Question

Astronomers oftenmeasure largedistances usingastronomical units(AU) where 1 AU isthe average distancefrom Earth to theSun. In the image, drepresents thedistance from a starto the Sun. Using atechnique called"stellar parallax,astronomers determinedO is 0.00001389degrees.1. How faraway isthe starfrom theSun inastronomical units?Showyourreasoning.2. Write anexpression tocalculated for anystar.

Answer 1

In the given right triangle of the figure

we have that

sin(O)=1/d ----> by the opposite side divided by the hypotenuse in a right triangle

solve for d

d=1/sin(O)

`d=(1)/(sin\left(0.00001389^o\right?)`

d=4,124,966.13 AU -----> two decimal places

the expression to calculate d for any star is equal to

`d=(1)/(sin\left(O\right))`