Reading assignment: Chapter 14.1-14.4 Homework : (due Monday, Oct 31, 2005): Problems: Q5, Q10, 1, 3, 7, 12, 20,

1. Chapter 13 Reading assignment: Chapter 14.1-14.4 Homework : (due Monday, Oct 31, 2005): Problems: Q5, Q10, 1, 3, 7, 12, 20,

2. 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

3. 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:

4. 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:

5. 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

6. All nine planets of the solar system

7. 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.

8. Black board example 14.4 How is related to U = m·g·h?

9. 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.