9.1. Kepler’s Laws http://www.ck12.org
9.1 Kepler’s Laws
Objectives
The student will:
- Understand Kepler’s Laws.
- Use Kepler’s Third Law to solve problems.
Vocabulary
- epicycle
- geocentric:A model of the planets in which Earth is at the center of all other planets.
- heliocentric:The model of the planets in which all planets revolve around the Sun. This is the model that
was eventually proven correct. - period
Johannes Kepler (1571 - 1630) (Figure9.1) was a German mathematician and astronomer. He read Nicholas
Copernicus’sDe Revolutions, which proposed that both Earth and the other planets revolved around the Sun. The
problem was that up until that point, there was no proof of Copernicus’s ideas. In fact, thegeocentricmodel, which
placed the Earth at the center of the rest of the planets, gave better predictions. Copernicus had intriguing ideas, but
he assumed that the orbits were perfect circles. It was up to Kepler, a superior mathematician as well as a profound
thinker, to put his idea on a firmer basis.
Kepler’s life story is one of triumph over adversity. He was born into a time when religious wars between Catholics
and Protestants ravaged central Europe. Kepler held the very modern view that no one should be persecuted for their
religious beliefs.
In 1600, Kepler met Tycho Brahe (1546 - 1601) (Figure9.2), arguably the greatest naked-eye astronomer who ever
lived (the telescope had not yet been invented). Tycho had accumulated a wealth of planetary data over a period of
twenty years of painstaking observations. In particular, the data he collected on Mars was the most extensive ever
compiled. Through a rather roundabout series of events, Kepler acquired Tycho’s Mars data, and eventually, after
Tycho’s death, acquired (by theft) the remainder of the data. Both Tycho and Kepler were fascinating historical
figures, and certainly deserve more time than this lesson can afford.
Over the next twenty years Kepler used that data to fully establish theheliocentricmodel and overthrow the
geocentric model of Ptolemy. Kepler’s work established what has come to be known as Kepler’s Three Laws of
Planetary Motion. We state them below.
- The orbital paths of the planets about the sun are ellipses with the sun at one focus. A circle is the set of