kepler’s laws. 2.5 the laws of planetary motion law 2. imaginary line connecting sun and planet...
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Kepler’s Laws
2.5 The Laws of Planetary Motion
Law 2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times
2.5 The Laws of Planetary Motion
Law 3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis
More Precisely 2-1: Some Properties of Planetary Orbits
Semimajor axis and eccentricity of orbit completely describe it
Perihelion: closest approach to Sun
Aphelion: farthestdistance from Sun
Another way to say them• The path of the planets about the sun is elliptical in shape, with
the center of the sun being located at one focus. (The Law of Ellipses)
• An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm
• The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)
Easy math
If planet A is 4 units from the sun then what is its orbital period. (a3 = p 2)
Keplar’s laws
http://www.youtube.com/watch?v=GcKiG-CuvtA
Let’s watch different planets in action
• http://astro.unl.edu/classaction/animations/renaissance/kepler.html
2.7 Newton’s LawsGravity
For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them
2.7 Newton’s LawsGravity
The constant G is called the gravitational constant; it is measured experimentally and found to be
G = 6.67 x 10-11 N m2/kg2
But let’s look at an easier way
Fgm1m2/d2
The force of gravity is proportional to the product of the mass of the two objects divided by the distance squared
White board problem
If Marvin is 36 lbs how much is his weight if he is at 2r (distance from Earth)
Weight = 36/22 36/4=9lbs
So if this is true and astronauts at the space station are still within the earth’s gravity, why do they experience weightlessness???
http://www.youtube.com/watch?v=2V9h42yspbo
Vomit Comet
http://www.youtube.com/watch?v=2V9h42yspbo
2.8 Newtonian Mechanics
Escape speed: the speed necessary for a projectile to completely escape a planet’s gravitational field. With a lesser speed, the projectile either returns to the planet or stays in orbit.
So what did Einstein have to say about gravity?
But what is gravity, what is it that attracts to objects to one another? http://www.youtube.com/watch?v=O-p8yZYxNGc
http://www.youtube.com/watch?v=DbhuRcmSkMg&feature=related