Concept explainers
The circumferences of the two orbits, the separation between the stars, the total mass of the system and the individual mass of each star.
Answer to Problem 18P
The circumferences of the two orbits are
Explanation of Solution
Write the equation for the circumference of first orbit.
Here,
Write the equation for the circumference of second orbit.
Here,
Write the expression for the separation between two stars.
Here,
Write the expression for the angular speed.
Rewrite the expression for the separation between the stars.
Write the expression for the distance of first star by using equation (IV).
Here,
Write the expression for the distance of second star by using equation (IV).
Here,
Write the equation for the total mass of a visual binary system by using (V).
Here,
Write the expression for the total mass of the system.
Here,
Write the expression for the center of mass by using equation (VI) and (VII).
Here,
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Solving equation (XI) and (XII), value of the individual masses of star.
Thus, the circumferences of the two orbits are
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Chapter 9 Solutions
Bundle: Foundations Of Astronomy, Loose-leaf Version, 14th + Webassign, Printed Access Card, Single-term
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