


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

According to Kepler’s Second Law, objects that are closer
to the sun orbit faster than objects that are far away. Therefore,
Halley’s comet must be traveling much faster when it is near the
Earth than when it is off near Pluto.
