# Kepler's Laws

# First Law

**The planets (and nearly all other objects in the solar system) move in paths, which have the form of ellipses. The sun stands in one of the two focuses.***Italic text*
The defining characteristic of an ellipse is

x+y=contant

Note: Thus a circle is a special case of an ellipse. The eccentricity of an ellipse

After Phythagoras is valid

e2 + b2 = d2

In addition, it is valid

A = D (because of x + y = (A + e) + (A e))

and thus

e2 + b2 = a2 thus

e = \ {a^2 sqrt - b^2} called the accentricity \ varepsilon = \ frac {e} {A}

# A1. Aphelion and Perihel

Show that the average value from the largest and the smallest distance of a planet of the sun (aphelion, Perihel) is equal to the large shaft section of the course.

# A2. Comet Path

The comet Encke has a distance of 0,339 and/or 4,094 astronomical units (AE) of the sun in the Perihel and aphelion of its course.

- a) Compute the large and the small shaft section as well as the numeric eccentricity of the course!
- b) Manufacture a design true to scale of the ellipse path! (1AE corresponds to 2 cm)

# A3. Mars Path

Johannes Kepler counted 8 years, in order to find out that Mars describes not a circular path, but an ellipse around the sun. Its results were astonishing exactly, although the numeric eccentricity of the course only \ varepsilon = 0,093 amounts to.

- a) Compute the small shaft section, if the large shaft section A = 1.524 amounts to AE, and the difference of the shaft sections in %!
- b) Manufacture a design true to scale of the coordinate system!
- c) Which largest and/or smallest distance of the sun can reach Mars?