Question

Two stars in a binary system orbit around their center of mass. The centers of the two stars are 6.39×10¹¹ m apart. The larger of the two stars has a mass of 3.67×10³⁰ kg, and its center is 2.15×10¹¹ m from the system's center of mass. What is the mass of the smaller star?

Answer 1

To determine the mass of the smaller star in the binary system, we can use Newton's reformulation of Kepler's third law. However, without the period of the stars' orbit, it is not possible to calculate the mass of the smaller star.

Step-by-step explanation:

To determine the mass of the smaller star in the binary system, we can use Newton's reformulation of Kepler's third law. According to Kepler's third law, the period (P) of the stars' orbit is related to the sum of their masses (M₁ + M₂) and the distance between them (D) as follows:

D³ = (M₁ + M₂) P²

In this case, we know that the centers of the stars are 6.39×10¹¹ m apart, the mass of the larger star (M₁) is 3.67×10³⁰ kg, and its center is 2.15×10¹¹ m from the system's center of mass. To find the mass of the smaller star (M₂), we can rearrange the equation:

M₂ = D³ / (P²) - M₁

Substituting the known values, we get:

M₂ = (6.39×10¹¹)³ / (P²) - 3.67×10³⁰

Unfortunately, the question does not provide the period of the stars' orbit, so it is not possible to calculate the mass of the smaller star without this information.