Recent content by ck99

Homework Statement This isn't really a coursework question, but I thought this might be the best place for it. I have some data on two different CO line emissions from an object. Can I work out the temperature of that object by using the ratio between the intensities of the two lines, and...

Thank you for your response; I understand now how that result is reached but now I don't see how it relates to my problem. In this text, it says that flux F = L/(4∏D2) where D is the distance from the source and L is its luminosity. Then it says that intensity I = F/Ω, which implies that I =...

Hi folks, can someone help explain this in words of one syllable or less? I am looking at a text that compares flux and intensity of a distant source, and it states that ∫∫dΩ = ∏ I know that dΩ = sinθ dθ d∅ but I don't understand where the given result comes from. What are the...

I was just reading about how the redshift-relation for angular diameter distance is calculated, and the example in my textbook used a matter-dominated universe to calculate the formula. It seems to rely heavily on the relationships between t, a(t) and H(t), which are different in radiation...

Homework Statement Integrate field equations for a universe filled with radiation and with k = +1, λ = 0. Find ρ(a) ρ(t) and a(t). Find lifetime of the universe. Homework Equations Use first Friedmann equation which reduces to a'2/a2 + a-2 = kρ where k = 8∏/3 The Attempt at...

Ah, thanks! I as trying Taylor expansions and all sorts of things. I think it was the second step I was missing. Cheers!

Hi mfb and thanks very much for your response. Just to clarify, when you say "Right." do you mean 1) Right, you have not expanded the brackets correctly 2) Right, you have expanded the brackets correctly If I was any sort of mathematician I am sure I would be able to tell which you mean, but...

Homework Statement Show that, for low energy photons scattered by ultrarelativistic electrons, the cange in frequency of the photon is given by (v'-v) / v = [(Ω'-Ω).β] / [1-Ω'.β] Homework Equations The full/general form of Compton scattering is given by v'/v = (1-Ω.β) /...

Ah, thanks for the help but I think that derivation is beyond the scope of this course. (certainly it's beyond me!)

Homework Statement I am trying to integrate the PLanck function to get the Stefan Boltzmann law. After factoring out constants, and substituting x = hv/kT I am left with the following integral: B(T) = ∫ x3/(ex - 1) dx integrated from 0 to ∞ The next step in my notes is that the result...

Thanks TSny, I managed to compute the derivative correctly and that can also be put in terms of positive, increasing functions of T so I am sure that is adequate proof.

Homework Statement Prove that the Planck function increases monotonically with temperature. Homework Equations Bv(T) = 2hv3c-2(ehv/kT - 1)-1 The Attempt at a Solution I first went through this piece-by-piece, but I am not a mathematician so I don't know if this constitutes...

Homework Statement (Everything here is frequency dependant, but I have left off the v from all the variables to minimise chance of typos - hopefully that is ok but please let me know if not and I will try and retype!) The equation of radiative transfer is dI/dτ = -I + S We guess...

Oh. I differentiated u instead of integrating. Some days there is not enough coffee in the world . . .

Homework Statement Hi folks, I am sure this is very simple but there are not enough steps given in this calculation for my simple brain to get from the beginning to the end! σ = ∫ (dσ/dΩ) = ∫ r2sin2θ (no integral limits given) σ = 2∏r2 ∫ (1 - u2) du (integral from -1 to 1) σ = 8∏r2 / 3...