29:106/186 RADIO ASTRONOMY
First Homework Set...January 24,2000
Due: February 2, 2000
(1) A sphere 100 meters in diameter is at a temperature of 290K and may be
considered a blackbody radiator. It is at a distance of 200,000 km. What is the
intensity of radiation received from it? What is the flux density in Janskys?
(2) A blackbody radiator has a temperature of 100K. At what frequency will the
Rayleigh-Jeans approximation give a 1% error for the intensity of radiation?
Give the result for a blackbody at 1000K.
(3) Explicitly show that Wien's Law (or, as it is referred to in the textbook,
Wien's displacement law) can be obtained from the Planck function.
(4) Assume that the Green Bank radio telescope, with a diameter of 100 meters,
is observing the radio source 3C147 at a frequency of 4750 MHz. The part of the
spectrum which is amplified (we call it the bandwidth) is 100 MHz wide. How much
power (in Watts) is delivered to the receiver? You may assume that all radiation
incident on the antenna is delivered to the receiver. In the parlance of radio
astronomy, this would correspond to an aperture efficiency of 100 %.
(5) A radio source has a flux density of 1.0 Janskys at 2700 MHz. The image of the
source shows it to be square (you hear the ``X-Files'' theme at this point)
and of uniform brightness. The side of the square is 20 arcseconds. What is the
temperature of the equivalent blackbody that would give the same intensity and
flux density? This is referred to as the brightness temperature of the
source.