How does one calculate the parallax of stars?

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Answer 1 · 2017-01-27T03:42:35

See explanation

If S is a star observed from E, at an angle #alpha# to the

horizontal and the same star is observed again, after half a year,

at #angle beta#,

the parallax #angle p =|beta-alpha|#.

The distance of the star is now approximated as

#1/p AU=1/(63242 p)# light years, where p is in radian measure.

Note that the distance across, between the two positions of E, is

solar-system/the-earth)'s orbit = #2 AU = 2 xx 149387871# km and

#ES xx sin (p/2) = 1 AU#, nearly, and .

as p is small,

#sin (p/2) = p/2#, nearly, and so,

ES = 1/p AU, nearly.

Vice versa, we can predict this p for the half year interval, if the

distance of the star is already known.

For example, the nearest S Proxima Centauri is at a distance ES =

4.246 ly, and this gives

Half year parallax #p = 1/(4.246 xx 53242)#

#=0.0136# radian

#=0.077945^o#

# = 4' 40.6''# .