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You've just discovered a new X$-$ray binary, which we will call Hyp$-$X$1("$Hyp$"$ for hypothetical$).$ The system Hyp$-$X$1$ contains a bright, B$2$ mainsequence star orbiting an unseen companion. The separation of the stars is estimated to be $25$ million kilometers, and the orbital period of the visible star is $4$ days.

Part A

Use Newton's version of Kepler's third law to calculate the sum of the masses of the two stars in the system. $($Hint$.$ See Mathematical Insight Measuring Stellar Masses in the textbook$)$ Give your answer in kilograms.

Express your answer in kilograms to two significant figures.

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Hint $1.$ How to approach the problem

Use Kepler's third law, which relates the orbital period and the separation of the stars in a binary system to the sum of their masses. Convert the given values to appropriate units and rearrange the equation to solve for the sum of the masses. Pay attention to the units and constants involved to ensure accurate calculations.

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Part B

Calculate the sum of the masses of the two stars in the system in solar masses $(M_{\text{S}\text{u}\text{n}}=2\mathrm{.}0{10}^{30}kg).$

Express your answer as a multiple of Sun's mass to two significant figures.

View Available Hint$($s$)$

Use Kepler's third law, which relates the orbital period and the separation of the stars in a binary system to the sum of their masses. Convert the given values to appropriate units and rearrange the equation to solve for the sum of the masses. Pay attention to the units and constants involved to ensure accurate calculations.