ORBITS AND GRAVITY: KEPLER AND NEWTONJanuary 25, 2005 Chapter 2, Pages 4259Next Two Classes: Observing and Research ProjectsThursday February 3: Chapter 3, Pages 6072Johannes Kepler (Germany, 1571−1630): Used the observations of Tycho Brahe to derive “laws”I. The orbit of a planet about the Sun is an ellipse with the Sun at one focusA. Special cases: circle and lineII. A line joining a planet and the Sun sweeps out equal areas in equal intervals of timeA. Implication: For any INDIVIDUAL object in orbit around Sun, the closer it is to Sun, the faster it travels. E.G., a comet in a highly elliptical orbit will move much faster when it closerSun and much slower when it is farther from Sun.III. The squares of periods of the planets are proportional to the cubes of their semimajor axes.p2 a3A. Implication: When comparing the MEAN distances of two objects, the farther you are fromthe Sun, the slower you go in your orbit.IV. Based solely on observations. Not on physics!Isaac Newton (England, 1643−1727): Used Kepler’s Laws and Galileo’s experiments to derive theoriesof motion and gravity.NEWTON'S LAWS OF MOTIONI. A body at rest stays at rest, a body in motion moves in a straight line, unless operated on by an outside force.II. Force equals mass times acceleration: F maIII. When one body exerts a force on a second body, the second body exerts an equal and opposite forceon the first body.1NEWTON'S LAW OF UNIVERSAL GRAVITATIONI. Every particle attracts every other; force depending only on mass and distance. Inverse square law.F Gm1m2/d2 Newtons (N) [kg2/m2] [m1 = mass1; m2 = mass2; m is meters]G 6.6710-11Nm2/kg2Going back to F = ma (second law):Acceleration (a) m/s2 [on Earth, a g 9.8m/s2]and Weight Force gmass2If: mass1 Mass (Earth) = MEand: mass2 Mass (you) Then: g mass2 GME/RE2 mass2 [RE = radius of Earth = distance (d) from the Earth’s center; center of mass]Therefore: g GME/RE2 This is true for all objects in
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