The parallax of a star in the small angle approximation is: [planet-host star orbit radius]/[other star distance so it is proportional to the size of a planet's orbit. imagine an intelligent and curious civilization has evolved on the planet trappist-1e, an earth-sized, temperate, and possibly habitable world orbiting a late m-type star of mass o. o8 mo at a distance of 12 pc from the sun. the orbital radius is only 0.028 au. these "trappistees" want to figure out how far the stars are using the parallax method. (a) [5 pts] from the ground, astrometric precision is often limited by the typical "seeing", or blur, of the atmosphere, which on a good night is o.50". what is the most distant star (in pc) for which we can measure a parallax with this resolution? what is the most distant star the trappistees can measure with this resolution (b) [5 pts] the european gaia spacecraft is capable of measuring parallaxes as small as o. ooo30" (30 microarcseconds). what is the most distant star (in pc) for which we can measure a parallax using this facility? what is the most distant star for which the trappistees can measure a parallax with their own gaia?