1. The Solar System Planetary Orbits

2. Johannes Kepler December 27, 1571 – November 15, 1630
German mathematician, astronomer and astrologer
Kepler’s 3 Laws of Planetary Motion

3. Law #1
#1 -The orbit of every planet is an ellipse with the Sun at one of the two foci
Explanation:
Planets revolve in an ellipse around the sun.
An ellipse has two fixed points called foci that are on either side of the center of the axis
The sun lies at one focus and is not the center of Earth’s orbit
Planet

4. Law #2
#2 - A line joining a planet and the Sun sweeps out equal areas during equal intervals of time
Closer to Sun = faster in orbit because of gravitational pull of Sun on planet
Perihelion
Aphelion
Planet moves faster
Planet moves slower
Covers equal areas in
Equal amount of time

5. All measurements are in cm
Law #3
Law #3 - Mathematical formula to prove Law 1 + 2
Eccentricity = distance between the foci
length of the major axis
e = d/L
In ESRT
Foci
All measurements are in cm
Length of Major Axis

7. Eccentricity = distance between the foci length of the major axis
In ESRT
E= 2.2 cm E=
4.1 cm
E= 0.537
Eccentricity is always numbers past the decimal point…to the nearest 1000ths place.
NEVER more than 1
NEVER less than 0
Eccentricity has no label!
2.2 cm
4.1 cm

8. If the two foci are located near the ends of the axis, an ellipse is long and narrow… highly elliptical
Many comets have this type of path
If the foci move closer together, the shape of the ellipse becomes more circular
A circle has NO eccentricity
e = 0
A straight line is the maximum eccentricity
e = 1
e=0
e=0.150
e=0.305

9. E= 0.356
E= 0.015
E= 0
E= 0
E= 0.569
E= 0.897

10. Eccentricity of an Orbit Lab This lab is on the Regents Exam
Video

11. December 2012