What is the total mass of a binary star system with P = 20 yr and a = 10 AU

Question

Quizplus · Accepted Answer

Using Kepler's Third Law, we can calculate the total mass of the binary star system. We have P = 20 years (the period of the system) and a = 10 AU (the semi-major axis of the orbit).

First, we need to convert the period to seconds:
P = 20 years = 20 x 365.25 days x 24 hours x 60 minutes x 60 seconds = 630720000 seconds

Next, we can use Kepler's Third Law:
M = 4π²a³/GP²

where M is the total mass of the system, a is the semi-major axis, G is the gravitational constant, and P is the period. Plugging in the numbers, we get:

M = 4π²(10 AU)³/(6.6743 x 10^-11 m³/kg/s²)(630720000 seconds)² 
M ≈ 2.5 solar masses

Therefore, the answer is B) 2.5 solar masses.

What Is the Total Mass of a Binary Star System