Question

Use the ratio form of Kepler’s third law, StartFraction T Subscript A Baseline over T Subscript B Baseline EndFraction Superscript 2 Baseline. = , and the data provided to determine the time it takes Mars to orbit the Sun. Round your answer to the nearest tenth

Answer 1

Using Kepler's Third Law ratio form, the time Mars takes to orbit the Sun is known to be approximately 1.88 Earth years, based on its semimajor axis of 1.52 AU.

Step-by-step explanation:

The student is asking about Kepler's Third Law, which describes the relationship between the orbital period of a planet and its distance from the Sun. To find the time Mars takes to orbit the Sun, we use the law in its ratio form: (TA / TB)2 = rA3 / rB3, where T represents the orbital period and r represents the orbital radius or semimajor axis. Since we know from the given information that Mars' orbital period is 1.88 Earth years, we can state that TMars = 1.88 years, and therefore, Mars completes its orbit around the Sun in approximately 1.88 Earth years. The semimajor axis for Mars is then calculated to be about 1.52 astronomical units (AU).