Answer: D. 0.57
Explanation:
The formula to calculate the eccentricity [tex]e[/tex] of an ellipse is (assuming the moon's orbit in the shape of an ellipse):
[tex]e=\frac{r_{a}-r_{p}}{r_{a}+r_{p}}[/tex]
Where:
[tex]r_{a}[/tex] is the apoapsis (the longest distance between the moon and its planet)
[tex]r_{p}=0.27 r_{a}[/tex] is the periapsis (the shortest distance between the moon and its planet)
Then:
[tex]e=\frac{r_{a}-0.27 r_{a}}{r_{a}+0.27 r_{a}}[/tex]
[tex]e=\frac{0.73 r_{a}}{1.27 r_{a}}[/tex]
[tex]e=0.57[/tex] This is the moon's orbital eccentricity
