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Beamwidth of the SRT

Objective:  Students will measure the beamwidth of the Small Radio Telescope and compare with the diffraction limit for the telescope and wavelength.

Introduction:  Students should have completed the “Beamwidth of the Eye” activity or should at least read the introduction to that activity.

To interpret the data we get from the telescope, we need to know the beamwidth.   Because of the large wavelength of the radio waves the SRT is “seeing”, the beamwidth will be fairly large.  Since we know the sun is small compared to the beamwidth of the telescope, we can measure the beamwidth by scanning across the sun.

It is worth mentioning here that the SRT does not emit a beam.  The telescope only takes in radio waves and measures them.  The “beam” we are referring to is the path of the radio waves that we detect.  Radio waves that come from within the beam are detected, and radio waves from outside the beam are not.

Procedure:

1. Write a command file to scan across the sun in azimuth, starting 40° to the east of the sun and going to 40° to the west of the sun in 1° increments.  Make sure your command file records the data and calibrates the telescope on a part of the sky similar in elevation to the sun.  Use a frequency of 1419 MHz.  For more information, see the “Command File” section of the manual.

2.       Record the elevation of the sun at the time your measurements are made.

Analysis:

1.       Open your data in a spreadsheet.  One column should be Azimuth and the other should be Temperature. 

2.       Correct your angle for elevation.  A degree of azimuth at a high elevation is smaller than a degree of azimuth at low elevation.  Make an angle column using the formula: angle = azimuth * cos(elevation).

3.       Plot the angle (x-axis) vs the temperature (y-axis), and print the graph (full page).  Draw a smooth curve of the data.  (Don’t connect-the-dots).

4.       Draw a horizontal line at the minimum temperature you measured.

5.       Draw a horizontal line at the maximum temperature you measured.

6.       Draw a horizontal line at the average of the maximum and minimum temperatures.

7.       Find the two angles where the temperature curve intersects the average temperature line.

8.       The difference between these two angles is the beamwidth of the SRT.

9.       Find the diffraction limit of beamwidth for a telescope the same size as the SRT at 1419 MHz.

Discussion Questions:

1.       How does the beamwidth you measured compare to the diffraction limit you calculated?

2.       What factors other than diffraction could affect the beamwidth of the SRT?

3.       How large would a radio telescope at 1419 MHz have to be to have approximately the same beamwidth as your eye?

Things to Try: 

1.       Measure the beamwidth of the SRT by scanning the sun in elevation.

2.       Radio astronomers are interested not just in the beamwidth but in the shape of the beam.  Measure the shape of the SRT beam by writing an appropriate command file and making a surface plot of the results.  (This is not a small project).

3.       Could you measure the beamwidth of the SRT using something a source other than the sun?  Try and see.

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