Kepler's Laws of Planetary Motion

Planetary Motion

  Some Facts and Definitions:

 The plane of the Earth's orbit  around the Sun is called
  the Ecliptic. Indeed, all planets - with the exception of
  Mercury and Pluto - move within 3 deg of the ecliptic.
  In fact, all constellations of the zodiac also lie along the
  ecliptic.


Sagittarius (Nov. 22 - Dec. 21)

Viewed from the Earth, the ecliptic is also the path traced by the Sun
through the sky. The Earth's axis is tilted towards the ecliptic by 23.5
degrees. So the  planes of the ecliptic and the celestial equator are also
at an angle of 23.5 degrees to each other in the sky. Mercury's orbit has
a 7-degree tilt relative to the ecliptic, while Pluto's orbit is inclined a
full 17 degrees. The orbits of all the planets are ellipses and not circles,
as Copernicus assumed. However, with the exception of Pluto, all orbits
are almost circular. Pluto's orbit is so elliptical that it crosses the one of
Neptune.

 


  Kepler's Laws of Planetary Motion:


 

  1. The orbit of the planets are ellipses - NOT CIRCLES
       with the Sun located at one of the focus of the ellipse.


 

  2. A line from the planet to the sun sweeps over
       equal areas in equal intervals of time. Hence,
       the planet moves faster when closer to the Sun.

          

  3. A planet's orbital period squared is proportional
       to its average distance from the Sun cubed:
                  P2 (years) = a3 (AU)
 
Planet Distance to the Sun Period of the Orbit Distance3/ Period2
Mercury 0.3871 0.24084 1.00000
Venus 0.7233 0.61515 0.99998
Earth 1.0000 1.00000 1.00000
Mars 1.5237 1.88080 1.00003
Jupiter 5.2028 11.8670 1.00006
Saturn 9.5388 29.4610 0.99997
Uranus 19.180 84.0130 0.99966
Neptune 30.061 164.793 1.00031
Pluto 39.440 247.700 0.99990
Orbital Properties of Planets and Kepler's Third Law: