# jan14_10 - AST201 - 14 Jan. 2010 th Announcements...

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Announcements • Assignment 2 is now available on line. • Readings are assigned at end of each lecture. • Don't forget: Term Test March 2. Today: * Gravity * Light * Properties of Matter and Light AST201 - 14 th Jan. 2010

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4.4 The Universal Law of Gravitation Our goals for learning: What determines the strength of gravity? How does Newton’s law of gravity extend Kepler’s laws? Let's begin by looking at what Kepler discovered Let's begin by looking at what Kepler discovered between 1600 and 1618 using Tycho Brahe's between 1600 and 1618 using Tycho Brahe's observations of planetary positions with time . . observations of planetary positions with time . ..
Kepler's First Law Orbits are ellipses (see Section 3.3 in Ch. 3 )

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Kepler's Second Law The Law of Equal Areas
(ex)-David Dunlap Observatory (in Richmond Hill) Law of Equal Areas

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This is the Result of Conservation of Angular Momentum Conservation of angular momentum means: (mass) X speed X radius = constant Kepler's Second law says: Speed X radius = constant (The mass stays constant anyway. Hence Kepler's Law is simply a statement of the conservation of orbital angular momentum by each planet.)
Kepler's Third Law Period squared = average distance from Sun cubed (when the period is in Years, distance in AU) NB: 1 AU = average distance between Sun & Earth P 2 = A 3 More generally : period squared = a constant X total mass X (average distance between two bodies) cubed

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Kepler's Third Law
Kepler's Laws For planets in the Solar System: 1 . Planets move in elliptical orbits, the Sun at one focus. 2 . As a planet moves around its orbit, it sweeps out equal areas in equal times. 3 . More distant planets orbit the Sun at slower average speeds, precisely obeying: (Period in years) 2 = (average distance from Sun in AU) 3

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Newton was able to explain (and in fact predict) Kepler's strictly empirical laws using his three Laws of Motion and the Law of Gravity. He was able to predict a lot more! Kepler found his Laws from observation, but did not know why they worked. ..
What determines the strength of gravity? The Universal Law of Gravitation: 1. Every mass attracts every other mass. 2. Attraction is directly proportional to the product of their masses. 3. Attraction is inversely proportional to the square of the distance between their centers.

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How does Newton’s law of gravity extend Kepler’s laws? • Ellipses are not the only orbital paths. Orbits can be: – Bound (ellipses) – Unbound • Parabola • Hyperbola Kepler’s first two laws apply to all orbiting objects, not just planets
Center of Mass Because of momentum conservation, orbiting objects orbit around their center of mass

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Newton and Kepler’s Third Law His laws of gravity and motion showed that the relationship between the orbital period and average orbital distance of a system tells us the total mass of the system. Examples:
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## This note was uploaded on 03/02/2010 for the course AST AST201 taught by Professor Mochnacki during the Spring '10 term at University of Toronto- Toronto.

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jan14_10 - AST201 - 14 Jan. 2010 th Announcements...

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