If you found an exoplanet whose mass was the same as Jupiter's,but the planet orbited its star with a period of 2 years and a semimajor axis of 1 AU,what would be the mass of its star? For reference,Jupiter has a semimajor axis of 5.4 AU and an orbital period of 12 years.

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semimajor axis of its orbit. In this case, the planet has the same mass as Jupiter, but its orbital period is 2 years and its semimajor axis is 1 AU. Jupiter's orbital period is 12 years and its semimajor axis is 5.4 AU. So, the ratio of the square of the orbital periods is (2/12)^2 = 1/36, and the ratio of the cubes of the semimajor axes is (1/5.4)^3 = 1/185. Therefore, the mass of the star must be 36/185 = 0.25 times the mass of the Sun.

If You Found an Exoplanet Whose Mass Was the Same