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

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**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

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**Kepler’s 1st Law: Planets orbit in ellipses with the Sun at one focus.**

(farthest extent) (closest approach)

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

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

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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

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**ORBITAL MOTION --- why do planets orbit on ellipses?**

--- why does any object regardless of composition fall? --- why do objects sometimes orbit, or sometimes fall?

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**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.

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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

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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.

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So… WHAT IS AN ORBIT?

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So… WHAT IS MASS?

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