# How is the semi-major axis found if perihelion and aphelion distance are known?

## For example, if an asteroid has a perihelion distance of 2.0 and an aphelion distance of 4.0 AU, what is the semi-major axis?

Given that the orbit is an ellipse with semi major axis a and eccentricity e, then the aphelion distance is $a \left(1 - e\right)$ and the aphelion distance is $a \left(1 + e\right)$. Adding the two together gives $2 a$.