The stars Mizar and Alcor in the Big Dipper bucket represent an optically binary system (distance to Alcor 81.2 light years).

The stars Mizar and Alcor in the Big Dipper bucket represent an optically binary system (distance to Alcor 81.2 light years). Mitsar has the following characteristics: parallax 0.041 ”, radial velocity -9 km / s, proper motion 0.13 ” / year. Which star is closer? What is Mitsara’s full speed?

1) (calculating the distance to the Earth)
Let’s calculate the distance to Mitsar 1 / 0.041 = 24pc. This distance is 24 / 0.307 = 78 light years. That is, Mizar is closer to the Earth.
2) (calculation of transverse speed)
Let’s find the transverse speed of the star Mizar. The star passes through the year: 0.13 ” * 24pc = 3.12 AU. = 3.12 * 150000000km = 4.68 * 10 ^ 8km. This means that the transverse speed is vtr = s / t = 4.68 * 10 ^ 8 / (365 * 24 * 60 * 60) = 15 km / s.
3) (full speed calculation)
We find the full speed from the Pythagorean theorem V = sqrt (15 * 15 + 9 * 9) = 17.5 km / s

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