Parallax is an effective way to measure distance to nearby stars because it relies on geometry. When astronomers use parallax, they are measuring how a star appears to move against its background. The unit parsec refers to the distance that an object would have to be from the Earth to have a parallax angle of \\\\( 1 \\\\) arc-second.In the figure above, the angle, \\\\( \\alpha \\\\) is the angle that is measured by the Earth on opposite sides of the sun. The parallax angle, \\\\( p \\\\) is half of this angle.\\\\( p=\\frac{1}{2}\\alpha\\\\)If we defines \\\\( p \\\\) to be \\\\( 1 \\\\) arc-second, then our object will be \\\\( 1 \\\\) parsec away. Since light from the sun takes \\\\( 8 \\\\) minutes and \\\\( 20 \\\\) seconds to reach the Earth,. we know that;\\\\( 1 AU=8.33 \\\\) light minutesWe can use this information to convert our parsec into light years with the tangent formula.\\\\( tan(p)=\\frac{8.33 \\quad light \\quad minutes}{d}\\\\)Or;\\\\( d=\\frac{8.33 \\quad light\\quad minutes}{tan(p)}\\\\)If we convert \\\\( p \\\\) to radians, than we can use the small angle approximation, \\\\( tan(\ heta)\\approx \ heta\\\\).\\\\( 1 arc-second=4.85 \ imes 10^{-6} \\\\) radiansPlugging this in for \\\\( p \\\\) and using the small angle approximation;\\\\( d=\\frac{8.33 \\quad light\\quad minutes}{4.85\ imes 10^{-6}}\\\\)=\\\\( 1.72 \ imes 10^6 \\\\) light-minutes=\\\\( 3.26 \\\\) light years