How is the distance between stars and the earth calculated?

1 Answer
Mar 18, 2016


Stellar parallax is the apparent angular displacement of a star when observed from two sufficiently-spaced known locations

A convenient choice is the same observatory, with time spacing that is (sufficiently large integer) N days.

If N is the exact number of 24-hour days and #alpha# is the parallax angle, the distance of the star is
#sin(Ntheta/2)/sin(alpha/2)# AU,
where #theta=360/356.256363# deg = 0.985609113 deg.

For conversion to light years (ly), use 1 AU = #1/62900#ly, nearly.

The arc of the Earth's orbit for N days subtends N#theta# deg at the Sun.

Sample Data: N = 7, #alpha# = 0.003" = 8.333 E-07 deg.

The approximation to the distance of the star
= #sin(7X0.9856)/sin(8.333 E-07)#AU

= 8.259 E+06 AU

= 131.3 light years.

(It is assumed that the precision in the Radio Telescope for parallax is as good as 0.001".)