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Lecture 10

AS101 Lecture 10

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Wilfrid Laurier University
Patrick Mc Graw

Lecture 10 2/6/2013 12:23:00 PM Does the Universe Revolve around you? Part II Review: Ptolemaic Model:  Geocentric (centered on Earth)  Based on uniform circular motion (objects move in circles at constant speeds)  Explain retrograde motion of planets using epicycles (circles on circles.) Review: Copernican Model:  Heliocentric (centered on the sun)  Kept the idea of uniform circular motion.  Explains retrograde motion as the result of inner planets moving faster and overtaking the outer ones.  Mercury and Venus are inside the earth’s orbit, so they always appear close to the sun. Copernican Model”  Superior planets: o The planets that orbit farther away from the sun. o (from earth, the superior planets are Mars, Jupiter, Saturn and Uranus and Neptune.)  Inferior planets: o The planets that are closer to the sun o (from earth, these are Mercury and Venus.)  superior planets can appear in the opposite direction from the sun, but inferior planets are always on the same side of the sky as the sun.  Retrograde motion occurs when Earth and a superior planet are on the same side of the sun Tycho Brahe and Johannes Kepler:  Using Brahe’s observations, Kepler developed a new, more accurate heliocentric model.  Abandoned uniform circular motion Keplers second law: a line from a planet to the sun sweeps over equal areas in equal times:  This means that a planet moves fastest at is perihelion (closest to the sun) and slowest at its aphelion (farthest away) Keplers third law: a planets orbital period squares is proportional to its average distance from the Sun cubed:  Note: the first and second laws describe each planet’s orbit, but the third law describes a comparison between orbits of different planets.  If we use the earth to compare all the other planets to, then we can say P^2 = a^3  Where P is the orbital period in earth-years and a in the planets average distance from the sun in a.u.  Example: o An asteroid orbits at a distance of 4 au from the Sun. How long does it take to make an orbit? o A = 4 o P^2 = a^3 = 4^3 = 64 o P = the square root of 64 = 8 o ANSWER: 8 years  Example: o Another object orbits the sun once every 27 year. What is its average distance from the sun? o P=27 o A^3 = P^2 = 729 o A- 9, because 9^3 = 9x9x9=729 o ANSWER: 9 au Galileo Galilei:  Helped solidify the Copernican revolution by overcoming some objections to the heliocentric view.  Made telescope observations that helped confirm the heliocentric picture and weaken the justification for the geocentric model.  Though experiments, began to understand motion better, a process continued later by Newton.  He did not invent the telescope, but he was the first person known to have used telescopes to look at astronomical objects. Galileo’s Telescope Discoveries:  Observed spots (imperfections) on the sun, and mountains and valleys on the moon,  These observations challenged the idea of perfect, unchanging heavens, and suggested other worlds like Earth.  Saw four moons orbiting Jupiter  This showed that orbits could happen around other objects besides earth.  Observations of the phases of Venus confirmed that Venus orbits the sun.  (in Ptolemaic model, Venus would only appear as a crescent— Galileo saw a whole cycle of phases. Though Question:  can you ever see Jupiter in a crescent phase? Sir Isaac Newton:  Understood planetary motion as governed by universal laws that also apply on earth.  Completing the work Galileo had begun, completely revised our understanding of motion, weeping away more of the objections to the heliocentric model.  Invented a new type of math. o (Calculus) to use in studying motion. Newton’s First Law:  An object at rest remains at rest unless a force acts on it; an object in motion continues in a straight line at constant velocity unless a force acts on it.  That means there’s nothing “perfect” or natural” about circular motion.  Any change in either speed or direction is called acceleration and requires force. Acceleration:  Which of the following are accelerating (as scientists use the word)? o A stopped train that starts moving again o A ball speeding up as it falls o A car slowing down by breaking o A car going around a curve at a constant speed o A figure skater making a figure eight.  ANSWER:  All of the above. According to Newton’s first law, none of those can happen without a force. Universal Gravitation:  The moon and planets undergo accelerated motion, so there must be a force acting on them (otherwise, the
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