I am asked to find the parallax of a star "Spica" as observed at $30.1$ $AU$ from the Sun.

I want to use the small-angle formula: $\alpha=\frac{206265*D}{d}$ where $D$ is the baseline, $d$ the distance to the star and $\alpha$ the angular size in arcsec. I feel like this problem cannot be solved with the given information because we do not know $D$.

The study book answer is $\alpha=0.36''$. I know from another exercise that if Spica is at an angular distance $\alpha=0.012''$, then the distance to Spica is $d=271.36$ $ly$. Could that help?


Parallax is calculated as, in arcseconds, the reciprocal of the distance in parsecs. That's it; those are the only things you need to know.

The small-angle approximation will only help you find the distance given the angular size of the object, not the parallax. The two are quite different quantities; don't confuse them.


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