Kepler laws

Kepler laws describe the motion of planets around the Sun. These laws state that[1]:

Kepler's laws. The applet initially simulates the pair of Sirius A and Sirius B but the orbit parameters can be adjusted. The equal are sectors first show up when enough history accumulates to draw them.

  1. The orbit of a planet is an ellipse with the Sun at one of the two foci (another foci has no obvious special meaning).
  2. The line connecting the planet to the sun sweeps out equal areas in equal times. The visualization shows two such sectors.
  3. The square of the rotation period is proportional to the cube of the semimajor axis of the orbit:

Kepler's laws were radical claims; at the time of they publication many were convinced that planet orbits are perfect circles. Most of the planetary orbits are rather close to circles, so it is not immediately evident that they are ellipses.

For elliptic orbit, the distance between planet and Sun changes (as much as twelve times for some dwarf planets like 90377 Sedna) but the sum of distances between the planet and both focuses of the ellipse remains the same.

The second law (the law of areas) indirectly requires planet to move faster when it is closer to the Sun. For the circular orbit, the speed is stable as distance to the Sun is constant.

Kepler's laws can be derived from Newton inverse square law of gravity, assuming that the planet is not affected by gravity of other bodies apart the Sun. These laws also apply to other stars if they have planets, also to binary stars if one of them is much smaller. When masses are not very different, both objects rotate around the shared mass center (barycenter) with neither one staying at a focus of an ellipse. If one mass is much larger, this barycenter stays inside the boundaries of that stellar body.

Computing the planet position as a function of time on the base of Kepler's laws is quite sophisticated; actually it does not look much more difficult to solve Newton equations with some numeric method instead.


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