🤖The problem
Why is it not widely used and what are some flaws?
First of all, there are many theories/formulas/practices to calculate the distance between celestial bodies but using trigonometry to calculate it is the most common practice.
Parallax angles of less than 0.01 arcsec are very difficult to measure from Earth because of the effects of the Earth's atmosphere.
Earth based telescopes are limited to measure the distances to stars about 1/0.01 or 100 parsecs away. Space based telescopes can get accuracy to 0.001, which has increased the number of stars whose distance could be measured with this method.
There is no single solution to this method, almost every approach to this problem has differed accuracy.
The General form of this equation becomes a little bit clustered since there are many different parameters in trigonometry approach alone.
How it's done
According to some case-studies, the star has to be observed from two points of Earth's orbit ( from Jan and Jul ), after observing from different points, the difference noticed is later used to calculate the distance. Further the observed point, lesser the parallax angle.
The relationship between the parallax angle p (measured in seconds of arc) and the distance d is given by d = 206,264 AU/p; for a parallax triangle with p = 1, the distance to the star would correspond to 206,264 AU. By convention, astronomers have chosen to define a unit of distance, the parsec, equivalent to 206,264 AU. The parsec, therefore, is the distance to a star if the parallax angle is one second of arc.
A more familiar unit of distance is the light‐year, the distance that light travels (c = 300,000 km/s) in a year (3.16 × 10 7 seconds); one parsec is the same as 3.26 light‐years.
The nearest star, α Centauri, has a parallax angle of 0.76″. Therefore its distance is d = 1/0.76″ = 1.3 pc (4 ly). The ground‐based limit of parallax measurement accuracy is approximately 0.02 arc second, limiting determination of accurate distances to stars within 50 pc (160 ly). The European Hipparcos satellite, in orbit above the atmosphere and its blurring effects, can make measurements with much higher precision, allowing accurate distance determinations to about 1000 pc (3200 ly.
By - Jahan Shah
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