Kepler's Laws of Planetary Motion - Zero Eccentricity

Zero Eccentricity

Kepler's laws refine the model of Copernicus. If the eccentricity of a planetary orbit is zero, then Kepler's laws state:

1. The planetary orbit is a circle
2. The Sun is in the center
3. The speed of the planet in the orbit is constant
4. The square of the sidereal period is proportionate to the cube of the distance from the Sun.

Actually the eccentricities of the orbits of the six planets known to Copernicus and Kepler are quite small, so this gives excellent approximations to the planetary motions, but Kepler's laws give even better fit to the observations.

Kepler's corrections to the Copernican model are not at all obvious:

1. The planetary orbit is not a circle, but an ellipse
2. The Sun is not at the center but at a focal point
3. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed is constant.
4. The square of the sidereal period is proportionate to the cube of the mean between the maximum and minimum distances from the Sun.

The nonzero eccentricity of the orbit of the earth makes the time from the March equinox to the September equinox, around 186 days, unequal to the time from the September equinox to the March equinox, around 179 days. The equator cuts the orbit into two parts having areas in the proportion 186 to 179, while a diameter cuts the orbit into equal parts. So the eccentricity of the orbit of the Earth is approximately

close to the correct value (0.016710219). (See Earth's orbit). The calculation is correct when the perihelion, the date that the Earth is closest to the Sun, is on a solstice. The current perihelion, near January 4, is fairly close to the solstice on December 21 or 22.