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 =
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. U will get smaller (more negative) as r gets ________.
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.