Transcript (t)= t. At the same time a man starts a distance L from the center and

Physics 218 Challenge Exam will take place on
December 3. Please come and participate!
DATE: Monday, December 3, 2007
TIME: 6:00 p.m.
LOCATION: 202T ENPH
Platform rotates with a constant angular
velocity 0. At t = 0 it starts rotating with
angular acceleration (t)=t. At the same time
a man starts a distance L from the center and
walks in along a straight line painted on the
platform towards the center. He decreases his
distance from the center at a constant rate, V0.
What force does the platform exert on the
man, as a function of his distance from the
center?
Johannes Kepler (1571 – 1630)
Kepler hypothesized that a physical force moved
the planets, and that the force diminished with
distance.
Planets closer to the sun feel a stronger force and
move faster.
Elliptical orbits – key to the problem of the planetary
motion
A platform rotates with a constant angular
velocity 0. At t = 0 it starts rotating with
angular acceleration (t)=t. At the same time
a man starts a distance L from the center and
walks in along a straight line painted on the
platform towards the center. He decreases his
distance from the center at a constant rate, V0.
What force does the platform exert on the
man, as a function of his distance from the
center?
Kepler’s Laws of Planetary Motion
1. The orbits of the planets are ellipses with the
sun at one focus.
c
Eccentricity e = c/a
Eccentricities of Ellipses
1)
2)
e = 0.02
3)
e = 0.1
e = 0.2
5)
4)
e = 0.4
e = 0.6
Eccentricities of Planetary Orbits
Orbits of planets are virtually
indistinguishable from circles:
Most extreme example:
Earth: e = 0.0167
Pluto: e = 0.248
LAW 2: A line joining a planet/comet and the Sun
sweeps out equal areas in equal intervals of time
The closer to the sun, the
larger the orbital velocity
Planetary Orbits (2)
• A line from a planet to the sun sweeps
over equal areas in equal intervals of time.
• A planet’s orbital period (P) squared is
proportional to its average distance from the
sun (a) cubed:
Py2
= aAU
3
(Py = period in years;
aAU = distance in AU)