It's easy to forget how huge the Universe is...
Yeah, the numbers of planets is huge. But they're really, really, really far apart.
The fastest spacecraft at the moment is probably Voyager 1 at 17 km/s.
The speed of light is roughly 300,000 km/s.
The closest Earth-size planet found around another star thus far is 493 light years away.
It would take Voyager 1 a long time to get there:
493 * 300,000 / 17 = 8.7 million years.
It takes a lot of energy for significant mass to go fast. Unless practical controlled fusion or some other similar power source is available, the distance are simply too vast to get there because there isn't enough power.
What about radio and so forth? 1/r^2 is a killer. Signal power drop off at that rate. Double the distance and the signal strength drops by a factor of four. 100,000 watts is a lot for a US radio station. That's 80 dBm (dB relative to 1 mW). The minimum relatively easily detectable signal is -192 dBm (at 4K in space) - a ratio of 272. Increasing power by a factor of 10 increases the dBm value by an addition of 10.
So some quick math with a dBm calculator gives (ignoring all losses and only considering the 1/r^2 falloff):
100,000 W --- 80 dBm --- distance = 1
25,000 W --- 74 dBm --- distance = 2
6,250 W ----- 68 dBm --- distance = 4
1,563 W ----- 62 dBm --- distance = 8
So each doubling of distance cuts the dBm by 6.
0.0000000000000000000001 W is -190 dBm. 80 + 190 = 270 / 6 = 45 doublings. 2^45 = 3.5E13.
So if you're in space receiving 100,000 W at 1 km from the transmitter, you would be at the minimum detectable signal from that transmitter at 3.5E13 km = 3.7 light years. Anything farther away than that cannot be distinguished from noise. A factor of 4 in power only gets you a factor of 2 in distance, so it gets expensive quickly...
So the other civilization would need a big-honking transmitter to have any hope of another planet around another star detecting any radio signal they transmit.
Note that lasers have the same 1/r^2 falloff. Their advantage is they're directional, but that didn't affect the calculation above (I assumed I was detecting all of the power at the starting distance). Basically, you're painting the inside of a balloon. As the balloon gets bigger, the thickness of the pain[t] has to fall - less power.
With luck, there aren't too many errors in this - that would be embarrassing. ;-)
Bottom line: We may not be alone, but we're very unlikely to ever have contact with anyone else so we might as well assume we are (though looking and listening is not a worthless endeavor).
[edit:] Missing [t]
Cheers,
Scott.
The fastest spacecraft at the moment is probably Voyager 1 at 17 km/s.
The speed of light is roughly 300,000 km/s.
The closest Earth-size planet found around another star thus far is 493 light years away.
It would take Voyager 1 a long time to get there:
493 * 300,000 / 17 = 8.7 million years.
It takes a lot of energy for significant mass to go fast. Unless practical controlled fusion or some other similar power source is available, the distance are simply too vast to get there because there isn't enough power.
What about radio and so forth? 1/r^2 is a killer. Signal power drop off at that rate. Double the distance and the signal strength drops by a factor of four. 100,000 watts is a lot for a US radio station. That's 80 dBm (dB relative to 1 mW). The minimum relatively easily detectable signal is -192 dBm (at 4K in space) - a ratio of 272. Increasing power by a factor of 10 increases the dBm value by an addition of 10.
So some quick math with a dBm calculator gives (ignoring all losses and only considering the 1/r^2 falloff):
100,000 W --- 80 dBm --- distance = 1
25,000 W --- 74 dBm --- distance = 2
6,250 W ----- 68 dBm --- distance = 4
1,563 W ----- 62 dBm --- distance = 8
So each doubling of distance cuts the dBm by 6.
0.0000000000000000000001 W is -190 dBm. 80 + 190 = 270 / 6 = 45 doublings. 2^45 = 3.5E13.
So if you're in space receiving 100,000 W at 1 km from the transmitter, you would be at the minimum detectable signal from that transmitter at 3.5E13 km = 3.7 light years. Anything farther away than that cannot be distinguished from noise. A factor of 4 in power only gets you a factor of 2 in distance, so it gets expensive quickly...
So the other civilization would need a big-honking transmitter to have any hope of another planet around another star detecting any radio signal they transmit.
Note that lasers have the same 1/r^2 falloff. Their advantage is they're directional, but that didn't affect the calculation above (I assumed I was detecting all of the power at the starting distance). Basically, you're painting the inside of a balloon. As the balloon gets bigger, the thickness of the pain[t] has to fall - less power.
With luck, there aren't too many errors in this - that would be embarrassing. ;-)
Bottom line: We may not be alone, but we're very unlikely to ever have contact with anyone else so we might as well assume we are (though looking and listening is not a worthless endeavor).
[edit:] Missing [t]
Cheers,
Scott.
