# 地球必須發出多少電磁傳輸噪聲才能引人注目？ - How much electromagnetic transmission noise does Earth have to emit to be noticeable? -开发者知识库

From time to time I'll see things talking about how thanks to all of our radio communications, we're effectively broadcasting our existence to the entire universe. However, when I did some back-of-the-envelope calculations a while ago I found something interesting - by the time a radio station's broadcast reaches Alpha Centauri (the solar system closest to ours), ignoring any effects of our atmosphere, a 1 m^2 receiver would, on average, receive a single photon every seven hours. Of course that is only a single radio station, but throwing more radio stations into the mix would just make the signal less coherent and indistinguishable from random noise. When you consider the sun as well, it seems like all of the Earth's radio signals would be a drop in the bucket.

How much noise would the Earth have to broadcast in order to change that? For this question, the goal is for the noise broadcast from Earth to still be noticeable by the time it reaches a distance of 500 light years (that only covers about 0.01% of the galaxy). You can assume that alien civilizations are looking for signals of intelligent life, but not that they are focused on our solar system.

## 1 个解决方案

### #1

8

First off, this question is just the inverse of this question. So, apologizes to MichaelKjorling, I'm going to crib his answer to get some results.

# Assumptions

• In order to be noticeable at 500 light years, we need to be able to detect us at that distance.
• 為了在500光年處注意到，我們需要能夠在那個距離探測到我們。

# What is the attenuation over 500 light years?

Free space path loss in decibels (dB) is given by

$$20\log_{10}\frac{4\pi d}{\lambda}$$ where $d$ is the distance between antenna and $\lambda$ is the wavelength of the frequency in question.

$$20 \ log_ {10} \ frac {4 \ pi d} {\ lambda}$$其中$d$是天線與$\ lambda$之間的距離，是所討論頻率的波長。

In the US, the highest energy general transmission (as far as I can tell) are UHF stations in the 512-608 MHz range. This may be an important thing to revisit; emission into space is determined heavily by directional broadcasting characteristics. But we'll just use this assumption for now and say that the wavelength is 0.5 meters. Meanwhile, 500 light years is $4.7\times10^{18}$ meters.

Plugging into the equation above, free space path loss is 401 decibels. That is a lot! This means power is $10^{40}$ lower at the receiver than at the emitter.

The rating of a receiver is the smallest signal that it can pull out of the noise background. Following MichaelKjorling's answer, assume that an alien civilization specifically searching for us can detect the signal at -200 dBm. In addition, assume a 80 dBi antenna gain from a dish like Arecibo.

# How much noise do we have to put out?

Free space path loss is -400 dB; antenna gain at a foreign civilization is 80 dB and the signal detection threshold is -200 dB. Therefore, signal emission strength must be 120 dBm at the source to make it detectable. This is equivalent to $10^{12}$ mW or 1 GW of emission power.

# Conclusions

The Earth is almost certainly not gong to reach this power level. WBCT is the most powerful FM radio station in the US, with effective radiated power of 320kW, or about 85 dB. But this dish is not pointed into space, and so its emissions are further attenuated by the atmosphere before reaching into deep space. There is really no reason to increase the power of such a dish, becase it already has plenty of power to reach the horizon. Any direct signal's line of sight is limited by the horizon; once past the horizon the signal no longer reaches the surface and coverage moves up into the atmosphere, where it isn't really useful.

Furthermore, if you start increasing the emission power of lots of different radio communications methods, then they will start interfering with each other. A 120 dB signal emerging from the earth's atmosphere will bounce of the moon and back to Earth at a much higher power than it will reach 500 light years away.

So, all in all, the Earth is unlikely to ever emit enough noise to reach a planet 500 ly away. Now, a directed signal is another story...

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