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Pull out a ½ sheet or use the back of your old quiz Weekly Schedule Today • Hw # 2 due • Quiz # 2 • Geocentric vs. Heliocentric models • Kepler’s Laws – Astronomy InteracGves • Newton and Gravity – Lecture tutorials Thursday • ElectromagneGc spectrum – Lecture Tutorials • Lab # 3-‐ Spectral Analysis Lab Geocentric model (Earth centered) Retrograde motion of planets Favored by: Aristotle, Ptolemy, and others Planets: • Move with respect to fixed stars • Change in brightness • Change speed • Have retrograde motion- eastward • Are difficult to describe in earthcentered system Ptolemy's retrograde model Heliocentric model (Sun-‐centered) Copernican system Explains retrograde motion, Galileo’s observations Fashioned by: Copernicus, Galileo, Brahe, Kepler Mars' actual motion Venus' retrograde motion Galileo’s observations support the Heliocentric Model • Your group should select what it believes to be Galileo’single most important astronomical observaGon. Explain what he observed using sketches and why it was most important. (See pages 29-‐30 in your book) Observations of Galileo: • The Moon has mountains, valleys, and craters. • The Sun has imperfections, and it rotates. • Jupiter has moons. • Venus has phases. All these were in contradiction to the general belief that the heavens were constant and immutable. Direct conflict with church, made to retract claims under threat of torture, house arrest 1616-1633 Church publicly apologized in 1992!!! Kepler’s Laws-‐ based on Copernican's model • 1st: Planets have EllipGcal orbits not circular orbits with the sun at one focus drawing_ellipse_with_string Kepler’s Laws • 2nd Law: Equal areas over equal Gmes *Planets move faster closer to Sun Kepler's 2nd Law During which part of the planet’s orbit would the planet move with the greatest speed? A. A B. B C. C D. D 10 Kepler’s Laws • 3rd Law: p2 = d3 – Square of period of planet’s orbital mo6on is propor6onal to cube of semimajor axis. *Planets further away from Sun have longer periods Astronomical unit (AU) Average distance between Earth and Sun If a small weather satellite and the large InternaGonal Space StaGon are orbiGng Earth at the same alGtude above Earth’s surface, which object takes longer to orbit once around Earth? A. A) The large space staGon B. B) The small weather satellite C. C) They would take the same Gme What would happen if Mercury and Jupiter were to switch places in their orbits around the sun? A. Jupiter would have a shorter orbital period than before B. Mercury would have a shorter orbital period than before C. Neither of the two planets would have any change in their orbital periods Imagine a newly discovered planet is 3 AU from the Sun. Which of the following best approximates the orbital period of this planet? A. 1 year B. 3 years C. 5 years D. 9 years Choose your answer below (Class Ac)on: Eccentricity of Shapes, Kepler’s 2nd Law, Kepler’s 3rd Law) 25% 25% !D 25% !C http://astro.unl.edu/classaction/ questionsList.html 25% !B A B C D !A 1. 2. 3. 4. Consider a planet orbiGng the Sun. If the mass of the planet doubled but the planet stayed at the same orbital distance, then the planet would take A. more than twice as long to orbit the Sun. B. exactly twice as long to orbit the Sun. C. the same amount of Gme to orbit the Sun. D. exactly half as long to orbit the Sun. E. less than half as long to orbit the Sun. Newton used physics to explain Kepler’s Laws. Newton s laws of motion explain how objects interact with the world and with each other. Newton s first law: An object at rest will remain at rest, and an object moving in a straight line at constant speed will not change its motion, unless an external force acts on it. Newton s Laws Newton s second law: When a force is exerted on an object, its acceleration is inversely proportional to its mass: a = F/m Newton s third law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. Gravity On Earth’s surface, the acceleration due to gravity is approximately constant, and directed toward the center of Earth. 9.8m/s2 Weight = mass x gravity Mars has 0.38 the gravity Earth has. What would you weigh on Mars? Calculate this. Which of the following best describes how you would weigh on the Moon versus Earth? A. You would weigh the same B. You would weigh more on the moon C. You would weigh less on the moon D. You would have more mass on the moon, but your weight would not change Moon gravity Demo Force of gravity depends on mass and distance. Distance follows the inverse square law If the distance between two masses quadruples, how much does the gravitational force between them lessen? Mass (force)= 1/d2 Newton s Laws Gravity The gravitational pull of the Sun keeps the planets moving in their orbits. If the sun were twice as massive its pull on Mars would be A. Unchanged B. Twice as much C. Half as much D. Four Gmes as much Choose your answer below (Class Ac)on: Gravity, f and d, direc)on, Spaceship to Moon, satellite orbits) A. A B. B C. C D. D http://astro.unl.edu/classaction/ questionsList.html Newton s Laws Massive objects actually orbit around their common center of mass; if one object is much more massive than the other, the center of mass is not far from the center of the more massive object. For objects more equal in mass, the center of mass is between the two. The force of gravity between two planets depends on: A. 1) Masses and distance apart B. 2) Planetary atmospheres C. 3) RotaGonal moGons D. 4) All of these Newton s Laws Kepler s laws are a consequence of Newton s laws. Write 1 sentence to explain this figure: