Binary Star System Homework: M1=1.24, M2=3.04, Epsilon=0.691

[jderm]

Homework Statement

Consider a binary star system in
which the two stars have masses M1 = 1.24 solar masses and
M2 = 3.04 solar masses. The period of star 1 is 142 yr. The
eccentricity of star 1 is $$\epsilon$$ = 0.691. Use G = 6.67259 × 10−11
Nm2/kg2, take the astronomical unit to be 1.4959787069e11
m, and take the solar mass to be 1.9891e30 kg.

Homework Equations

T²=4*pi²*a³ / G*(m1+m2)

The Attempt at a Solution

solving for the semimajor axis for m1 seems like the logical step from here. Is there a reason this equation wouldn't work?
i get 6.611e12 m or 44.192 solar lengths

 

[mark726]

.

Hello there,

Thank you for your post. Your approach to solve for the semimajor axis is correct. The equation you have used is the Kepler's third law, which relates the period of an orbit to the semimajor axis and the masses of the objects involved. In this case, you have correctly substituted the given values for the period and the masses of the stars.

The semimajor axis you have calculated, 6.611e12 m or 44.192 solar lengths, is indeed the correct value. This means that the average distance between the two stars in the binary system is about 6.611 trillion meters, or 44.192 times the distance between the Earth and the Sun.

I hope this helps. Keep up the good work in your scientific endeavors!