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

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

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

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

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

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

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

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.

M1M2 Fg = G --------- d2 Mass 1 Mass 2 Distance d2 Fg ---------- ---------- ------------ --------- --------------------- 1 1 1 1 (1)(1)/(1) = 1 2 1 1 1 (2)(1)/(1) = 2 1 2 1 1 (1)(2)/(1) = 2 1 1 2 4 (1)(1)/(4) = 1/4 2 2 1 1 (2)(2)/(1) = 4 2 2 2 4 (2)(2)/(4) = 1 1 2 1/2 1/4 (1)(2)/(1/4) = 8

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.

So… WHAT IS AN ORBIT?

So… WHAT IS MASS?