This requires knowing a value for the perihelion, but when you have it you can simply plug it and the semi-major axis a into the equation given. For example if the perihelion was half the distance of the semi-major axis:

e = 1 - 0.5/1 = 0.5

But if the perihelion was the same as the semi-major axis (no point on the orbit is closer than any other):

e = 1 - 1/1 = 0 (no eccentricity, perfect circle).

Mar 6th, 2015

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