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 itPerihelion: closest approach to SunAphelion: 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