Question

A comet's perihelion distance is 2 AU and its aphelion distance is 86 AU? What is the comet's semimajor axis? What is its orbital period?

Answer 1

The comet's semimajor axis is 44 AU and its period is 291.86 years.

Explanation:

The comet follows an elliptical orbit according to Kepler's laws. Given the semi-major axis distance `a` and the eccentricity `e`. The perihelion distance is:

`a(1-e)=2`

Te aphelion distance is:

`a(1+e)=86`

Adding the equations gives:

`2a=88`

Dividing by 2 gives the semi-major axis distance `a=44`AU.

Kepler's third law relates the period `T` in years to the semi-major axis `a` in AU:

`T^2=a^3=44^3`

Cubing and taking the square root gives `T=291.86` years.