Kepler’s Laws of Planetary Motion Newton’s Laws of Gravity
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Presentation on theme: "Kepler’s Laws of Planetary Motion Newton’s Laws of Gravity"— Presentation transcript:
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 ellipseeccentricityincreasingcircleeccentricity=0ellipseeccentricity = 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 v21sweep = m r vAt each point in the orbit, the mass (m) is the same… no effect1. As distance (r) increases… velocity (v) decreases in proportion2. 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 dThe FORCE of attraction, called GRAVITY, is Fg, given by the above.
10 If Gravity turned off magically, the planets would move off in straight paths, where the direction depends upon the instantaneous velocityFgThis behavior is Netwon’s 1st Law of MotionA body continues in uniform motion (straight line constant speed) unlessA force is acting upon it.