1. Kepler’s Laws
Ms. Jeffrey- Physics

2. Kepler’s Three Laws
Johannes Kepler discovered that planets do not orbit the sun in a circular path
they move in an elliptical path around the sun.
Kepler’s First Law: The paths of the planets about the sun are elliptical in shape, with the center of the sun being at one focus.
Kepler’s Second Law: An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time.
Kepler’s Third Law: The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

3. Kepler’s First Law: The Law of Ellipses
The paths of the planets about the sun are elliptical in shape, with the center of the sun being at one focus.
Works for other two-body situations, such as the Earth and the moon; The Earth and satellites etc.

4. Eccentricity
The amount of elongation or flatness in a planet’s elliptical orbit is defined as its orbital eccentricity.
An orbital eccentricity of 0 is a perfect circle
An eccentricity close to 1.0 is nearly a straight line.
The focus (the sun) is further and further from the center of the ellipse.

5. Kepler’s Second Law: THE LAW OF EQUAL AREAS
An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time.
When the planet is closest to the sun (Perihelion), it is moving the fastest.
When the planet is furthest from the sun (Aphelion), it is moving the slowest.
Therefore, planets do not move at constant speeds.

6. Earth needs to move slower over here to cover the same area as C to D.
Earth needs to move faster over here to cover the same area as A to B.

7. Kepler’s Third Law: thE Law of Harmonies
The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.
T2 ~ R3
This law relates the amount of time for the planet to complete one orbit around the Sun to the planet’s average distance from the Sun.
PERIOD (T) - the time for one complete revolution around the sun.
Distance (R) – the distance of the planet to the sun.
The Earth is one A.U. (Astronomical Unit) from the sun.
It takes one year to complete our revolution around the sun.

8. Saturn orbits the sun at a relative distance of 10. 0 A. U
Saturn orbits the sun at a relative distance of A.U. What is its orbital period?
Kepler’s Third Law

9. Kepler’s Third Law
How far away from the sun will an asteroid be if it was to have an orbital period of 2.0 years?

11. What is Kepler’s First Law?

12. In an ellipse, where is the center of the sun located?
Draw an ellipse, and where the sun may be located.

13. According to Kepler’s second law, which section of area takes longer for the planet to travel?

14. What is another name for Kepler’s Second Law?

15. Where does a planet move the fastest relative to the sun?

16. What is the planet’s position called when it is closest to the sun?

17. What is the planet’s position called when it is furthest from the sun?

18. What does it mean that gravity is Universal?

19. What does eccentricity mean?

20. Which scientist stated that Force of gravity is inversely proportional to distance?

21. What two factors does the force of gravity depend on?

22. Using Newton’s law of gravitation, why does the planet move fastest when it is closest to the sun?

23. If Jupiter is 5.2 AU from the sun, what is its period about the sun?

24. If the period of Neptune orbiting the sun is 164 Earth years, how far is Neptune from the sun in AU’s?