Kepler’s Laws
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/a3 is the same for every planet. The semimajor axis is the longer one, along which the two foci are located.
Example
Every 76 years, Halley’s comet passes quite close by the Earth. At the most distant point in its orbit, it is much farther from the sun even than Pluto. Is the comet moving faster when it is closer to Earth or closer to Pluto?
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.
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