Transcript Chapter 13b

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):
I.
Planets move in _____________ paths around the sun. The
sun is in one of the focal points (foci) of the ellipse
II.
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.
2
2
3
3
T
 const.
a
T a
Thus, for any two planets:
2
 T1   a1 
    
 T 2   a2 
3
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:
2
2
T
19 s
 2.97 10
3
3
a
m
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
All nine planets of the solar system
Gravitational potential energy
m1  m2
U (r )  G 
r
• 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
m1  m2
U (r )  G 
r
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.