Astronomers observe two stars, A and B. a. Star A has a parallax of 0.04 arcseco

Question

Astronomers observe two stars, A and B.
a. Star A has a parallax of 0.04 arcseconds. Calculate the distance to star A. [1 point]

b. Star B has a spectrum that is identical to that of star A, indicating that the two are the same type of star with the same luminosity. However, the brightness of star B as observed from the Earth is only 0.0001 (10-4) times that of star A. Calculate the distance to star B. [3 points; note: even if your value of the distance to star A is incorrect, you will get full credit for this part if you otherwise do the math correctly.]

Explanation / Answer

a. given

parallax of 1st star = phi = 0.04 arc sec

distance d= 1/phi = 25 parsecs = 7.714*10^17 m

b. distance to star B = d2

form brightness ratio

0.0001 = (d2/d)^2

hence

d2 = 0.25 parsecs = 7.714*10^15 m

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