The star S0-2 orbits Sagittarius A* (the galactic center of the Milky Way)with a period of 15.2 years and a semimajor axis of about 1000 AU.What does Kepler's third law suggest as the total amount of mass inside the orbital radius of S0-2?

Question

Quizplus · Accepted Answer

Kepler's third law states that for any orbiting body, the square of its orbital period is proportional to the cube of the semi-major axis of its orbit. Using this law, we can calculate the total mass enclosed within the orbit of S0-2 using the equation M = (4π²a³)/(G T²), where a is the semi-major axis, T is the orbital period, and G is the gravitational constant. Plugging in the values, we get M = (4π² x (1000 AU)³)/(G x (15.2 years)²) ≈ 4.3 x 10⁶ M, where M is the total mass enclosed within the orbit of S0-2. Therefore, the best choice is C.

The Star S0-2 Orbits Sagittarius A* (The Galactic Center of the Milky