The radial velocity of Aldebaran (a Taurus) is 54 km / s, and its own motion is 0.2² / year. Determine the space velocity

The radial velocity of Aldebaran (a Taurus) is 54 km / s, and its own motion is 0.2² / year. Determine the space velocity of the star if its parallax is 0.05².

By definition, at a distance of 1 parsec, the radius of the earth’s orbit is seen at an angle of 1 ″.
The distance to the star is 1 / 0.05 = 20 pc, therefore, its own motion in linear units is per year (150 million km) · (20 pc) · (0.2 ″ / year), i.e. about 600 million km / year ≈ 20 km / s. This velocity component is directed perpendicular to the star’s radial velocity. Adding the components according to vector laws (using the Pythagorean theorem), we get that the total speed of the star is 58 km / s.

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