# Voicemail for ET Service(Racket)?

The intention is to deliver voice messages to the stars. If you assume a voice message carries information at a data rate of C bits per second, doing the calculation of how far, D, the message can travel before it cannot be received at that rate gives the following expression:

D2 <= 2 &pi 2 P (Rr Rt/&lambda)2 /C N0

Where D is the distance, P is the transmitted power, Rr is the radius of the receiving antenna, Rt is radius of the transmitting antenna, &lambda is the radio wavelength used and N0 is the noise level of the receiver. This is a BEST case scenario.

Cell phones code voice in the neighborhood of C = 10,000 bits/second. So let's take this as the minimum data rate that can support voice communications -- cell phones are extremely stingy with spectrum and try to pack voice signals into as little space as possible. So this figure is a reasonable lower bound.

According to the web site, Rt is approximately 2 meters and &lambda is about 0.125 meters. Let's assume an Arecibo-sized listening antenna on the other end (Rr = 150 meters) that's chilled down to 3 degrees Kelvin. Plugging all that in gives:

D <= (1.7 X 1013) sqrt(P) meters

Now, let's assume that they're transmitting at a whopping P = 1 Megawatt. The signal will only be received properly about 2 lightyears away (a LY is about 1016 meters). However, it turns out that the actual FCC Part 15.247 rule under which they are operating allows only one watt of radiated power, so the actual distance is one thousand times less -- roughly four times the distance from the sun to pluto. And if I remember correctly, the nearest star is about 4 light years away.

One must remember that the above is a best case scenario.

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