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

                          

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

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