Recent content by Kyrios

Homework Statement This is a question on multiple coulomb scattering in a wire chamber momentum p = 500MeV/c wire resolution = 120 microns distance from wall to wire = 0.01m radiation length of wall material X_0 = 2E-3 m mass of charged particle m_{\pi} = 139.6 MeV/c^2 charge z = 1 How thick...

How can I simply assume that \omega = 0? It says that w is a constant. Since the previous question was for the case of the stationary observer, I'm quite sure that this one isn't after the same answer. Although I cannot see any way around it

I have already worked out the proper time for a stationary observer, \Delta \tau = 6 \pi GM. The question specifically states that the observer is not at fixed coordinates, but moving with \phi = \omega t and emitting a photon while orbiting.

Homework Statement An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant. The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...

Yes this is all that was given, unfortunately, so I'm having trouble explaining why exactly it is zero

Homework Statement Show U^a \nabla_a U^b = 0 Homework Equations U^a refers to 4-velocity so U^0 =\gamma and U^{1 - 3} = \gamma v^{1 - 3} The Attempt at a Solution I get as far as this: U^a \nabla_a U^b = U^a ( \partial_a U^b + \Gamma^b_{c a} U^c) And I think that the...

Homework Statement How do I calculate the temperature at which a galactic scale perturbation enters the horizon? This would be for radiation domination. Homework Equations \left( \frac{\delta \rho}{\rho} \right)_{\lambda_0} (t) = \left( \frac{a(t)}{a_{eq}} \right) \left( \frac{\delta...

So would this be done by calculating H_{eq} at equality, and then expanding with scale factor, L(z=0) = L_{eq} (1 + z_{eq}) ? If I do that, it gives a value a little under 150 Mpc.

Homework Statement If light traveled a distance L = H_{eq}^{-1} at M-R equality, how large does this distance expand to at present? (in Mpc) Homework Equations z_{eq} = 3500 \Omega_m = 0.32 at present \rho_c = 3.64 \times 10^{-47} GeV^4 present critical density The Attempt at a...

so I get this: DH = \frac{z(z+2) - z^2 q}{2} = 0.232 \frac{dq}{dz} = \frac{4DH - 2z}{z^3} = 66 \Delta q = \frac{dq}{dz} \Delta z \Delta z = \frac{0.06}{66} = 9 \times 10^{-4} The error seems really small..?

ok, so H = \frac{1}{r_c} H = \frac{1}{a}\frac{da}{dt} = \frac{1}{r_c} \int_{0}^{a} \frac{1}{a} da = \int_{0}^{t} \frac{1}{r_c} dt ln(a) = \frac{1}{r_c} t a = \exp(\frac{t}{r_c}) Which is akin to dark energy domination a \propto \exp(Hr_c) ?

Homework Statement For the equation q = \frac{z(z+2) - 2DH}{z^2} q = -0.6 \pm 10\% , and z = 0.2. D and H are known exactly. I have to find the error in z that will give an answer of q = -0.6 \pm 10\% Homework EquationsThe Attempt at a Solution I have considered rewriting the equation...

Yes r_c is a constant which is called the cross over scale. I don't think we need to know the value of it

Homework Statement For the equation H^2 = \frac{8 \pi G \rho_m}{3} + \frac{H}{r_c} how do I find the value of H for scale factor a \rightarrow \infty , and show that H acts as though dominated by \Lambda (cosmological constant) ? Homework Equations \rho_m \propto \frac{1}{a^3} H > 0...

How can I find out what the momentum is in the CoM frame? Do I still need the CoM frame?