Kepler’s Laws of Planetary MotionNewton’s Laws of Gravity

circleeccentricity=0

ellipseeccentricity = 0<e<1

eccentricityincreasing

PLANETARY MOTION --- what kind of curves do planets follow in their orbits?

Two obvious closed ovals: the circle and the ellipse

Kepler’s 1st Law:

Planets orbit in ellipses with the Sun at one focus.

(closest approach)(farthest extent)

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

1

2

sweep = m r v

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 proportion2. 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.

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

Fg = G ---------M1M2

d2

2 2 2 4 (2)(2)/(4) = 1

1 2 1/2 1/4 (1)(2)/(1/4) = 8

Fg

If Gravity turned off magically, the planets would move off in straight paths, where the direction depends upon the instantaneous velocity

This behavior is Netwon’s 1st Law of MotionA 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?