From: utzoo!decvax!harpo!eagle!karn
Newsgroups: net.space
Title: Re: RE: Pioneer 10 Transmissions
Article-I.D.: eagle.921
Posted: Thu Apr 28 00:26:05 1983
Received: Thu Apr 28 19:23:08 1983
References: <1575@ihldt.UUCP> alice.1781

I just did some calculations on Pioneer's likely maximum range.
I had to make some educated guesses on numbers, so my conclusions may be
somewhat off; if anyone has the correct figures, let me know and I'll
update my calculations.

Receiving station assumptions:
200' dish, 50% illumination efficiency (half the intercepted energy is lost)
8 GHz operating frequency; wavelength = 3.75 cm
50 degree Kelvin receiving system temperature T (good, but probably worse
than the real figure)
100 Hz receiver bandwidth B (assuming a pretty slow data rate)
A 10 db signal-to-noise ratio is required (probably too high)

Such a dish would have a gain of +71 dbi (decibels above an isotropic or
"point source" antenna).  The receiver would have a noise floor of
KTB = 1.38E-23 * 50 * 100 = 6.9E-20 watts, or -191.6 dbW. (K =
Boltzmann's constant)

Pioneer 10 assumptions:
8 watt transmitter output = +9 dbW
5' dish with 50% illumination efficiency == +39 dbi gain
EIRP (effective isotropic radiated power) = +9 + 39 = +48 dbW

Maximum allowable path loss X would therefore be

+48 dbW - X + 71 >= -191.6dbW + 10; X <= 300.6 db

The path loss in db is given by 

22 + 20*log(distance in wavelengths)

Solving for distance, we get 7.9E13 wavelengths, about 3E12 meters
or 10,000 light-seconds.  Pluto's orbital semi-major axis is about
5.9E12 m, so I'm at least in the right order of magnitude.
Keeping everything else constant, the signal-to-noise ratio
decreases by 6 db for each doubling of the distance, i.e., going to 6E12
meters would decrease the signal-to-noise ratio to 4 db.
In any case, I'm sure that they don't have a lot of signal to spare,
and that contact couldn't be kept with such a system very far outside
the solar system even if the isotope generator were to last
indefinitely.  On the other hand, if you were to use the Arecibo dish...

Phil