The radius of Mars’s orbit around the Sun is about four times the radius of Mercury’s orbit. If Mars takes 687 Earth days per revolution, estimate the length of one Mercury year.
Options

Question

The radius of Mars’s orbit around the Sun is about four times the radius of Mercury’s orbit. If Mars takes 687 Earth days per revolution, estimate the length of one Mercury year.

G1 Physics · Accepted Answer

Step 1: Kepler’s third law gives T² ∝ r³ for planets orbiting the same Sun. Step 2: Thus T(Mercury)/T(Mars) = (r(Mercury)/r(Mars))³ᐟ². Step 3: Since r(Mars) = 4r(Mercury), the ratio is (1/4)³ᐟ² = 1/8. Step 4: T(Mercury) = 687/8 = 85.875 Earth days. Step 5: Among the printed options, 88 Earth days is the nearest (and approximately Mercury’s known period). Final answer: 88 Earth days, Option A.