the sun in January and most distant from the sun in July. • Because the Earth is closest to the sun in July and most distant from the sun in January. www.assignmentpoint.com

  23. 0 Autumnal Equinox (beg. of fall) Summer solstice (beg. of summer) July Winter solstice (beg. of winter) Fall Summer Winter Spring January Vernal equinox (beg. of spring) www.assignmentpoint.com

  24. Kepler’s Third Law 0 • A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed: Py2 = aAU3 (Py = period in years; aAU = distance in AU) Orbital period P known → Calculate average distance to the sun, a: aAU= Py2/3 Average distance to the sun, a, known → Calculate orbital period P. Py = aAU3/2 www.assignmentpoint.com

  25. It takes 29.46 years for Saturn to orbit once around the sun. What is its average distance from the sun? • 9.54 AU • 19.64 AU • 29.46 AU • 44.31 AU • 160.55 AU www.assignmentpoint.com

  26. Think critically about Kepler’s Laws: Would you categorize his achievements as physics or mathematics? • Mathematics • Physics www.assignmentpoint.com

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