Question

1. construct an explanation that supports the claim that perihelion and aphelion locations can be used to determine the length of a year (one orbit) for planets in our solar system.

Explanation:

Kepler's laws of planetary motion are key. The second law (equal - area law) and third law (harmonic law \(T^{2}\propto a^{3}\), where \(T\) is the orbital period and \(a\) is the semi - major axis of the elliptical orbit). The perihelion (\(r_{p}\)) and aphelion (\(r_{a}\)) distances are related to the semi - major axis \(a=\frac{r_{p} + r_{a}}{2}\). Once \(a\) is known from perihelion and aphelion data, using Kepler's third law, we can calculate the orbital period \(T\) (the length of a year for the planet).

Answer:

By using Kepler's laws, specifically the third law \(T^{2}\propto a^{3}\), and knowing that \(a=\frac{r_{p}+r_{a}}{2}\) (where \(r_{p}\) is perihelion and \(r_{a}\) is aphelion), the length of a planet's year (orbital period \(T\)) can be determined.