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If a probe, equipped with a current state-of-the-art antenna, were to send data to Earth from Proxima Centauri orbit, what power would the antenna need to emit for the signal to be usefully readable on Earth, using our best reception antennas / radiotelescopes?

I know the power requirements scale quadratically with distance, but I don't have any good data points to extrapolate - e.g. we still have no problems receiving from Voyager 2, far as it is, so its antenna is well above the required minimal output level (and far from state-of-the art).

SF.
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Let's start with the basics, and work our way out to an answer. The distance to Proxima Centauri is about 40 trillion km. That leads to a power loss of 664 dB, an incredible amount. Compared to Voyager 1, which is currently about 20 billion km away, an increase in the channel power of 172 dB is required. That means making the signal 10^8 times more powerful to maintain the same level of power.

Okay, so what is the best that we could do? DSN uses a 70m antenna, Arecibo is a 300m antenna. That leads to about a 16 times increase in power. That covers a very small portion of the required power.

Let's assume somehow we had a 300m antenna on the spacecraft itself. Voyager's antenna is 3.7m. This is a 6500 increase in power, quite significant. Combined with the use of Arecibo, that would lead to a roughly 100,000 increase in power, or 100 dB. Of course, launching a 300m antenna is virtually impossible.

The bottom line is, this would be extremely difficult using RF power. Using visible is much simpler, as the required dish sizes are much smaller.

Bottom line, it would take an enormous increase in power to make interstellar communication possible, although

PearsonArtPhoto
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  • Original Voyager antenna being 19 watt, 10^8, about 2 gigawatts. With Arecibo, but no 300m antenna, we're down to ~0.5MW range, and we definitely can afford some antenna size increase. – SF. Jun 22 '16 at 12:09
  • Has enough research been done to establish what requirements might be needed for laser comms at that distance? – Jerard Puckett Jun 22 '16 at 14:19
  • The drop in dB is the same, but lasers have a higher dish/dB drop compared to radio waves. I can't find the exact size, but a mirror of a meter or so for the spacecraft and the size of a large telescope on Earth would be more than sufficient. Lasers require very accurate pointing, however, which is part of the problem. – PearsonArtPhoto Jun 22 '16 at 14:26
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    "launching a 300m antenna is virtually impossible" - actually, a stiff and well-aligned solar sail could be able to do the job. – asdfex Jun 22 '16 at 18:14
  • @asdfex: Probably even larger; especially that with 300m the power densities involved could be still harmful to the sail. – SF. Jun 23 '16 at 01:14