If a binary system has a period of 4 years and a separation of 5 AU, then the total mass is 7.8 solar masses.

Question

Quizplus · Accepted Answer

The total mass of a binary system can be calculated using the formula:$$M = \frac{4\pi^2 a^3}{G P^2}$$where:* M is the total mass of the system in solar masses* a is the semi-major axis of the orbit in AU* G is the gravitational constant* P is the period of the orbit in yearsPlugging in the given values, we get:$$M = \frac{4\pi^2 (5 AU)^3}{(6.674 × 10^{-11} m^3 kg^{-1} s^{-2})(4 yr)^2} = 7.8 M_{\odot}$$Therefore, the total mass of the binary system is 7.8 solar masses, which is consistent with the given statement.

If a Binary System Has a Period of 4 Years