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: farthest
distance 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=GcKiGCuvtA
Let’s watch different planets in action
• http://astro.unl.edu/classaction/animations/r
enaissance/kepler.html
2.7 Newton’s Laws
Gravity
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 Laws
Gravity
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
Fgm1m2/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=2
V9h42yspbo
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=Op8yZYxNGc
http://www.youtube.com/watch?v=DbhuRcmSk
Mg&feature=related