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The Inverse Square Law

The ultimate goal of SETI is to detect the presence of an intelligent, communicating extraterrestrial life form. To do that, we expect that we will need to detect electromagnetic radiation, such as radio signals or laser pulses. How difficult will it be to detect these signals?

Radio signals, light, sound, and many other phenomena obey the Inverse Square Law. Stated simply, this law says that the intensity of a signal is dependant on the square of our distance from the signal's source. If we move twice as far away from a radio tower, our radio receives a signal only 1/4 as strong as we initially saw. If we see a flashlight from 100 meters away, and then move to 300 meters (3x as far), the light that falls on our eyes will be 1/9 as strong as before.

The most powerful radio transmitters on Earth send out signals at about 250,000 Watts. Standing 100 meters from that radio transmitter gives an intensity of roughly 200 Watts per square meter. If we moved to 10 kilometers (100x the distance) we would see a signal of just 0.02 Watts per square meter, still more than enough to detect.

In fact, a talented amateur can build a radio telescope with a sensitivity to detect 1023 watts per square meter! With such a radio telescope, we could detect much more distant signals. How far away could we detect our powerful radio station?

The telescope is 2x1024 times as powerful as it needs to be to detect our transmitter at a distance of 100 meters. By the inverse square law, we could move 1.4x1012 times as far away, for a total distance of 1.4x1014 meters, and still detect our radio signal very faintly.

140 trillion meters - that's 87 billion miles! This distance sounds like a lot, and it is... but compared to the distance between stars it's very small. That large distance is only 0.015 light years. The nearest stars are over 4 light years away.

Large scientific radio telescopes are many times more sensitive, but every 100x increase in sensitivity leads to only a 10x increase in distance. We could make a telescope a million times more sensitive and only be able to hear the strongest signals from 15 light years away, a tiny distance on the galactic scale.

The inverse square law is one of the things that makes it very, very difficult for us to detect signals from another civilization. Those signals must be broadcast very strongly, and we must listen very closely, if we are to have a hope of detecting them.

You will have an opportunity to practice with the Inverse Square Law on the homework.

Солнечная система и ее тайны