You measure the parallax angle for a star to be 0.1 arcseconds. What is the distance to this star?
10 parsecs =32.8 light years = 2.06 X 10^6 AU.
The formula for distance is d = 1/(parallax angle in radian) AU.
Here, for 1 second parallax angle, the distance is 1 parsec.
So, for 0.1 second, it is 10 parsecs= 10 X 206364.8 AU.
Nearly, 62900 AU = 1 light year (ly). So, this distance
#= 2062648/62900= 32.79 ly.
If the angular measurement is 3-sd .100 second. the answer is 32.8 ly..In this case, the precision for angular measurement will be up to 0.001 sec.The answer is given for this precision. This is important, when you convert, from one unit to another