The eccentricity \( e \) of an orbit can be calculated using the formula:
\[ e = \frac{r_a - r_p}{r_a + r_p} \]
where \( r_a \) is the distance at aphelion and \( r_p \) is the distance at perihelion.
From the problem, we know:
\[ r_p = 0.45 r_a \]
Now, we can substitute \( r_p \) into the equation for the eccentricity:
- First, substitute \( r_p \):
\[ e = \frac{r_a - 0.45 r_a}{r_a + 0.45 r_a} \]
- Simplify the expression:
\[ e = \frac{r_a (1 - 0.45)}{r_a (1 + 0.45)} = \frac{0.55 r_a}{1.45 r_a} \]
- Notice that \( r_a \) cancels out:
\[ e = \frac{0.55}{1.45} \]
- Now, perform the division:
\[ e \approx 0.3793 \]
Rounding to two decimal places gives us \( e \approx 0.38 \).
Thus, the planet's orbital eccentricity is 0.38.