Project Cyclops, A Design... - Department of Earth and Planetary ...

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The polar equation of the secondary mirror is From equations (8) and (9) we then have r I = fl(e + l) a(e 2 - 1) I +ecosO_ l+ecos01 (I6) sin 0 _ 1 sin 01 l+cos02 m l+cos01 We see from Figure I-I that 02 1 01 1 d tan - tan - (I10) 2 m 2 m 4/ tan 02 and therefore rl sinOt (e2 - l)sinOl ._a -- r_ cos 01 2e+(e 2 + l)cos O_ that (I7) Thus the Cassegrainian system behaves exactly like a simple paraboloid having m times as great an f/d ratio as the primary mirror, at least as far as paraxial rays are concerned. For either case the illumination of the primary mirror will be given by sin 02 (e 2 - l)sin 0 (e 2 + l)+2e cosO, (I8) .... cos 2 -- (I11) ¢o 2 cos 0 2 2e+(e 2 +l)coS Ol (e 2 + I)+2e cosOi 09) where 0 is the angle subtended at the feed. Thus for a given uniformity of illumination we can use a primary mirror having an lid ratio 1[m times as large. 210
APPENDIXJ PHASINGOFTHE LOCALOSCILLATOR The phase of the local oscillator signal at each antenna site must have a value proportional to the distance from the antenna to one of the arriving plane wavefronts. Note that this is a phase correction, modulo 2rt-and not a time delay correction-since the local oscillator is a monochromatic signal. Due to the sidereal rotation of the earth, this phase setting will continuously vary with time, depending on the antenna coordinates, the source coordinates and the reference phase. Thus, it is necessary to incorporate a variable (modulo 2n) phase shifter into each local oscillator. This phase shifter may also be used to compensate for phase errors in the RF system provided these errors are known. Consider a phase shifter with an initial setting of _o' which is chosen to put the local oscillator in the correct phase for the arriving wavefront. As the antenna tracks the source, this plane wavefront tilts and the phase setting must be varied also. When the phase setting reaches 2n, the phase shifter is reset to zero phase as ¢D Z I.-- I-- to o_zrr "lel n- O --I --I 0 ._t (..1 o 0 J -- I ! / I / I / ,y TIME, sec Figure J-1. Required phase shift versus time. shown in Figure J-1. This phase change is equivalent to a frequency offset in the local oscillator signal of Af=-- To obtain negative offset frequencies it is required that the phase shifter to be driven from 27r to 0° thus obtaining a negative slope. Microwave phase shifters may be either digital or analog type devices. Digital phase shift devices essentially operate by switching different lengths of transmission line in and out of the signal transmission path. Analog phase shift devices operate by varying the effective permittivity or permeability of the transmission path. Consider the phase ramp approximation of Figure J-2. A system like this would be very easy to control because of its digital nature. Klein and Dubrowsky (ref. 1) have built a frequency translator of this type. In general, their results were good, However, because of the digital nature of the device, sidebands are created at frequencies related to the time per bit. The amplitudes of the peak sidebands decayed with bit size as shown in Figure J-3. From this it is seen that many bits must be used to obtain low sideband amplitudes. However, as the number of bits increase, so does the complexity of the driver of the phase shifter. It is doubtful if a phase shifter of this type would have any significant advantage over an analog phase shifter, and since the analog phase shifter will not have any sidebands, it is preferable for this application. The phase shift may be controlled in an analog manner either mechanically with a rotating vane phase shifter or electrically with a ferrite phase shifter. Both 1 T 211
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(NASA-CR- 11_5) PROJECT CYCLOPS: A
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CR 114445 Available to the public A
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At this very minute, with almost ab
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ACKNOWLEDGMENTS The Cyclops study w
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COMMUNICATION BY ELECTROMAGNETIC WA
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APPENDIX A - Astronomical Data ....
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t _ 2
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of the living beings evolved by the
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Figure2-1. M3I,the great galaxy in
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self.Thus,wecaninterpretFigure2-2as
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magnitude (low brightness) end, the
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Red Giant. The transition from main
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tion, as the central part of the cl
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TABLE 2-4 SELECTED NEARBY STARS WIT
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tideraisingforcesasr--_ where ,v =
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3. Is it possible that living syste
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lawsof natural selection, more like
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starsthroughout the Galaxyhave also
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if the longevity of that life is ty
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The imaginative reader will have no
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Lookingfar ahead,supposewe aresucce
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usuallyterritorial expansion by the
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IOO IO 1 [ [ J [ J I J i [ i I i I
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order with what Morrison has descri
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The quantity gtPt is often called t
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which might result from synchronous
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1. Wewillnothavenough resolving pow
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normalwith the meanat o x/--2. When
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Chapter11 in analyzingthe dataproce
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Therangelimitisthenfoundbyequating_
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TABLE 5-3 PARAMETER Wavelength Tran
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angeanddirectlyasthesquareof antenn
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"_ i i i i i p = STELLAR DENSITY AT
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I-- g u. O >- I--- .d tit (]O 0 0.
