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Chapter 2 Patterns in the Sky (LOOKING UP/OUT) 2.1 2.2 2.3 2.4 2.5 Earth Spins on its Axis Revolution About the Sun Leads … Motions and Phases of the Moon Eclipses: Passing through a Shadow Motions of the Planets in the Sky Let’s back up a bit and start from the beginning We trace modern science to the Greeks. Why? 1. Tried to understand nature without resorting to supernatural explanations. (debate and challenges of ideas) 2. Used mathematics to give precision to their ideas. 3. Applied reasoning to observations. 4. Applied the concept of MODELS. Greek astronomy: their observation was: They saw the celestial bodies move around them (Earth): GEOCENTRIC model Eratosthenes measures the Earth (c. 240 BC) Plato, Aristotle ---> Earth is the center and the heavens must be “perfect” defined as perfect spheres and perfect circles. Ptolemy Ptolemaic model was the most sophisticated version of the geocentric model (A.D. 100-170) It was sufficiently accurate to remain in use for 1,500 years! The geocentric universe Greek geocentric model (c. 400 B.C.) But this model was not perfect … because of an observation Dr. Ted Snow’s web page at The University of Colorado, Boulder Retrograde Motion 1. Planets usually move slightly eastward from night to night relative to the stars. 2. But sometimes they go westward relative to the stars for a few weeks: apparent retrograde motion This needs to be explained with the geocentric model Dr. Ted Snow’s web page at The University of Colorado, Boulder Epicyles Review this brief history of ancient astronomy: The Earth OBVIOUSLY stands still (Ptolemaic model) therefore: 1. The Sun rises and sets, orbiting the Earth (geocentric model) 2. The moon rises and sets (it does orbit Earth!) 3. The stars all rise and set together, rotating about point, centered on the Earth (geocentric model) 4. If the Earth revolved around the Sun, the positions of the stars would appear to change (parallax), but, stars did not appear to exhibit parallax . Greeks Library of Alexandria Islamic Science Preservation House of Wisdom (Baghdad) 800 A.D. European Science Renaissance Europe (1453) • Copernicus realized the Solar System was heliocentric—centered on the Sun. • Planets exhibit apparent retrograde motion due to their distances from Earth. – Appear to turn around. Nicolas Copernicus (1473-1543, Poland) • • • • • • The center of the Solar System is near the Sun. (published 1543) Parallax: Earth-Sun distance <<< distance to the stars. The rotation of the Earth accounts for the apparent daily rotation (diurnal motion) of the stars. The apparent annual cycle of movements of the Sun is caused by the Earth revolving round the Sun. The apparent retrograde (backward) motion of the planets is caused by the motion of the Earth around the Sun The planets follow circular orbits around the Sun. Recall the Ptolemeic/geocentric model http://cygnus.colorado.edu/Animations/mars2.mov So, in a mere 1500 years, we went from: Ptolemic/geocentric model Copernican/heliocentric model http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g37/graphics/g37_copernicus.gif http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g37/graphics/g37_ptolemy.gif Tycho Brahe (1546-1601, Denmark) Geocentrist • Compiled the most precise measurements of the planets’ positions for his time, with no telescope • Observed a supernova (1572), and showed it was at the distance of the stars, not close to Earth http://www.space.com/24712-tycho-supernova-mach-1000-shock-wave.html • He could not detect a stellar parallax, and proposed that stars were too far away or Earth is the center of Universe. Earth being the center. • Hired Kepler Quadrant Johannes Kepler (1571-1630, Germany) • Brahe assigned him the tough problem of Mars’ retrograde motion. (Cannot explain retrograde if Earth is at the center) • Found that planetary orbits were heliocentric and elliptical (not circular) Heliocentric = centered around the SUN If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.” 1400 1500 1600 1700 Copernicus + Tycho + Kepler = Kepler’s Laws • Kepler’s 1st Law: Planet orbits are ellipses. • Each ellipse has two foci. • The Sun is at one focus of a planet’s elliptical orbit. An ellipse is characterized by: semi-major axis (the distance between the two foci) eccentricity • Each orbit has a shape and a size. • The eccentricity describes how elongated the ellipse is and how far the foci are separated. EARLY PERSEID METEORS: Earth is entering a broad stream of debris from Comet Swift-Tuttle, source of the annual Perseid meteor shower. Meteoroids in the outskirts of the stream are now hitting Earth's atmosphere, producing as many as 10-15 meteors per hour according to worldwide counts from the International Meteor Organization. NASA's network of all-sky meteor cameras captured 17 Perseid fireballs on the nights of July 28th through 30th. Here are their orbits: • Kepler’s 2nd Law: the Law of Equal Areas. As a planet moves around its orbit, it sweeps out equal areas in equal times. tB areas: A=B=C slow tA tC fast tA = tB = tC • Consequences: A planet will go fastest when closest to the Sun. It will go slowest when farthest from the Sun. slow tA tC fast • Kepler’s 3rd Law: A planet’s orbital period depends on its distance from the Sun orbital period (P) is the time to orbit the Sun once. distance (a), actually the average distance 2 P = 3 a P is in units of years a is in units of A.U. Kepler’s 3rd Law • Consequences: – Distant planets take longer to orbit the Sun. – Distant planets travel at slower speeds. Summary • How did Copernicus, Tycho, and Kepler challenge the Earth-centered idea? Copernicus created a sun-centered model Tycho provided the data needed to improve this model Kepler found a model that fit Tycho’s data • What are Kepler’s three laws of planetary motion? 1. The orbit of each planet is an ellipse with the Sun at one focus 2. As a planet moves around its orbit it sweeps our equal areas in equal times 3. The time for planets to orbit the Sun is related to its distance from the Sun: P2 = a3 Summary Kepler’s three laws of planetary motion 1. The orbit of each planet is an ellipse with the Sun at one focus 2. As a planet moves around its orbit it sweeps our equal areas in equal times 3. The time for planets to orbit the Sun is related to its distance from the Sun: P2=a3 AstroTour Kepler’s laws Click here to launch this AstroTour (Requires an active Internet connection.) End of Chapter 2 Now you know !