Intro to Planetary Motion.notebook
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November 13, 2011
Jan 46:51 PM
Chapter 7 Gravitation
Objectives Relate Kepler's laws of planetary motion to the
law of universal gravitation. Calculate orbital speeds and periods Solve orbital motion problems Relate weightlessness to objects in free fall Describe gravitational fields Describe views on gravitation
Jan 46:56 PM
Activity Follow instructions on page 171 of your textbook.
Each of you has a clean sheet of paper, a ruler, and protractor.
What shape do you get for the orbital path of Mercury?
Jan 47:08 PM
Orbital Positions of Planets and Comet ChuryumonGerasimenko
Jan 47:10 PM
Historical Perspective
Ancient Times Planets and Sun believed to revolve around Earth Followed theories of Ptolemy (c. 100 AD)
Copernicus (1473 1543) Believed objects revolved around the Sun. Orbits were circular
Jan 47:21 PM
Tycho Brahe (1546 1601) Believed that the Sun and Moon orbited Earth with
everything else orbiting the Sun. Died (murdered?) without proving his theory which
was later disproven by his student (killer?), JohannesKepler.
Jan 47:34 PM
Johannes Kepler (1571 1630) Assistant to Tycho Brahe Disagreed with Brahe about the orbits of planets
Believed Copernicus' heliocentric model Used Brahe's measurements to relate the laws of
motion to the planets.
Intro to Planetary Motion.notebook
2
November 13, 2011
Jan 47:43 PM
Kepler's Laws of Planetary Motion
1st Law Orbital paths of all planets around the sun are ellipses.
The sun is one focal point. Also applies to comets
2nd Law Planets move faster when closer to the Sun and slower
when they are further away. An imaginary line sweeps out from the sun sweeps
out equal areas over equal time intervals.
Each of the first two laws applies to each celestial body individually.
Jan 47:49 PM
Kepler's Law (cont'd)
3rd Law The square of the ratio of the periods of any two planets
revolving about the Sun is equal to the cube of ratio oftheir average distances from the Sun.
TATB( ( rA
rB( (=
Applies to a group of several objects.
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Jan 48:10 PM
Example
Galileo measured the orbital sizes of Juptier's moons using the diameter of Jupiter as a unit of measure. He found that Io, the closest moon to Jupiter, had a period of 1.8 days and was 4.2 units from the center of Jupiter. Callisto, the fourth moon from Jupiter, had a period of 16.7 days. Using the same units that Galileo used, predict Callisto's distance from Jupiter.
Jan 48:18 PM