Practice Questions Flashcards
B(v) of a blackbody is
B(v) = 2kT/λ^2
B(v) is measured in
W m^-2 Hz^-1 sr^-1
where Jy = Js^-1 m^-2 Hz^-1
where Js^-1 = W
S = ∫B(θ,φ) dΩ
dΩ = sinθdθdφ
and for small angles
(θ/2)^2 π
converting from degrees to radians
radians = degree π/180
S is measured in
W m^-2 Hz^1
converting from arc seconds to radians
radians = arc π/180*3600
L = 4πR^2S
where R is the distance away
to convert from ly to meters
ly = 3x10^8 * 60 * 60 * 24 * 365.25
gain =
gain = 4π/Ω(A)
Ω(A) =
λ^2/A(e)
w = kTΔv
where w is the power received per unit bandwidth
and Δv is the bandwidth
w = 1/2 S A(e) Δv
where S is the flux density and A(e) the effective area
derive
w/Δv = 1/2 A(e) ( ∫sky) B(θ,φ)P(θ,φ) dΩ
equating w = 1/2 S A(e) Δv and w = kTΔv
substituting for S
derive
Ta = A(e)/λ^2 ( ∫sky) Tb(θ,φ)P(θ,φ) dΩ
starting from
w/Δv = 1/2 A(e) ( ∫sky) B(θ,φ)P(θ,φ) dΩ
replace B for Tb
rearrange for Ta
For Ω(s) «_space;Ω(A)
P ~ 1
=> S = B Ω(s)
Ω(A) =
∫ P(θ,φ) dΩ
dΩ = sinθdθdφ
for small angles
dΩ = (θ/2)^2 π
A(g) =
πD^2/4
A(e) =
ηπD^2/4
what is the beam efficiency of a radio telescope
beam efficiency = power in main lobe/total power
η(B) = Ω(M)/Ω(A)
phase error =
φ = 2π/λ 2ε = 4πε/λ
errors reduce the efficiency of the dish by a factor of
in argand plane, overall voltage response is down by ~ cosθ
=> power response down by
η = (cosθ)^2 = cos^2(4πε/λ)
what is the system temperature of a radio telescope
total noise power per unit bandwidth = kT(sys). Where T(sys) includes contributions from all noise sources
T(sys) =
T(source)+T(background) +….
kT(source) =
1/2 S A(e)