If a comet has a perihelion of $1.4 \mathrm{AU}$ and an aphelion of $5.1 \mathrm{AU}$, what is the semi-major axis of the comet's orbit? Express the answer using two significant figures.
axis:
What is the period of the comet's orbit around the Sun?
period:

Step 1 ：Given that the perihelion distance of the comet is \(1.4 \, \text{AU}\) and the aphelion distance is \(5.1 \, \text{AU}\).

Step 2 ：The semi-major axis of an ellipse, which is the shape of a comet's orbit, is the average of the distance at perihelion (closest approach to the sun) and aphelion (farthest distance from the sun).

Step 3 ：We can calculate the semi-major axis by adding the perihelion and aphelion distances and dividing by 2.

Step 4 ：\(\text{semi-major axis} = \frac{\text{perihelion} + \text{aphelion}}{2}\)

Step 5 ：Substituting the given values, we get \(\text{semi-major axis} = \frac{1.4 + 5.1}{2}\)

Step 6 ：Calculating the above expression, we find that the semi-major axis of the comet's orbit is \(\boxed{3.25 \, \text{AU}}\).