Need help with Measures of Stars! How do I do this?

Question

Heres the information given. Please help! I'm in dire need of some assistance!

Star: 65 Tau
mv = 4.20
Mv = x <-------Need to find this one
d (pc) = 40
parallax (sec in arc) = 0.25

Star: alpha Pic
mv = x <------Need to find this one
Mv = 1.8
d (pc) = 20
parallax (sec in arc) = .050

Star: 58 Ori
mv = x <-------Need to find this one
Mv = -6.0
d (pc) = 200
parallax (sec in arc) = .005

and finally...
Star: HR 2491
mv = -1.5
Mv = x <------Need to find this one
d (pc) = 2.5
parallax (sec in arc) = .400

Then she wants us to do these...
1) Which star would appear the faintest in the sky?
2) Which star is closest to the earth?
3) Which star would have the greatest surface temperature?
4) Which star has the greatest diameter?

Answer 1

The pc (parsec) distance of the first example should be 4.0 and not 40. That should be obvious from the parallax of 0.25.

You should have a formula that relates Mv to mv - I can't quote it offhand.
You won't know the faintest star until you do that sum. It will be the one with the largest mv.

The closest is the one with the largest parallax

The hottest one will be the one that has the biggest Mv (real brightness rather than visual)

The biggest one I assume will be the one with the smallest Mv, assuming that the dimmest one in absolute terms will be a red giant. Not sure about that logic. Betegeuse is a red giant but is quite bright. I am sure that the expanded size of red giants compensates somewhat for their realtive coolness.

Better ask your prof about that one.

Answer 2

Apparent magnitude, mv, absolute magnitude, Mv, distance, d (pc), and parallax are all related by the formulas in the source. Read it and do the math to answer 1 and 2.

You really can't answer 3 and 4 with only the distance and magnitude information given above, but since the names of the stars are given, you could look each one up in wikipedia or whatever to find that information.