To determine the orbital period of a planet around the Sun given its semi-major axis, we can use Kepler's Third Law of Planetary Motion. The law states that the square of the orbital period (P) of a planet is proportional to the cube of the semi-major axis (a) of its orbit:
\[ P^2 = a^3 \]
where:
- \( P \) is the period in Earth years,
- \( a \) is the semi-major axis in astronomical units (AU).
Given that the semi-major axis \( a \) is 2.3 AU, we can plug this value into the equation:
\[ P^2 = (2.3)^3 \]
Calculating \( (2.3)^3 \):
\[ (2.3)^3 = 12.167 \]
Now, we take the square root of both sides to find \( P \):
\[ P = \sqrt{12.167} \approx 3.48 \text{ years} \]
So the closest answer from your options is \( \text{3.49 years} \).