Question

The orbit of a spacecraft around the Sun has a perihelion distance of 0.1 AU and an aphelion distance of 0.4 AU. What is the semimajor axis of the spacecraft? What is its orbital period?

Answer 1

The major axis is the sum of the perihelion and aphelion distances so it is equal to

(0.1 + 0.4) = 0.5 AU

and the semi-major axis is half of the major axis,

= half of (0.1 + 0.4) = half of 0.5 = 0.25 AU.

From Kepler’s 3rd law, P2 = a3 = (0.25)3 = 0.015625 years.