If the Sun were orbited by a star of 1.8 solar masses at Jupiter's distance of 5.2 AU (or,more precisely,the Sun and the other star were orbiting each other 5.2 AU apart),what would be the orbital period of the system? (You might want to compare your answer with the actual orbital period of Jupiter,11.9 years.)

Question

Quizplus · Accepted Answer

The orbital period can be calculated using Kepler's third law. For a binary system, the formula is P^2 = a^3 / (M1 + M2), where P is the period in years, a is the semi-major axis in AU, and M1 and M2 are the masses of the two bodies in solar masses. Here, a = 5.2 AU, M1 = 1 solar mass, and M2 = 1.8 solar masses. Solving gives P ≈ 7.1 years.

If the Sun Were Orbited by a Star of 1