How many astronomical units (A.U.) make 1 parsec? Consider a sunlike star at a distance of 2 parsecs. When it is seen through

Question

(a) How many astronomical units (A.U.) make 1 parsec? 

(b) Consider a sunlike star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be (1/2)° from the earth. Due to atmospheric fluctuations, eye can’t resolve objects smaller than 1 arc minute.

(c) Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about 1/2 A.U. from the earth. Calculate what size it will appear when seen through the same telescope.

(Comment : This is to illustrate why a telescope can magnify planets but not stars.)

Answer 1

(a) By definition of parsec

(b) At 1 A.U. distance, sun is (1/2°) in diameter. Therefore, at 1 parsec, star is (1/2/2 x 10⁵) degree in diameter = 15 × 10^-5 arcmin.

With 100 magnification, it should look 15 × 10^-3 arcmin. However, due to atmospheric fluctuations, it will still look of about 1 arcmin. It can’t be magnified using telescope.

At 1 A.U. sun is seen as 1/2 degree in diameter, and mars will be seen as 1/1600 degree in diameter.

At 1/2 A.U, mars will be seen as 1/800 degree in diameter. With 100 magnification mars will be seen as 1/8 degree 60/8 = 7.5 = arcmin.

This is larger than resolution limit due to atmospheric fluctuations. Hence, it looks magnified.