29:106/186 RADIO ASTRONOMY
Ninth Homework Set...April 12, 2000
Due: April 19, 2000
(1) The brightness distribution of a source consists of a point source
with a flux density of 1.0 Janskys and a Gaussian source with a flux
density of 2.0 Janskys and an angular size 
arcseconds.
The centers of the two sources coincide.
Calculate the visibility function. Plot the amplitude and phase of the
visibility function as a function of (u,v).
(2) You are observing the source in problem # 1 at a frequency of
610 MHz. What kind of baseline coverage would you need to adequately
measure the structure of the source?
(3) A source has a brightness distribution like that in Problem 1, with
the following important exception. The point source is offset to the
north by 3 arcseconds and to the east by 2 arcseconds. Qualitatively
describe the visibility employing a sketch which includes as many important
features as you are capable of discerning. Explain what you have drawn.
(4) Show that for any radio source the visibility function at
zero baseline equals the total flux S.
(5) A point double source has one component with a flux density of 2 Janskys
and another of 1 Jansky. The separation between the components is 2
milliarcseconds. Observations are made at a frequency of 5000 MHz. What is
the minimum value of the amplitude of the visibility function? What baseline
would be necessary to measure the minimum?