1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Received power by a radiotelescope

  1. Nov 25, 2011 #1

    RHK

    User Avatar

    1. The problem statement, all variables and given/known data

    The specific power received by a radiotelescope is given by:

    [itex]P_\nu = A \int {I_\nu (θ,\phi) f (θ,\phi) dθ d\phi}[/itex]

    where:
    θ, [itex]\phi [/itex] are the angular coordinates on the celestial sphere around the pointing direction;
    [itex]I_\nu [/itex] is the angular distribution of the specific intensity of the source (in units of W/m2 Hz std);
    A f(θ, [itex]\phi [/itex]) is the effective area of the antenna in the direction (θ, [itex]\phi [/itex]).

    The radiotelescope, operating at a frequency of 3 GHz, of area A= 1000 m2 and with f(θ, [itex]\phi [/itex])= 1 for θ0>θ and f(θ, [itex]\phi [/itex])= 0 for θ>θ0, with θ0=1.9 arcminutes, is pointed in the direction of Mars (distance from the Earth d= 56 x 106 km, diameter D= 6794 km), which has an emission approximated with a black body at T=210 K.
    Calculate the detected power by the antenna in a band with Δ[itex]\nu[/itex]=30 GHz around the working frequency.

    [The specific intensity of a black body is: [itex]\frac{2h}{c^2}\frac{\nu^3}{e^{h\nu/KT}-1}[/itex]
    K=1.381 x 10-23 J/K
    h = 6.6 x 10-34 J s ]

    2. Relevant equations

    The intensiy of a black body

    3. The attempt at a solution

    I can not go so far.
    Just I have calculated the angular diameter of Mars: δ=arctan D/d = 25"=0.417'.

    Any suggestion please?
    I can not how to carry out the result, but I think that this is a particular educational exercise.
    Thanks in advance.
     
  2. jcsd
  3. Nov 27, 2011 #2

    RHK

    User Avatar

    Can I have just a start please?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Received power by a radiotelescope
  1. Power output (Replies: 4)

  2. Nuclear power homework (Replies: 2)

Loading...