Defining a Parsec
The parsec is another convenient unit of distance used in astronomy created as a result of the widespread use of parallax to measure distances. 1 parsec is defined as the distance from the Sun to a star if the maximum observed parallax shift of the star is 2’’. Represented visually: the length of BC in Fig. 3 is equal to 1 parsec if ∠ p = 1 arcsecond 10 and AB equals to 1 AU.
Thus, the value of a parsec in kilometres is:
which approximates to 3.7 light years. A long time ago, the Millennium Falcon made it through the Kessel Run using a hyperspace route which is 12 parsecs long. With very small angles around the range of that most stellar parallax fall in, the tangent of x is equivalent to x itself, represented visually on graph to the right:
With very small angles, there is no discernible difference between the tangent of x and x itself
The graph allows an approximation of the previous
Fig. 4: Red line: y = tan x, blue line: y = x
equation to be made, the distance to a star in parsecs
is therefore simply the reciprocal of
its parallax.
Solar Parallax
Solar parallax was first calculated by Aristarchus of Samos. Aristarchus believed that during a half moon, the moon forms a right triangle with the Sun and Earth (as shown in Fig. 6), and measured the Moon-Earth- Sun angle (φ in Fig. 6) to be approximately 87 degrees. He concluded the distance from Earth to Sun is slightly less than 20 times the distance from Earth to moon (calculated with tan(87)). Due to observation errors, this value is incorrect. The actual angle is 89° 50' (89.833°), meaning the distance from Earth to the Sun is actually more than 300 times (tan(89° 50')) longer than the distance from Earth to the moon. Although his data is wrong, they were based on the correct geometrical principles of parallax.
10 1 degree = 3600 arcseconds, 360 degrees in a complete circle so 1 degree corresponds to 60 arcminutes, 1 arcminute corresponds to 60 arcseconds
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