Question

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

Answer 1

There is not enough information to calculate the apses distances.

Explanation:

The period `P` and semi-major axis `a` are not sufficient to calculate the apses distances as the eccentricity of the orbit can't be determined.

If the eccentricity `e` is known then the perihelion distance is `a(1-e)` and the aphelion distance is `a(1+e)`.

In fact the period and semi-major axis can be calculated from each other using Kepler's third law. For our solar system if `P` is in years and `a` is in AU then `P^2=a^3`.