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

"_ i i i i i
p = STELLAR DENSITY AT
DISTANCE 1"1 FROM
GALATIC
MID-PLANE
[) = STELLAR DENSITY ON
is a good approximation out to R _ 500 light-years. So
long as the cube law holds the range to which we must
search varies only as the cube root of p. A thousand-toone
uncertainty in p produces as ten-to-one uncertainty
P_o
.I
, o SOLAR
1o7
i I I I irT_--
CUBE
LAW_
/
/
/
/
/
10 6
.01 t I i I 1 /
0 1000 2000 30 oo
Figure 6-1. Empirical approximation for number of
stars per unit volume.
this relation to points taken from the reference. Thus we
find for the number n of stars within R light-years of the
Sun
n : Po f_ rr(R2-h2) --Po p
dh
i
10 2 ;
: 2npoho log +
ha 2
(3)
Taking ha = 850 light-years and Po = 5.4×10 -4
/(ligt't-year) 3 (thereby stretching the approximation to
include F0 through K7 stars) we obtain the curve shown
in Figure 6-2. Using these values ofn(R) in equation (1)
we plotted the curves of Figure 6-3. It is evident from
Figure 6-2 that the simple cube law
IO i
I I _ I i i i lllJ. L___.L__LLLLL___
IO t 10 2 10 3
RANGE, light years
10 4
4/T
n : Po--
3
R 3 (4)
Figure 6-2. Number of FO through K7 stars versus
range.
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