if a giant star 100 times the diameter of the sun, is 1 parsec from earth, what would its angular diameter be?

Question

If a giant star 100 times the diameter of the sun, is 1 parsec from earth, what would its angular diameter be?

 

Answer 1

To calculate the angular diameter ofd a star, you can use the small angle formula:

θ = D/d

θ = angular diameter in radians

D = actual diameter of the object

d = distance to the object

Convert radians to arcseconds: 1 radian = 206,265 arcseconds

Given:

1. Diameter of the Sun: D_Sun ≈ 1.392 X 10⁸ km
2. Diameter of the Star: D_star = 100 x D_Su = 1.392 X 10⁸ km
3. Distance: 1 parsec = 3.086 x 10¹³ km

Step 1: Plug into small angle formula

θ = 1.392 X 10⁸ km/ 3.086 x 10¹³ km = 4.51 X 10^-6 radians

Step 2: Convert radians to arcseconds

θ = (4.51 X 10^-6 radians) x 206265 ≈ 0.93 arcseconds

Answer:

The angular diameter is approximately 0.93 arcseconds

It would be about the size of the full moon.