What are the angular diameters in appropriate units eg 0001
What are the angular diameters (in appropriate units, e.g. 0.001 = 1 mas or 1800 =30 ) of the following, as seen from Earth?
a) The Sun.
b) Betelgeuse, with MV = 5.5, mV = 0.8, and R = 650R.
c) The galaxy M31, with R 30 kpc at a distance of D 0.7 Mpc.
Solution
a) andular diameter q = 2 arctan (d / 2D)
d diameter if the star , D is the distance to the star
for sun d = 10^6 km and D = 149.6 * 10 ^6
q = 2 arctan ( 10^6 / 149.6 * 10 ^6 )
~0.765 radians
b) distance to Betelgeuse in parsec is D = 10 [mv - MV )+5 ]/ 5
D = 10 [0.8-(-5.5)+5 ]/ 5
D = 181.970 parsecs
and d = 2* 650Ro = 2* 650 * 2.257 * 10^-8 parsecs
for Betelgeuse q = 2 arctan (d / 2D)
= 2 arctan (2* 650 * 2.257 * 10^-8 / 181.970 )
= 1.847*10^-5 radians
c. The galaxy M31
q = 2 arctan (d / 2D)
= 2 arctan (2 * 30 * 10^3 pc / 0.7 * 10 ^6 pc)
= 9.798 radians
