Question

The radius of Martian orbit around the Sun is about 1.5 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

• A. \( 225 \text{ Earth days} \)
• B. \( 172 \text{ Earth days} \)
• C. \( 124 \text{ Earth days} \)
• D. \( 88 \text{ Earth days} \)

Hint:

Apply Kepler's Third Law: \(T^2 \propto r^3\). Set up a ratio comparing Mars and Mercury: \( \left( \frac{T_{Me}}{T_M} \right)^2 = \left( \frac{r_{Me}}{r_M} \right)^3 \). Substitute the given values and solve for \(T_{Me}\). Remember that \(r_{Me}/r_M = 1/1.5 = 2/3\).