Astronomy Principles and Practice Fourth Edition.pdf

Problems—Chapter 21 373
Problems—Chapter 21
1. Determine the smallest angle on the sky that can be resolved by a radio dish of 100 m diameter working at a
wavelength of 10 cm.
How does this compare with a 5 m optical telescope operating at wavelengths around 500 nm
2. A radio dish of 25 m diameter observes a point source providing a flux density of 140 m(illi)Jy. Calculate
the power received if the bandwidth is 20 MHz.
3. A small radio dish with a narrow beam (less than 1 2 ◦ ) is directed to a plain wall of a building with a surface
temperature of 27 ◦ C (300 K). It is then directed to the Sun (6000 K). Estimate the ratio of the signal strengths
for the two signals.
4. A dish type antenna has a diameter D but is used with an aperture efficiency of η. Show that the beam solid
angle may be written as
A =
4λ2
π D 2 η
where λ is the operating wavelength.
Suppose a telescope of diameter 25 m has an aperture efficiency of 0·6 and is used at a wavelength of 3 cm,
determine the solid angle of the beam.
If the beam comprises a simple cone, determine the diameter of the circular patch that is resolved on the sky.