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...
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...
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...
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...