To find the orbital eccentricity \( e \) of a moon given the shortest distance (periapsis, \( r_p \)) and the longest distance (apoapsis, \( r_a \)), you can use the following formula for eccentricity:
\[ e = \frac{r_a - r_p}{r_a + r_p} \]
From the problem, you are given that \( r_p = 0.27 r_a \).
First, let's express \( r_p \) in terms of \( r_a \):
\[ r_p = 0.27 r_a \]
Now substitute \( r_p \) into the eccentricity formula:
\[ e = \frac{r_a - 0.27 r_a}{r_a + 0.27 r_a} \]
This simplifies to:
\[ e = \frac{r_a(1 - 0.27)}{r_a(1 + 0.27)} = \frac{1 - 0.27}{1 + 0.27} = \frac{0.73}{1.27} \]
Now, calculate the value:
\[ e = \frac{0.73}{1.27} \approx 0.5748016 \]
This rounds to approximately \( 0.57 \).
Thus, the moon's orbital eccentricity is approximately 0.57.