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

APPENDIX
R
RADIO VISIBILITY OF
NORMAL STARS WITH
CYCLOPS
Broadband radiometric techniques permit the meas- B =
urement of very small increases AT in the system noise
temperature T. If the RF bandwidth is B and the output r =
is integrated for r sec the rms fluctuation in the readings then
so obtained
will be given by
2× 10s Hz (both polarizations used)
60 sec
T
o = _
V-T
(R1)
R = 2.75X10 -l° d, T, light-years
;k 6+ Ts
(R3)
The conventional limit of detectability is taken as AT = o.
This corresponds to setting SIN = 1 in equation (D15).
From equation (R1) and equation (22), Chapter 5, we
find the range limit to be
RADIO RANGE OF THE SUN
Substituting d o = 1.392X109 meters for d, in
equation (R3) gives
7rd,dr(T, II/2 1/4
R = ------_\-_--] (Br) (R2)
R o ....
0.3825 (_._ To I 1/2
(R4)
X + Tsky ]
where:
dr = receiving antenna aperture
d, = diameter of star
T, = effective temperature of star
X = radio wavelength
If we take
dr = 104m
T = 16 + Tsk_
for the range at which the Sun could be detected. Using
the values of To(h ) and Tsky(X ) given in Chapter 5, we
obtain the ranges in light-years given in Table R-1. These
data have been plotted in Figures R-I and R-2 using
antenna aperture as the abscissa.
TABLE
R-I
X(cm) R o (quiet) R o (active)
1 380 410
3.16 310 595
10 190 1047
31.6 107 1630
100 29 1170
241