B1 - geometric parallaxes

• uses the stellar position on the sky to measure distances

image: H Celga

• $\alpha$ is the parallactic angle, and $d$ the distance to the star
• using small angle approximation:

• $1$ parsec is when $\alpha =1^{"}$
• the closest star, proxima centauri is at $d=1.3\text{pc}$
• so, for most stars, $\alpha$ is much smaller, ie. $\alpha <1^{"}$
• this sets the limit at $\alpha =1^{"}$ from the ground without adaptive optics
• adaptive optics (AO) uses lens/mirror deformations to account for atmospheric turbulences
• with repeated measurements and AO, $\alpha \approx {0.01}^{"}⟹100\text{ pc}$ limit from the ground