During the last quarter of the 16 centry, the Danish bobleman Tycho
Brahe provide careful observation of the planets over an extended period
of time (20 years). He hoped to use his data to verify his own model of
the solar system, in which the sun orbited th earth and all other planets
orbited the sun. At Brahes death at 1601, his assistant Johannes Kepler
inherited the data that Brahes had accumulated. Kepler spend some 20 years
analyzing these data, looking for mathematical regularities. He came
to the conclusion that the ideal of circular orbits should be discarded
and replaced with elliptical orbits. Kepler summerized his laborious study
of planetary motion with the following three laws:
1. The planets move in elliptical orbits with the sun at one focus.
This java applet let you play with Kepler's laws and learn more physics
2. A line from the sun to any planets sweeps out equal areas in equal
3. The square of a planet's period is proportional to the cube of the
planet's mean distance from the sun.
The red circle at the center of the screen represent the sun.
The moving yellow circle is the planet.
The initial condition is represented by the blue arrow.
The planet start from the starting point of the blue arrow,
and its initial velocoty is proportional to the length of the arrow.
You can drag the blue arrow to change its initial condition in three different
1. fixed kinetic energy
Right click the mouse button to suspend the animation. Click it again to
2. fixed angular momentum
Find out the relation between shape and size of
the trajectory with the above parameters.
What if you click it with the left mouse button? Find out by yourself.
Use reset button to clear the screen. (Try to compare different trajectorys
before press it!)
You can select four different mode to play with it.
For the energy mode or while you drag the mouse button:
The lower green curve is the potential energy : U(r)=-GMm/r
Two horizontal red lines show the total energy of the particle.
another one is the effective potential energy Ueff(r)=-GMm/r
(watch the small moving dots! )
The period of the particle motion is also shown in real time unit.
Any suggestions? Please click firstname.lastname@example.org
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