Question

For the moon O, with an orbital period of 1.77 days and an orbital radius of __ (fill in the blank), determine the mass of Jupiter.

Options:
A. 0.5 AU
B. 0.77 AU
C. 1.77 AU
D. 2.77 AU

Answer 1

To determine the mass of Jupiter based on the orbital radius and period of its moon, use Kepler's third law and set up a proportion. The correct answer is option D: 2.77 AU.

Step-by-step explanation:

To determine the mass of Jupiter based on the orbital radius and period of its moon, let's use Kepler's third law. According to Kepler's third law, the square of the period of a planet or moon is proportional to the cube of its orbital radius. In this case, the orbital period of the moon is 1.77 days, so square it to get 3.1329 days². We can set up a proportion using the known mass of Jupiter:

(Orbital Radius of Moon)³ / (Period of Moon)² = (Orbital Radius of Jupiter)³ / (Period of Jupiter)²

We can then solve for the orbital radius of Jupiter using the given options. Based on the options given, the correct answer would be Option D. 2.77 AU. Therefore, the mass of Jupiter can be determined by substituting the orbital radius of Jupiter (2.77 AU) into the equation and solving for the mass.