Download Kepler`s Laws of Planetary Motion

Kepler’s Laws of Planetary Motion
Planetary Motion Simulator:
http://astro.unl.edu/classaction/animations/renaissance/kepler.html
1. A scientific LAW mathematically describes some natural phenomenon.
2. Johannes Kepler, using the observations of Tycho Brahe, identified
relationships among the distance of the planets, the shapes of their
orbits, and their motion around the sun. Kepler had always been
convinced that there was some unifying order in the solar system. His
laws not only gave an accurate description of what was, but explained
why previous models had not been able to exactly describe the observed
motions of the planets.
3. Kepler’s laws are the first recorded mathematical descriptions of the
universe. They demonstrate not only the order of what appears
disorderly, but that math and science are inseparable.
4. As with Newton’s laws, which still work to describe motion, Kepler’s Laws
are useful in the present. The third Law, for example, can be used to
determine the relative distance of any body in the solar system.
THE LAWS:
First law: Planets move at elliptical orbits, with the sun at one focus. An
ellipse is an oval shape. If we were to draw and ellipse, we would use
two pins and a loop of string. Each pin would represent a focus.
The shape of the oval is not always the same. Some are rounder than
others. All orbits are described in terms of their eccentricity—more oval =
more eccentric.(NOTE: The orbits of the planets are pretty circular—see
table on page 553 of text. A value of “0” is a circle, “1” would be so
eccentric as to be a parabola, not a closed figure.)
USING THE SIMULATOR:
1. Under “orbit settings”, select Mercury and click OK. The
simulator will use the actual values for this planet.
2. Turn on (then off) “empty focus” and “semimajor axis.” (This is
for future reference.)
3. Start animation—observe.
a. Increase the eccentricity--what happens to the speed of the
planet when it gets closer to the sun?
b. Farther away?
4. Turn on “radial lines.” These represent the string in the left hand
picture above.
5. Hit “reset” in the top margin. Select Earth, then “OK.” Is this
orbit more or less elliptical than Mercury’s?
6. Start animation. Observe. Turn on Grid lines. Is it possible to
see the Earth speeding up and slowing down?
7. Turn on radial lines—what do you notice?
Second Law: The orbital speed of a planet varies so that a line joining the
sun and the planet will sweep over equal areas in equal times, This is best
seen in animation, but it might help to point out that in the diagram below,
each triangle has an equal area. The black dot is the sun, and small blue
dots are a planet at different points in its orbit.
USING THE SIMULATOR:
1. ONCE AGAIN, SLECT Mercury and click, “OK.”
2. Below the picture, adjust the size so the fraction says 1/12.
This means that every triangle that will appear will be 1/12
of a year.
3. Click “sweep continuously,” then “start sweeping.”
According to the Second Law, each of the 12 triangles has
an equal area, even though they are different shapes.
4. Reset the simulator. Set the controls for Earth, and click
OK. Create the colored triangles for Earth. What do you
notice about the shapes? Why does this happen?
Third LAW: The amount of time a planet takes to orbit the sun is
related to the size of its orbit. The relationship is:
P2 =
a3
Where P is the period of revolution in years, and "a" is the length
of the semimajor axis or the ellipse in AUs. (Simply put: the
farther away a planet, the longer it takes to orbit the sun)
b = semimajor axis
USING THE SIMULATOR:
1. Click on “third law” on the lower left side.
2. In “visualization options in lower right corner, turn on
orbits, planets and labels.
3. Start with Mercury, click OK, then turn on the animation.
4. One at a time, switch to the next planet further out,
remembering to click OK after each. Observation: