# 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