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

1. Wewillnothavenough resolving power toseparate
theplanetfromthestarat thedistances involved.
(OneAU subtends1 arcseeat a distanceof 1
parsecor3.26light-years.)
2. Evenif wehadtheresolution, wewouldnotknow
thepositionof theplanetrelativeto thestarand
wouldnotliketo addanotherdimension to the
search.
Asa resultweneedto determinehowmuchnoisethe
staritselfadds.
Oneconvenient measureof the starnoiseis the
increase
systemnoisetemperature it produces. This
temperature increase isgivenby
TABLE 5-1
_, T o (quiet) T o (active)
1 cm 6000°K 7000°K
3.16 1.6X 104 6X 104
10 5X 10 4 1.5X10 6
31.6 1.7X lO s 4× 107
100 5× 10 s 8× 10 a
If we assume an antenna diameter of 10 km and take
d, = 1.392×109 m and R = 9.46×1016 m = 10
light-years, we derive from equation (22) the values of
AT given in Table 5-2.
1 T(O #)g(O ,_)sin 0 dO d_
AT = 4r¢
=0 =0 (21)
where
T = temperature of field of view
g = antenna gain
The quantity AT is simply the average over all sources
in the field, with each direction weighted according to
the antenna gain in that direction. For a star on axis,
g(0,¢) will be constant at the value 4rtA,J_ 2 from 0 = 0
out to 0 = d,/2R, where d, is the diameter of the
star and R is the range. Over this same range of 0, T(0,q_)
will have the value T,, then drop to the normal
background value (which we have already included) for
0 > d,/2R. Thus for a star
AT = _ 27rAQ - cos d) T, _47_2R-------- lrdZ, Ar T- T, (22)
AT
A*Ar
T, _2R2
where A, = rid, 2]4 is the projected area of the star. This
relation has a familiar appearance; it is the free space
transmission law with A, now playing the role of the
transmitting antenna aperture area and T replacing
power.
The nearest stars of interest are at about 10 lightyears
range. Let us therefore compute AT for the sun at
a distance of 10 light-years. Because of its corona and
sunspot activity, the Sun's effective temperature at
decimeter wavelengths greatly exceeds its surface temperature.
From curves published by Kraus (ref. 2) we
take the following values to be typical:
TABLE 5-2
;k AT (quiet sun) &T (active sun)
1 cm 0.8 ° K 0.93 ° K
3.16 0.214 ° K 0.8 ° K
10 0.067 ° K 2° K
31,6 0.023 ° K 5.3 ° K
100 0.0067 ° K 10.7 ° K
We conclude that for antenna diameters up to 10 km
and for stars beyond 10 light-years, star noise at
microwave frequencies, though detectable, will not be a
serious problem unless the stars examined show appreciably
more activity than the Sun.
The ability of Cyclops to detect normal stars is
studied in Appendix R. We estimate that the 3-km
equivalent array should be able to see about 1000 stars
at h = 10 cm and about 4000 at X = 3.16 with a 1-min
integration
time.
Another measure of star noise, and a particularly
convenient one for determining the radiated intensity
necessary to outshine the star, is the total radiated
power per Hertz of bandwidth. Since this measure will
be important in the optical and infrared part of the
spectrum, we may assume that only blackbody radiation
is involved, The total flux radiated by a star having a
diameter d, and surface temperature T, is
2rr2 d2, hv 3
qb(v) = W/Hz (23)
c2 ehU/kT_l
Figure 5-3 is a plot of this function for the sun. We
see that to equal the brightness of the sun the total
power of an omnidirectional beacon (or the effective
radiated power of a beamed signal) at 10_t would have
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