| ENCOUNTER WITH TIBER Buzz Aldrin & John Barnes New York: Warner Books, 1996 |
Rating: 5.0 High |
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| ISBN 0-446-51854-9 | 560p. | HC/GSI | $21.95 | |
According to Encounter with Tiber, the 96-meter-wavelength transmission from the star Kahkehreif was found to have a beamwidth of 7 Astronomical Units (AU). That is seven times the radius of Earth's orbit around the Sun, or 651,000,000 miles. The significance of this for the story is that it means the beam just spans the orbit of Mars, where the Nisuans are later discovered to have left artifacts.
But I was curious what this told about the size of the transmitting array. What follows is a very preliminary calculation, based on a "Rule of Thumb" formula from Ref. 1.
Beam width in degrees is given by the "Rule-of-Thumb" equation
Rearranging this to solve for antenna aperture gives
where
| Wm | = 3dB beamwidth in meters |
| Wd | = 3dB beamwidth in degrees |
| D | = distance from Sun to Kahkehreif (Alpha Centauri), in meters |
| d | = antenna aperture in meters |
| λ | = wavelength in meters |
| k | = 70 degrees (proportionality constant, or fudge factor) |
| Wm | = 7 AU × (93×106 miles) × (2.2 km/mile) = 1.43×1012 meters |
| D | = 3×108 m/sec × (31.56×106 sec/year) × 4.3LY = 40.7×1015 meters |
| Wd | = Arctan (1.43×1012 m ⁄ 40.7×1015 m) = Arctan (3.52×10-5) = 2.02×10-3 degree |
| λ | = 96 meters |
Therefore, the size of the antenna array at the Kahkehreif transmitter site is:
| d | = k × (96 meters / 2.02×10-3 deg.) = 70 × (4.76×104) meters = 3.3×106 meters |
I submit that an antenna array 3,300 kilometers across is an impressive achievement in any solar system. I look forward to unpacking my own books and finding better equations than that found in Ref. 1, which is:
| Antenna Engineering Handbook (2nd edition) | |
| Johnson & Jask (editors) | |
| New York: McGraw-Hill, 1984 — page 1-15 |
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