1. Kepler’s Laws of Orbital Motion

2. Planets orbit the Sun in ellipses with the Sun at one focus
Kepler’s 1st Law
Planets orbit the Sun in ellipses with the Sun at one focus
perihelion
aphelion

3. Planets orbit the Sun in ellipses with the Sun at one focus
Kepler’s 1st Law
Planets orbit the Sun in ellipses with the Sun at one focus
The eccentricity of the ellipse is a measure of how “squished” the circle is:
0 ≤ e ≤ 1
e = 0  circle
e =  slightly ovalized
e =  Comet Halley
e = 1.00  parabolic orbit
perihelion
aphelion

5. Kepler’s 2nd Law
A line from the Sun to the planet will sweep out equal areas in equal times

6. Kepler’s 2nd Law
A line from the Sun to the planet will sweep out equal areas in equal times

7. (Average distance)3 = (Period)2
Kepler’s 3rd Law
(Average distance)3 = (Period)2
When expressed in “Earth terms”
(AU and years)
1 AU = average distance from Sun to Earth

8. If there were a planet twice as far from the Sun as the Earth is, what would its orbital period be in Earth years? A. B. C. D. E.

9. The book puts it like this:
Kepler’s 3rd Law
The book puts it like this:
T = (constant) r3/2

10. The book puts it like this: T = (constant) r3/2
Kepler’s 3rd Law
The book puts it like this:
T = (constant) r3/2
How do we come up with the constant?

11. Newton’s Law of Gravity and Uniform Circular Motion

12. Newton’s Law of Gravity and Uniform Circular Motion
“Newton’s Version of
Kepler’s 3rd Law”

13. Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B compared to that acting on A?
1 8
1 4
1 2
It’s the same. 2
Answer: B

14. The international space station orbits approximately 250 miles (402 km) above the Earth’s surface. What is its orbital period?

16. A geosynchronous satellite is one that has an orbital period equal to the Earth’s rotation period: one sidereal day = 23 hours, 56 min, 4 sec.
A geostationary satellite has that period and also a circular orbit along the equator (and thus appears stationary in the sky).
At what altitude above the Earth’s surface must a geostationary satellite orbit?

17. “Newton’s Version of Kepler’s 3rd Law” is also how we can determine the mass of a planet with moons, or a star with planets.
Use the period and distance of Jupiter’s moon Callisto to determine the mass of Jupiter.