Kepler’s Laws
After poring over the astronomical observations of his mentor Tycho Brahe (1546–1601),
Johannes Kepler (1571–1630) determined three laws of planetary motion. These laws are of great
significance, because they formed the background to Newton’s thinking about planetary
interaction and the attraction between masses. In fact, Newton later showed that Kepler’s Laws
could be derived mathematically from his own Law of Universal Gravitation and laws of motion,
providing evidence in favor of Newton’s new theories. Another point in favor of their significance
is that any one of them may appear on SAT II Physics.
Kepler’s First Law states that the path of each planet around the sun is an ellipse with the sun at
one focus.
Kepler’s Second Law relates a planet’s speed to its distance from the sun. Because the planets’
orbits are elliptical, the distance from the sun varies. The Second Law states that if a line is drawn
from the sun to the orbiting planet, then the area swept out by this line in a given time interval is
constant. This means that when the planet is farthest from the sun it moves much more slowly than
when it is closest to the sun.
It is important to remember that although Kepler formulated this law in reference to planets
moving around the sun, it also holds true for astronomical objects, like comets, that also travel in
elliptical orbits around the sun.
Kepler’s Third Law states that given the period, T, and semimajor axis, a, of a planet’s elliptical
orbit, the ratio T^2 /a^3 is the same for every planet. The semimajor axis is the longer one, along
which the two foci are located.
EXAMPLE