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

I--
g
u.
O
>-
I---
.d
tit
(]O
0
0.
1.0
.8
.6
.4
.2
0
I0
I
Figure 6-3.
P- i_O(_Bll'IT'f 'P_I_'STAROf 'DETECTING A 'SIGIIAL
io-3,0-4,0-5 jo-_
I0 2 10 3
RANGE,light years
, i , i i1,,
I I L I i[ll
Probability of contact versus range.
However, we must concede at least this much
uncertainty in p. If civilizations typically radiate megawatts
of power for their own purposes for 107 years we
might assign p the value 10-3 and be able to eavesdrop
on their signals out to some 60 to 100 light-years. If, on
the other hand, they typically radiate beacons for 104
years, then p might be as low as 10-6 and the beacons
would have to be detectable at 600 to 1000 light-years.
Beyond 1000 light-years the situation becomes rather
bleak. Not only does the cube law fail, but also the
radiative epoch becomes shorter than the round-trip
delay making two-way exchange unlikely. We cannot,
however, exclude the possibility that very advanced
races exist beyond this range, and have constructed very
powerful beacons and have used them for unknown
purposes for very long times, perhaps for aeons.
We must also point out that the curves of Figure 6-3
do not give a true picture of what happens as the
sensitivity of a receiver is increased, for as we increase
our receiver sensitivity, we not only extend the range for
a given radiated power, we also permit the detection of
weaker radiation from sources already within range, so
to speak. To the extent that beacons are less likely than
radio leakage, this capability increases the value we
should
assign to p for the nearer stars.
Since the range we must cover is so uncertain, only
some general conclusions emerge:
1. We should start the search with a modest system
capable of detecting beacons ,_t to perhaps 100
light-years.
2. We should expand the system as the search
proceeds (and is repeated) and continue the
expansion until success is achieved or until we are
able to eavesdrop on unintended radiation from
100 light-years range. The system should then be
able to detect beacons of reasonable power at
1000 light-years range.
3. If technologically feasible at any time we may
10 4
want to search for more distant powerful sources,
perhaps even to scan other galaxies.
THE NUMBER OF RESOLVABLE DIRECTIONS
The number of distinct directions in which an
antenna must be pointed to cover the sky is proportional
to its gain. An isotropic antenna has a gain of 1, and
would need to be "pointed" in only one direction; an
antenna radiating uniformly into a hemisphere would
have a gain of two and would need to be pointed in two
directions. Similarly, any antenna radiating uniformly
into a solid angle _2 would have a gain 41r/[2 and would
need to be pointed in this many directions. Actual
antennas do not have a uniform gain inside a given solid
angle and zero gain outside, and the number of
directions in which we must point them depends on the
loss we are willing to tolerate at the edge of each area
covered by the beam.
If the aperture is circular the beam intensity is given
by equation (2), Chapter 5, and if Ord/X) 0 = 1 the loss
at the edges is about 1.1 dB. If we accept this as
tolerable then 0ma x = Xhrd and the solid angle covered
per beam is
\Ttd/
The number of resolvable directions is therefore
g
(5)
4_
N = _ = 4g
I'z
(6)
Our requirement of 1.1 dB maximum loss results in
four times as many pointing directions as would be
needed with a uniform conical beam.
Figure 6-4 shows N as a function of operating
wavelength for circular antennas of different diameters.
We see that N is a large number even for antennas of the
size we might use for array elements. For example, a
100-m dish operating at 20 cm would have l0 T fields of
view in the sky. Figure 6-2 indicates that out to 1000
light-years there would be about 1.7×106 slars of
interest in the sky. Even if we image the entire field of
view of the array element, we will have only 0.17 stars
of interest per field, on the average. With I 0-m dishes we
could average 17 stars per field, but we would need I00
times as many dishes to realize a given total array
diameter. The simultaneous searching of several stars
does not appear too feasible.
55