Kepler's Laws
Kepler's Laws
 Each planet moves in an elliptical orbit with the sun as its focus.
 The ray from the sun to the planet sweeps out equal areas in equal
times.
 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 10^{9} 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 10^{9}) =
+
= 0 .528d
1 +
0.248
1  0.248
Hence
d = 2.2 x 10^{10
}To find the equation of the ellipse we use the formula
ed
r =
1 + ecosq
or
5.5 x 10^{9}
r =
1 +
.248cosq
^{
}Hence the closest distance that Pluto gets to the sun is 4.44
x 10^{9}
km. and the farthest distance it gets is 7.32 x 10^{9}
km.
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