Kepler's Laws

Kepler's Laws
  1. Each planet moves in an elliptical orbit with the sun as its focus.
  2. The ray from the sun to the planet sweeps out equal areas in equal times.
  3. The square of the period of the orbit is proportional to the cube of the mean distance between the planet and the sun.



Example    Pluto


For Pluto we have 

        a  =  5.9 x 109 km 

and 

        e  =  0.248 

where 2a is the length of the major axis.  We have

                                       0.248 d                  0.248 d
        2 (5.9 x 109)  =                           +                               = 0 .528d
                                      1 + 0.248               1 - 0.248

Hence

        d = 2.2 x 1010

To find the equation of the ellipse we use the formula 

                       ed
        r  =                              
                  1 + ecosq

or

                     5.5 x 109 
        r  =                                   
                  1 + .248cosq



Hence the closest distance that Pluto gets to the sun is 4.44 x 109 km. and the farthest distance it gets is 7.32 x 109 km.  

  

 

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