Question

# Suppose that two stars in a binary star system are separated by a distance of 70...

Suppose that two stars in a binary star system are separated by a distance of 70 million kilometers and are located at a distance of 200 light-years from Earth.

What is the angular separation of the two stars? Give your answer in degrees, then give your answer in arcseconds.

Express your answer using two significant figures.

Solution:

Suppose that two stars in a binary star system are separated by a distance of 70 million kilometers and are located at a distance of 200 light-years from Earth.

Distance between the stars = 70 x 10^6 km = d

Distance from Earth = R = 200 Ly = 200 * (9.46 x 10^12) km = 1892 x10^12 km

= 1.89 x 10^15 km

Angular separation in degrees = d / 2 pi R * 360

= [( 70 x 10^6) / 2 pi (1.89 x10^15) ] * 360

= 2.1 x10^-6 degrees

b) 2.1 x10^-6 x 60 x 60 arc seconds = 0.0076 arc seconds

= 7.6 x 10^-3 arc seconds

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