Question

A pair of starts orbit around one another in an elliptical orbit with a semi-major axis, "a", of 2 AU and with an orbital period, "P" of 1 year. What is the mass of the pair of stars?

Answer 1

The mass of the pair of stars can be determined using Newton's reformulation of Kepler's third law.

Step-by-step explanation:

The mass of the pair of stars can be determined using Newton's reformulation of Kepler's third law. The equation D³ = (M₁ + M₂)P² relates the semimajor axis (D) and the orbital period (P) to the sum of the masses of the two stars (M₁ and M₂). In this case, we are given the semimajor axis (a = 2 AU) and the orbital period (P = 1 year). Therefore, we can use the equation to solve for the mass of the pair of stars.

Plugging in the given values, we have:

2³ = (M₁ + M₂)1²

8 = M₁ + M₂

Since we have two unknowns, we can't determine the individual masses of the stars. However, we can find the sum of their masses, which is 8. Therefore, the mass of the pair of stars is 8 solar masses.