1. Kepler’s Laws of Planetary Motion Newton’s Laws of Gravity

2. eccentricity = 0<e<1
PLANETARY MOTION --- what kind of curves do planets follow in their orbits?
Two obvious closed ovals: the circle and the ellipse
eccentricity
increasing
circle
eccentricity=0
ellipse
eccentricity = 0<e<1

3. Kepler’s 1st Law: Planets orbit in ellipses with the Sun at one focus.
(farthest extent)
(closest approach)

4. Kepler’s 2nd Law:
A line from a planet to the sun sweeps out equal areas in equal times.

5. Kepler’s 2nd Law is a consequence of conservation of angular momentum

6. sweep = m r v 2 1
sweep = m r v
At each point in the orbit, the mass (m) is the same… no effect
1. As distance (r) increases… velocity (v) decreases in proportion
2. As distance (r) decreases … velocity (v) increases in proportion

7. ORBITAL MOTION --- why do planets orbit on ellipses?
--- why does any object regardless of composition fall?
--- why do objects sometimes orbit, or sometimes fall?

8. NEWTON’s LAW OF GRAVITY (Universal Attraction)
Consider two masses, M1 and M2, separated by a distance d
The FORCE of attraction, called GRAVITY, is Fg, given by the above.

9. M1M2
Fg = G d2
Mass Mass Distance d Fg
(1)(1)/(1) = 1
(2)(1)/(1) = 2
(1)(2)/(1) = 2
(1)(1)/(4) = 1/4
(2)(2)/(1) = 4
(2)(2)/(4) = 1
/ / (1)(2)/(1/4) = 8

10. If Gravity turned off magically, the planets would move off in straight paths, where the direction depends upon the instantaneous velocity Fg
This behavior is Netwon’s 1st Law of Motion
A body continues in uniform motion (straight line constant speed) unless
A force is acting upon it.

11. So… WHAT IS AN ORBIT?

12. So… WHAT IS MASS?