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Chapter 13. Reading assignment: Chapter 14.1-14.4 Homework : (due Monday, Oct 31, 2005): Problems: Q5, Q10, 1, 3, 7, 12, 20, . Kepler’s laws about planetary motion These laws hold true for any object in orbit. Kepler’s first two laws (1609):
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Chapter 13 Reading assignment: Chapter 14.1-14.4 Homework : (due Monday, Oct 31, 2005): Problems: Q5, Q10, 1, 3, 7, 12, 20,
Kepler’s laws about planetary motion These laws hold true for any object in orbit • Kepler’s first two laws (1609): • Planets move in _____________ paths around the sun. The sun is in one of the focal points (foci) of the ellipse • The radius vector drawn from the sun to a planet sweeps out equal areas in equal time intervals (Law of ____________). Area S-A-B equals area S-D-C
Kepler’s laws about planetary motion Kepler’s third law (1619): III. The ____________ of the orbital period, T, of any planet is proportional to the ____________ of the semimajor axis of the elliptical orbit, a. Thus, for any two planets:
Kepler’s laws about planetary motion Most planets, except Mercury and ________, are on almost a circular orbit Earth: Ratio of minor to major axis b/a = 0.99986. For planets around sun:
Black board example 14.3 The solar system Inner planets Further out: Saturn, Uranus, Neptun, Pluto Calculate the mass of the sun using the fact that the period of the earth’s orbit is 3.157·107 s and it’s distance from the sun is 1.496·1011 m. If the Mars year is 1.88 earth years, what is Mars’ distance from the sun
Gravitational potential energy • Notice the – sign • U = 0 at infinity • U will get smaller (more negative) as r gets ________. • “Falling down” means losing ______ potential energy. • Use only when _____ away from earth; otherwise use approximation U = mgh.
Black board example 14.4 How is related to U = m·g·h?
Black board example 14.5 The First Rocket Launch from Cape Canaveral (NASA); July 1950 At Earth’s surface a projectile is launched straight up at 10 km/s. To what height will it rise? Ignore air resistance.