Kepler's+Laws+of+Planetary+Motion

Kepler's Laws of Planetary Motion
By Haley http://www.redorbit.com/modules/reflib/article_images/8_d7f84ec36dbfda23aff1a01e00a4b5e6.jpg = =

=
 =====

=
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. =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">-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. <span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif';"> =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif';">KEPLER’S SECOND LAW OF PLANETARY MOTION =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif';"> <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">//The Equal Areas Law// =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> **<span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse. **<span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">-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. =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">-A planet executes elliptical motion with constantly changing angular speed as it moves about its orbit. =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">-The point of nearest approach of the planet to the Sun is called the perihelion; the point of greatest separation is called aphelion. =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">-The planet moves fastest when it is near perihelion and slowest when it is near aphelion. =====

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">- <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">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. ===== <span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif';"> ====<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif';">KEPLER’S THIRD LAW OF PLANETARY MOTION ==== ====<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif';"> <span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';">//The Harmonic Law// ==== ====<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 12pt; line-height: 115%; font-family: 'Arial','sans-serif';"> 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 Motio]n Retrieved on Feb. 23, 2009.

<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;">

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"> ======

=
<span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"><span style="font-size: 14pt; line-height: 115%; font-family: 'Arial','sans-serif'; mso-bidi-font-weight: bold;"> =====