How can orbital semimajor axis, eccentricity, and period be calculated if perihelion and aphelion are known?

The aphelion and perihelion formulas are,

Rp= a (one minus e) and Ra= a (one plus e)

By dividing the aforementioned equations, one can determine the eccentricity of orbit e.

To determine the semi-major axis, enter the obtained value of e into one of the equations above.

Using the following formula, you can determine the Period now that you know the Semi-Major axis.

T stands for Earth Years, and a for astronomical units (one AU for Earth).

The aphelion and perihelion distances can be averaged to determine the orbital semimajor axis. Eccentricity can be computed as e = (a - p) / (a + p), where 'a' is the semimajor axis and 'p' is the perihelion distance. Kepler's third law can be used to calculate the period (T) as T^2 = (4π^2 * a^3) / (G * M), where 'a' is the semimajor axis, 'G' is the gravitational constant, and 'M' is the mass of the central body.