Kepler's Third Law



Applet shows the planets Mercury, Venus and Earth revolving round the Sun. The distances and times of motion are scaled correctly. You should be able to notice that while orbits of Venus and Earth are nearly circular (The eccentricities of their orbits are 0.0068 and 0.0167 respectively), the orbit of the innermost planet Mercury has noticeable ellipticity. ( It has an eccentricity of 0.2056 ). The semi major axes of the orbits of the three planets are 0.3871, 0.7233 and 1 A.U. respectively. Time the periods of revolution of each planet by watching its motion and find the ratio of square of time period and the cube of semi-major axis for each planet. You would find the ratio to be a constant. It may be convenient to express the time of revolution in terms of a year and the semi major axis in terms of A.U., so that this constant is 1 for the planet Earth. Obviously the constant would be 1 for the remaining two planets also.

Option 1 causes planets to stop after one revolution of mercury.
Option 2 causes planets to stop after one revolution of venus.
Option 3 causes planets to stop after one revolution of earth.
Option 4 lets them all revolve continously.

Planetary Data

Planet Period of
revolution
Period of
rotation
 Semi 
major 
  axis (AU) 
Eccentricity
 around sun 
(in Years)
around own
 axis
Mercury 0.241 58.6 days 0.387 0.206
Venus 0.615 243 days 0.723 0.007
Earth 1.00 23 h 56 m 4 s 1.00    0.017
Mars 1.88  24 h 37 m 23 s   1.524 0.093
Jupiter 11.86 9 h 50 m  5.203 0.048
Saturn 29.46 10 h 25 m 9.54  0.056
Uranus 84.01 710 h 50 m 19.18 0.04
Neptune 164.79 16 h 30.07 0.008
Pluto 248.43 6.4 days 39.44 0.249