Answer to Question #166934 in Astronomy | Astrophysics for Marie

Question

a) Approximately 9000 stars are visible to the naked eye in the whole sky (imagine that you could see around the entire globe and both the northern and southern hemispheres), and there are about 41,200 square degrees on the sky. How many stars are visible per square degree? Per square arcsecond? 

b) People are often bothered when they discover that reflecting telescopes have a second mirror in the middle to bring the light out to an accessible focus where big instruments can be mounted. “Don’t you lose light?” people ask. Well, yes, you do, but there is no better alternative. You can estimate how much light is lost by such an arrangement. The primary mirror (the one at the bottom in Figure 6.6) of the Gemini North telescope is 8 m in diameter. The secondary mirror at the top is about 1 m in diameter. Estimate what fraction of the light is blocked by the secondary mirror. 

Answer 1

a) The whole sky is considered as a sphere called as Celestial Sphere.

Total no. of stars visible to the naked eye in the whole sky = 9000

Area of the whole sky in degrees = 41200 square degrees

No. of stars in 1 square degree = $\frac{9000}{41200}$ = 0.218

Also 1 degree = 60 arcminutes

1 arcminute = 60 arcseconds

Thus, 1 degree = 3600 arcseconds

Thus, No. of stars visible in per square arcsecond = $\frac{0.218}{3600\times3600} = 1.6\times10^{-8}$

b) $\frac{1}{8}\times100 = 12.5$ %