Kepler's Laws of Planetary Motion

By Haley
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KEPLER’S FIRST LAW OF PLANETARY MOTION
The Law of Ellipses
The orbits of the planets are ellipses, with the Sun at end of the foci.
-The Sun is not at the center of the ellipse, but is instead at one focus.
-The planet then follows the ellipse in its orbit, which means that the Earth-Sun distance is constantly changing as the -planet goes around its orbit.
KEPLER’S SECOND LAW OF PLANETARY MOTION
The Equal Areas Law
The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.
-The line joining the Sun and planet sweeps out equal areas in equal times, so the planet moves faster when it is nearer the Sun.
-A planet executes elliptical motion with constantly changing angular speed as it moves about its orbit.
-The point of nearest approach of the planet to the Sun is called the perihelion; the point of greatest separation is called aphelion.
-The planet moves fastest when it is near perihelion and slowest when it is near aphelion.
-The motion this law describes also tells us that the average distance from a planet to the Sun is equal to the length of the semimajor axis, which is half the length of the major axis.

KEPLER’S THIRD LAW OF PLANETARY MOTION

The Harmonic Law

The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes:

P1² R1³
— = —
P2² R2³

P represents the period of revolution for a planet and R represents its semimajor axis.
P1 stands for the first planet and P2 is representative of the second planet.
R1 is for the first semimajor axis f

Another way to express Kepler's Third Law is the squares of the orbital periods of the planets around the Sun are proportional to the cubes of the orbital semimajors axes:
P² = a³
P is the orbital period in Earth years.
a is the length of the semimajor axis in Astronomical Units.


Work Cited:
Kepler's Laws of Planetary Motion Retrieved on Feb. 23, 2009.
Johannes Kepler: The Laws of Planetary Motion Retrieved on Feb. 23, 2009.