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To determine the SETI range of radio telescopes, it is necessary to make assumptions about the transmitter power and dish size of the ETI's transmitting system. Planetary radar is one use of radio that ETI is unlikely to find a substitute for. By determining the power into the Arecibo dish necessary to have a planetary radar system capable of determining the exact orbit of an asteroid at a reasonable distance from earth it is possible to determine the power level and dish size that would give a reasonable ETI the ability to safeguard its planet by knowing the exact orbit of asteroids that might strike the planet. Using that information, I calculated the range of small SETI dishes in theory in the article Small Parabolic Dish Antennas and SETI, which was published in the November/December 1996 issue of Radio Astronomy, the journal of the Society of Amateur Radio Astronomers. I have received no comments indicating an error in the article.
However, knowing the range of a small dish antenna in theory does not mean that you know the actual range of a particular real dish when used for SETI. Real dishes are not perfect in shape, are not perfectly 100% (or even 50%) illuminated, and are subject to interference. When we had the radio telescope at the University of Indianapolis running, in a high interference area, it was necessary to determine its range in a SETI project.
It is possible to determine the SETI range of a real radio telescope by determining the flux of the smallest object it can observe. How to do that is explained in Radio Telescopes, A Simple Method of Comparing Their Performance and Determining Their SETI Range, published in March/April 2000 Radio Astronomy. A copy of that article is also on The SETI League website. It should be noted that the first article is pure theory, based on an ideal dish with 50 or 60% illumination and no interference! The later article is the practical one.
The only critical comment I received about the later article was a suggestion by a radio astronomer at Arecibo, who had just been employed by the SETI institute. He claimed that the radio astronomy (not SETI) formula for the minimum detectable flux I had used from Radio Astronomy, 2nd edition, by John Kraus, did not take into account determining the detection of a minimum flux by examination of the graph of the data over a period of time before, during and after the minimum detectable flux was in the beamwidth of the dish. He considered that to be a kind of visual integration of the data beyond the electronic integration time. I found that critical comment to be without merit, considering the graph which is Fig 3-15, in Radio Astronomy 2nd edition. That graph shows a typical radio telescope record of the minimum detectable flux as a graph of data before, during and after the minimum flux was in the beamwidth of the dish. See the development of the formula for minimum detectable temperature variation and minimum detectable flux at page 3-44 of Radio Astronomy, 2nd edition.
I hope these articles, especially the latter, are helpful to those considering using a radio telescope for SETI. I would ask anyone who actually analyzes the possibility of using a particular radio telescope for SETI and finds it is not adequate to consider using a larger dish instead of giving up on the search. The inadequate radio telescope will be great for learning radio astronomy techniques and related matters in preparation for the day the large dish is acquired.
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