1. Kepler’s Laws
CPA Physics

2. Geocentric View Points
Earth centered Universe
Aristotle
(Greek) BC
Ptolemy
(Alexandrian Greek)
85-65AD

3. Heliocentric Viewpoints
Sun centered Solar System
Aristarchus (Greek) BC
Copernicus (Poland and Italy)
Galileo Galilei (Italian)

4. Tycho Brahe (Danish)

5. Tycho Brahe
Worked on the Island of Hven near Copenhagen at the Uraniborg Observatory
Compromise Theory: The Sun orbits the Earth, but the remaining planets orbit the Sun.
Brahe passed along his observations to Johannes Kepler, his assistant.

6. Brahe’s Compromise Theory

8. Johannes Kepler
( ) German Astronomer

9. Kepler’s First Law (Law of Orbits):
Planets move in elliptical orbits with the Sun at one of the focal points.
E L L I P S E

10. Kepler’s Laws Animation

11. Kepler’s 2nd Law(The Law of Areas)
A line from the sun to a planet sweeps out equal areas in equal lengths of time.

12. Where is the speed of the earth greater, point B or C?

13. Kepler’s Laws Animation

14. Kepler’s Third Law ( Law of Periods or Law of Harmony)
The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun.
K for our Solar System

15. Kepler’s Third Law ( Law of Periods or Law of Harmony)

16. EXAMPLE:
An asteroid revolves around the sun with a mean orbital radius of three times that of the earth. What is the period of the asteroid in earth years?
ANS: 5.2y

17. The period of the Moon is 27. 3 days and its orbital radius is 3
The period of the Moon is 27.3 days and its orbital radius is 3.8 x 108m. What would be the orbital radius of an object orbiting Earth with a period of 20 days?
ANS – 3.09 x 10 8 m