Question

For a moon orbiting its planet, rp is the shortest distance between the moon and its planet andra is the longest distance between the moon and its planet. What is a moon's orbital eccentricity if rp is equal to 0.27ra?
A. 0.65

B. 0.27

C. 0.48

D. 0.57

D. IS THE CORRECT ANSWER!

Answer 1

Answer: D. 0.57

Explanation:

The formula to calculate the eccentricity $e$ of an ellipse is (assuming the moon's orbit in the shape of an ellipse):

$e=\frac{r_{a}-r_{p}}{r_{a}+r_{p}}$

Where:

$r_{a}$ is the apoapsis (the longest distance between the moon and its planet)

$r_{p}=0.27 r_{a}$ is the periapsis (the shortest distance between the moon and its planet)

Then:

$e=\frac{r_{a}-0.27 r_{a}}{r_{a}+0.27 r_{a}}$

$e=\frac{0.73 r_{a}}{1.27 r_{a}}$

$e=0.57$ This is the moon's orbital eccentricity