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

The orbital eccentricity \( e \) of an orbit can be determined using the closest (perigee or periapsis) and farthest (apogee or apoapsis) distances from the central body. The formula for eccentricity in terms of \( r_p \) (the closest distance) and \( r_a \) (the farthest distance) is:

\[
e = \frac{r_a - r_p}{r_a + r_p}
\]

In this case, we know that \( r_p = 0.27 r_a \). Let's denote \( r_a \) as \( r_a \) and \( r_p \) can be expressed in terms of \( r_a \):

\[
r_p = 0.27 r_a
\]

Now we can plug this into the formula for eccentricity:

1. Calculate \( r_a - r_p \):
\[
r_a - r_p = r_a - 0.27 r_a = 0.73 r_a
\]

2. Calculate \( r_a + r_p \):
\[
r_a + r_p = r_a + 0.27 r_a = 1.27 r_a
\]

3. Using these values in the eccentricity formula:
\[
e = \frac{0.73 r_a}{1.27 r_a}
\]
The \( r_a \) terms will cancel out:
\[
e = \frac{0.73}{1.27}
\]

4. Now, calculate that value:
\[
e \approx 0.5748
\]

This approximates to 0.57 when rounding.

So, the answer is **0.57**.