# A star has a parallax of .19 arc seconds. The stars has a proper motion of 7.2 arc seconds per years and a radial velocity of +260 km/s. How do you find the Tangential Velocity and the total velocity of the star?

Feb 1, 2018

${v}_{t} = 180 k m$ ${s}^{- 1}$

$v \approx 316 k m$ ${s}^{- 1}$

#### Explanation:

${v}_{t}$ is given by the formula: ${v}_{t} = \frac{4.75 \mu}{p}$, where:

• $\mu$ = proper motion (arc seconds per year)
• $p$ = parallax (arc seconds)

${v}_{t} = \frac{4.75 \cdot 7.2}{0.19} = 180 k m$ ${s}^{- 1}$

$v = \sqrt{{v}_{t} {\text{^2+v_r}}^{2}}$

$\textcolor{w h i t e}{v} = \sqrt{{180}^{2} + {260}^{2}}$

$\textcolor{w h i t e}{v} \approx 316 k m$ ${s}^{- 1}$