How to Calculate Distances and Luminosities of Stars?

[C.E]

Hi, I am quite new to astronomy and was wondering whether I had done the following question correctly (some of my answers seem unrealistic). Plus, how many significant figures should questions like these be answered to?

The star Rigel in the constellation of Orion has an apparent magnitude of 0.1 mag,
its parallax is 4.22 milli-arc seconds (mas). Betelgeuse, also in Orion, has an
apparent magnitude of 0.58 mag and a parallax of 7.63mas.

(i) Compute the distance from Earth to Rigel and Betelgeuse.

my attempt: distance to Rigel= 1/(4.22 x 10^-3) = 237 pc

distance to Betelgeuse = 1/(7.63 x 10^-3) = 131 pc

(ii) Using the above information, compute the absolute magnitude of both stars.
Which star has the higher luminosity?

I used M=m- 5log(d/10)

For Rigel M=0.1-5log(23.7)= -6.77 (this seems too low to me).

For Betelgeuse M=0.58 - 5log(13.1)=-5.0 (again I was not expecting a value this low)

Hence Rigel is brightest.

(iii) The Sun has an absolute magnitude of 4.83 mag. Determine the luminosity of
Rigel in solar luminosities.

L=L(sun)10^(M(sun)-M(R))/2.5 so L= 43700 L(sun) (again this does not seem realistic to me).

Any ideas?

 

[Ich]

Any ideas?

Yes: Wikipedia. Your answer seems to be correct.
BTW, there's a special homework section.