Astrophysics Questions: Calculating Distances, Intensities, and Magnitudes

[wasa]

guys please help me with these questions, we had to do the astrophysics course over the holidays by ourselves and I haven't quite understood these sections

1. How far from the Earth is 61 Cygnus

(a) in parsecs

(b) in light years

if it’s annual parallax is 0.29 arc seconds.

2. The intensity of the light that reaches the Earth from a particular star is seven times greater than that from a star whose apparent magnitude is 3.6. What is the apparent magnitude of the brighter star?

3. Find the ratio of the intensities of the light that reaches the Earth from two stars whose apparent magnitudes are (a) 1.4 and 3.9, (b) -0.72 and 4.28.

5. The average intensity of the Sun’s radiation at the surface of the Earth (after correction for absorption and scattering) is 1.37 x 103 W m-2. Calculate (a) the Sun’s luminosity (i.e. energy released per second), (b) its surface temperature on the assumption that it is a black body. (The mean distance of the Earth from the Sun =1.5 x 1011 m, radius of the Sun = 6.96 x 108 m, Stefan’s constant = 5.67 x 108 W m-2 K-4)

6. Vega (the fifth-brightest star) has an apparent magnitude of 0.03 and is 7.7 parsec from the Earth. Find its absolute magnitude

7. Star A has an absolute magnitude of 2 and an apparent magnitude of 8. Star B has an absolute magnitude of 4 and an apparent magnitude of 5.
a) It should be immediately apparent that star A is farther away than star B - how? b) what is the ratio of their distances from the earth

8. 1. A distant Cepheid variable is found to have a period of 25.0 days and an average apparent magnitude of 18.5. Use Fig 4.5 to estimate the distance to this particular Cepheid. (Note, if x = log10 y, then y = 10x – use the 10x key on your calculator.)

If anyone could give me any help I'd really appreciate it.

thanks

 

[fargoth]

first of all, welcome to PF!
now for your questions.. it doesn't seem like youve tried to answer these questions yourself before posting them... try solving them yourself (for the first one i'll suggest google) and if you encounter difficulties ask a specific questions about them, you don't really expect us to do your homework for you, do you?

 

[wasa]

ok, so i think i got the first one using d = 1/p, the second one i can't truly understand, should i be using some form of m-M = 5log10(d/10)?

 

[chroot]

For the first one, you need to use some trigonometry. Draw a triangle, and notice that the distance depends on the tangent of the parallax angle.

- Warren

 

[fargoth]

try this for the first one:
http://www.noao.edu/outreach/nop/nophigh/steve9.html

and as for the second question - youre on the right track.
this could help you if you hadnt solve it yet...
http://en.wikipedia.org/wiki/Absolute_magnitude