Question

Suppose an astronomer observes a binary star system where the stars are separated by 2.0 AU , and they have an orbital period of 7.0 years . Using Newton's version of Kepler's Third Law, find the combined mass of the stars.

Answer 1

Answer:

4.408 $\mathsf{M_{sun}}$

Explanation:

According to Kelper's Third Law, the equation of the combined mass (m₁+m₂) can be expressed as:

$(m_1 + m_2) = \dfrac{\text{(distance between stars)}^3}{\text{(orbital period)}^2}$

$\text{combined mass}(m_1+m_2)} =\dfrac{(6.0)^3}{(7)^2} \ M_{sun}$

$\text{combined mass}(m_1+m_2)} =\dfrac{216}{49} \ M_{sun}$

combined mass (m₁+m₂)  = 4.408 $\mathsf{M_{sun}}$