This question has to do with binary star systems, where 'i' is the angle of inclination of the system. Calculate the mean expectation value of the factor sin3i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if sin3i has its mean value. Hint: In spherical coordinates, (theta, phi), integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by sin3(theta). v1=100 km/s v2=200 km/s Orbital period=2 days M1=5.74e33 g M2=2.87e33 g

This question has to do with binary star systems, where 'i' is the angle of inclination of the system. Calculate the mean expectation value of the factor sin3i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if sin3i has its mean value. Hint: In spherical coordinates, (theta, phi), integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by sin3(theta). v1=100 km/s v2=200 km/s Orbital period=2 days M1=5.74e33 g M2=2.87e33 g

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Question

This question has to do with binary star systems, where 'i' is the angle of inclination of the system.

Calculate the mean expectation value of the factor sin³i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if sin³i has its mean value.

Hint: In spherical coordinates, (theta, phi), integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by sin³(theta).

v₁=100 km/s

v₂=200 km/s

Orbital period=2 days

M₁=5.74e33 g

M₂=2.87e33 g

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