Binary stars are pairs of stars that orbit each other. The period p of such a pair is the time, in years, required for a single orbit. The separation s between such a pair is measured in seconds of arc. The parallax angle a (also in seconds of arc) for any stellar object is the angle of its apparent movement as the Earth moves through one half of its orbit around the sun. Astronomers can calculate the total mass M of a binary system using: M = s^3 a^-3 p^-2. Here M is the number of solar masses. Assume the separation of a pair of stars is s = 18.1 seconds of arc, its parallax angle is a = 0.77 second of arc, and the period of the pair is 64.4 years. What would the mass be if the parallax angle were tripled but separation and period remained the same? Round your answer to the nearest hundredth. a) 0.12 solar masses b) 9.40 solar masses c) 0.01 solar masses d) 84.56 solar masses
Binary stars are pairs of stars that orbit each other. The period p of such a pair is the time, in years, required for a single orbit. The separation s between such a pair is measured in seconds of arc. The parallax angle a (also in seconds of arc) for any stellar object is the angle of its apparent movement as the Earth moves through one half of its orbit around the sun. Astronomers can calculate the total mass M of a binary system using: M = s^3 a^-3 p^-2. Here M is the number of solar masses. Assume the separation of a pair of stars is s = 18.1 seconds of arc, its parallax angle is
a = 0.77 second of arc, and the period of the pair is 64.4 years. What would the mass be if the parallax angle were tripled but separation and period remained the same? Round your answer to the nearest hundredth.
a) 0.12 solar masses
b) 9.40 solar masses
c) 0.01 solar masses
d) 84.56 solar masses
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