Question

The orbit of a spacecraft about the sun has a perihelion distance of 0.5 AU and an aphelion of 3.5 AU.? What is the spacecraft’s orbital period?

Answer 1

The period would be about 2.828 years.

Explanation:

The perihelion distance is `d_p=a(1-e)` and the aphelion distance is `d_a=a(1+e)`. Where `a` is the semi-major axis and `e`is the eccentricity of the orbit.

Adding the two equations gives `2a=d_p+d_a`. So the semi-major axis of the space craft is `2a=0.5+3.5`. Hence `a=2`AU.

Kepler's third law relates the semi-major axis to the orbital period `T^2=a^3`. For the spacecraft `T^2=8`. This gives an orbital period `T=2.828` years.