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andwidth that will still give near
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acquisitionphasefor otherraces.Supp
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1. They would transmit continuously
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and ¢-Ceti. No signals were detect
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vz .i g)mo PAGE NOr Ir[[,MZ 7. THE
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The price of incomplete sky coverag
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modest size.A largedatabaseontapeor
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THEAUXILIARYOPTICALSYSTEM Althoughn
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edetectedat 20,000light-years byCyc
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feeds must correct for spherical ab
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side of the dish and shade on the o
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TABLE 8-1 UNADJUSTED UNIT COST DATA
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7. Using huge specially designed ji
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9. THE RECEIVER SYSTEM The receiver
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whereP is the radiated power. Divid
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SHADOWED AREA SHADOWED AREA // // /
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Corrugatedhornssupportingbalancedhy
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o 50 ----- - _ T i 20 _,o 5 ,,,5 09
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TABLk ?- I A COMPARISON OF VARIOUS
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CENTRAL POINT STATION LSB LINE FREQ
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A02 .... + No (25) (i C 1 where No
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COAXIAL LINE DIRECTIONALCOUPLER FRE
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DeJager, J.T.:IEEETrans.onMicrowave
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pR_ING PA6E BLANK HOT FILMF_ 10. TR
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o-------------o_ _ o o o o ing of t
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addedto theother IF channel. The tw
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INPUT MHZ _PF 500 MHZ i : 575 T1 92
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azimuth _) has a delay (2a/c)sin 0
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stripline. For 2 _< k _< 6, appropr
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mation are common to all antennas i
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A cable pair costs about 20 cents/m
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11. SIGNAL PROCESSING The Cyclops s
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1.0 T t t I I r .9 -8 asynchronousl
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collimated coherent light. A simple
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power of the film and associated op
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samples simultaneously onto the sam
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outputs is assumed. COMPOSITE SIGNA
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SPECTRUM I n LINES M n LINES U SPEC
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signal andyet have a tolerable fals
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i --_- i i i i large values of n. T
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plottedin Figure11-15for various va
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All the1Fsignalswillarrivein phasei
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x:(1 +x) x 2 - _ -- (53) If we wish
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3's = unitcostof signal planelectro
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where0ma x is the maximum value of
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Roughestimates of the costs of buil
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12. CYCLOPS AS A BEACON Although th
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13. SEARCH STRATEGY The high direct
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distantgalaxies (oraninertialrefere
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Page 175 and 176: starsfrom/'18 to G5 could support a
Page 177 and 178: 14. CYCLOPS AS A RESEARCH TOOL Thro
Page 179 and 180: Only a few such galaxies have been
Page 181 and 182: 15. CONCLUSIONS AND RECOMMENDATIONS
Page 183 and 184: perhapsdecadesand possiblycenturies
Page 185 and 186: APPENDIX A ASTRONOMICAL DATA DISTAN
Page 187 and 188: PLANETARY Planet ORBITS Semimajor S
Page 189 and 190: APPENDIX B SUPERCIVILIZATIONS AND C
Page 191 and 192: ABIOLOGICAL CIVILIZATIONS Many writ
Page 193 and 194: 182
Page 195 and 196: tqOT APPENDIX C OPTIMUM DETECTION A
Page 197 and 198: to rmsnoise.Wenotethatthematchedfil
Page 199 and 200: APPENDIX D SQUARE LAW DETECTION THE
Page 201 and 202: If the output filter is very wide c
Page 203 and 204: if B/2 > T we can start instead wit
Page 205 and 206: Let us now introduce the normalized
Page 207 and 208: where h-- = expectation count of si
Page 209 and 210: APPENDIXE RESPONSE OF A GAUSSIAN FI
Page 211 and 212: APPENDIXF BASE STRUCTURES AZ-EL BAS
Page 213 and 214: ack,it shouldnotbenecessary to prov
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Page 219 and 220: PAGE BLANK NOT APPENDIX H POLARIZAT
Page 221: APPENDIX I CASSEGRAINIAN GEOMETRY C
Page 225 and 226: APPENDIXK EFFECTOF DISPERSION IN CO
Page 227 and 228: APPENDIX L TUNNEL AND CABLE LENGTHS
Page 229 and 230: where r = "Ym/'rs- If we let o-_--o
Page 231 and 232: L-4 we see that the length of IF ca
Page 233 and 234: APPENDIX M PHASING AND TIME DELAY A
Page 235 and 236: andobtain V = 2 (Ps [! + _(Ar)] +Pn
Page 237 and 238: L" D 226
Page 239 and 240: APPENDIX N SYSTEM CALIBRATION The p
Page 241 and 242: APPENDIXO THE OPTICAL SPECTRUM ANAL
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Page 245 and 246: APPENDIX P LUMPED CONSTANT DELAY LI
Page 247 and 248: Thevalueofthefinalcoilonthelineis =
Page 249 and 250: APPENDIXQ CURVES OF DETECTION STATI
Page 251 and 252: I I I I LE :E oo
Page 253 and 254: APPENDIX R RADIO VISIBILITY OF NORM
Page 255: io 3 - l rlrllll I I I ]l+,ll_ I _f
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