How can orbital semimajor axis, eccentricity, and period be calculated if perihelion and aphelion are known?
Ra = a(1+e), Rp = a(1 -e)
The formulas for Aphelion and Perihelion are,
Ra = a ( 1 + e) and Rp = a ( 1 - e )
if you divide the above equations you can get the eccentricity of the orbit e,
Place the obtained value of e in one of the above given equations to find out the Semi-major axis.
Now that you have the Semi-Major axis you can use the following formula to find the Period.
T is in Earth Years
a is in AU ( 1 AU in case of Earth).