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?

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Answer 1 · 2018-02-01T10:13:42

$v_{t} = 180 k m$ $v_t=180km$ $s^{- 1}$ $s^(-1)$

$v \approx 316 k m$ $v~~316km$ $s^{- 1}$ $s^(-1)$

$v_{t}$ $v_t$ is given by the formula: $v_{t} = \frac{4.75 μ}{p}$ $v_t=(4.75mu)/p$ , where:

$v_{t} = \frac{4.75 \cdot 7.2}{0.19} = 180 k m$ $v_t=(4.75*7.2)/0.19=180km$ $s^{- 1}$ $s^(-1)$

$v = \sqrt{v_{t}^{2} + v_{r}^{2}}$ $v=sqrt(v_t""^2+v_r""^2)$

$v = \sqrt{180^{2} + 260^{2}}$ $color(white)(v)=sqrt(180^2+260^2)$

$v \approx 316 k m$ $color(white)(v)~~316km$ $s^{- 1}$ $s^(-1)$