Final answer:
The semi-major axis of a comet's orbit, with a perihelion of 0.4 au and an aphelion of 7.4 au, is calculated by averaging these two distances. It is found to be 3.9 astronomical units (au).
Step-by-step explanation:
The student asks for the semi-major axis of a comet's elliptical orbit with a given perihelion and aphelion distance. To determine the semi-major axis of the comet's orbit, we use the fact that the semi-major axis is one-half the sum of the aphelion and perihelion distances. In this case, the perihelion distance is 0.4 astronomical units (au) and the aphelion distance is 7.4 au.
The formula to calculate the semi-major axis (a) is:
a = (perihelion + aphelion) / 2
Substituting the given values:
a = (0.4 au + 7.4 au) / 2
a = (7.8 au) / 2
a = 3.9 au
Therefore, the semi-major axis of the comet's orbit is 3.9 au.