Since nobody has posted on this for a while I thought I would add a few questions.
Keep in mind these are unrelated.
1) Derive the distance modulus relationship (prove that m-M = 5 log (D) - 5,, or if you want m-M = 5 log (D/10)).
2) Star 1 has the same absolute luminosity has Star 2. The apparent magnitude of Star 1 is 3, the apparent magnitude of Star 2 is 5, and the distance to star 1 is 13.6 pc. Calculate the distance to Star 2.
3) The radius of a giant molecular cloud is 100 pc. Calculate its mass in Msun.
I guess I will give it a shot to start this back up... well not the first one, but the others seem simple enough.
2) I got ~34.4 pc
3) I probably got a different answer than you, but here's my thought process:
Assuming the GMC is roughly spherical, the volume in pc^3 would be 4/3piR^3 which gets you 4188790.20479 pc^3
4188790.20479 pc^3 * (3.2407557442396⋅10^19)^3 cm^3 / 1 pc^3) = 1.425697893×10^65 cm^3
According to http://homepage.physics.uiowa.edu/~rlm/ ... on%201.htm
GMCs have densities of about 10^3 atoms per cm^3
Assuming this is all hydrogen gas... This means a density of about 10^3(1.67 x 10^-24) grams per cm^3 or 1.67*10^-21 grams per cm^3
Factoring in the volume of the GMC, you get a total of (1.67*10^-21)*(1.425697893×10^65) or 2.3809154813×10^44 grams
This is equal to 2.3809154813×10^41 kg
1 Msun is 1.989 × 10^30 kg, so 2.3809154813×10^41 kg * (1 Msun / 1.989 × 10^30 kg ) = 1.1970414687×10^11 Msun
This either means my math is wrong, my methods/information is wrong, or this is just a very unrealistic GMC considering the usual cap for the mass of a GMC is around 10^7 Msun...
I guess I should ask a question too...
If the period of a Type I Cepheid is 10 days, and the energy of one photon from the peak emission of a star with the same absolute magnitude as this variable star is 3.056E-19 Joules, then
A) What is the radius of this star in Rsun?
B) What is the spectral class of this star?
C) Assuming this star is on the main sequence, what is its density in kg/m^3?
Mac Hays, Durham Academy Science Olympiad