Kepler’s Laws

and on Tycho’s death, inherited both his job and his vast store of astronomical
observations. From Tycho’s data Kepler distilled three great empirical laws:
1. The Law of Orbits: The planets move in elliptical orbits, with the Sun situated
at one focus.
Figure 2.1 displays the geometry of a planetary ellipse. Note the dimensions a
and b of the semimajor and semiminor axes, and the Sun located at one focus.
2. The Law of Equal Areas: A line joining any planet to the Sun sweeps out
equal areas in equal times.
Figure 2.2 illustrates this law, showing the radial lines joining a planet with the
Sun, and areas swept out by the lines in equal times with the planet traveling
different parts of its elliptical orbit. The two areas are equal, and the planet
travels faster when it is closer to the Sun.
3. The Law of Periods: The square of the period of any planet about the Sun is
proportional to the cube of the length of the semimajor axis.
A planet’s period is the time it requires to travel its entire orbit—365 days for
Earth. Stated as a proportionality, with P representing the period and a the length
of the semimajor axis, this law asserts that
P^2 directly proportional to a3.