# 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?

Feb 17, 2017

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:

$a \left(1 - e\right) = 2$

Te aphelion distance is:

$a \left(1 + e\right) = 86$

$2 a = 88$

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.