Kepler's+First+Law+(1609)



//The orbit of each planet is an ellipse with the sun at one focus.//

At the time, this was a radical claim; the prevailing belief (particularly in [|epicycle]-based theories) was that orbits should be based on perfect circles. This observation was very significant at the time as it supported the [|Copernican view] of the Universe. This does not mean it loses relevance in a more modern context. A circle is just one form of an ellipse, but most of the planets follow an orbit of low [|eccentricity], meaning that they can be crudely approximated as circles. So it is not evident from the orbit of the planets that the orbits are indeed elliptic. However, Kepler's calculations proved they were, which also allowed for other planets farther away from the [|Sun] to have highly eccentric orbits (really long stretched out circles). These other heavenly bodies indeed have been identified as the numerous [|comets] or [|asteroids] by astronomers after Kepler's time. The [|dwarf planet] [|Pluto] was discovered as late as 1930, the delay mostly due to its small size and its highly elongated orbit compared to the other planets.

 Mercury || .25 .206 ||  ||   ||
 * Eccentricity e** is a number between 0 and 1. If **e** = 0, it is a circle. For an ellipse there are two points called foci (singular: focus) such that the sum of the distances to the foci from any point on the ellipse is a constant. For most of the planets one must measure the geometry carefully to determine that they are not circles, but ellipses of small eccentricity. Pluto and Mercury are exceptions: their orbits are sufficiently eccentric that they can be seen by inspection to not be circles.
 * =Examples of Ellipse Eccentricity= ||  ||   ||   ||   ||
 * Venus || .0068 ||
 * Earth || .0167 ||
 * Mars || .0934 ||
 * Jupiter || .0485 ||
 * Saturn || .0556 ||
 * Uranus || .0472 ||
 * Neptune || .0086 ||
 * Pluto



Drawing an Ellipse
Two pins, a length of string, a sheet of paper and a pencil are used to draw ellipses. The eccentricity of the ellipse is set by the spacing of the pins relative to the length of string stretched between the pins.

The eccentricity = (distance between the pins)/(length of string between the pins)
This basic property of the ellipse can be used to determine relationships between certain parameters of the elliptical orbit. The length of the string equals twice the semi-major axis and the distance between the pins is twice the distance, c = e a. When the pencil is at the semi-major axis, the right triangle formed by the axes and the string allows one to write: a2 = b2 + c2 So...**b = a ( 1 - e2)1/2** You can specify the shape of the ellipse that you wish to draw by its eccentricity, e or by its semi-minor axis, b. The size is determined by the semi-major axis.