How do you calculate the distances of the perihelion and aphelion if you know that the period is 76 years and the semi major axis is 17.94 AU?

Dec 14, 2015

You can't as you are missing either the semi-minor axis or eccentricity.

Explanation:

Kepler's 3rd law relates the period to the semi major axis as ${T}^{2} = {a}^{3}$. Now given the figures ${75}^{2}$ does equal ${17.94}^{3}$. In fact we only require one of these values as the other can be calculated from it.

To calculate perihelion and aphelion the eccentricity of the orbit is required. The eccentricity can also be calculated from the semi-major and the semi-minor axes.