If there was an earth-like populated by a species exactly as advanced as humans are today, how close would they have to be for us to detect them, and vice versa?
“Earth-like” should have been followed by “planet” in the OP.
That depends on whether they (we) are deliberately trying to make contact, or just going by incidental radiation.
The incidental answer is “we can’t, even if they were at the nearest star”.
You might do some reading on SETI (Search for Extraterrestrial Intelligence):
https://en.wikipedia.org/wiki/Search_for_extraterrestrial_intelligence
Obviously “it depends”. The OP is asking how possible it is given the best circumstances.
Oh, then it doesn’t matter at what the circumstances are.
That’s the answer for incidental radiation (like picking up on ordinary TV broadcasts). We could do it if we were actively trying, but then you have to ask how much resources we’re trying with. And also depends on us aiming our antennas at each other to fairly high precision.
Given that we are both actively trying with direct antennas, how far away could we detect them?
Given that they are like us with satellites and broadcast media, how far away could we detect them if we were looking in the right place?
But that involves another assumption. That the other intelligences are even aware of the universe outside of their own planet.
We live on a planet with partial cloud cover that allows us to think about the stars, what they are and who might be out there.
Intelligences of an aquatic planet with life or one with permanent cloud cover might never even be curious about the outside.
I’m pretty sure that if they’re at the same stage as us, they’d be curious about what you find when you go up. After all, we’ve been in the Marianas Trench [/straightline]
Since they’re “exactly as advanced as humans are today,” they’ve already broken through any water/air or cloud barriers, and have already explored other planetary objects in their system, if any.
Since humanity seems intent on suicide, I’d say no comparable civilizations will last long enough to contact another.
The hard upper limit is however long they’ve been sending signals off-planet, so if they’ve been sending out radio signals for 100 years then 100 light years is the cut off. In reality, any signal would become indistinguishable from background noise well before that.
There are various scenarios, with widely-varying detection ranges: incidental RF leakage, intentional directional RF beams, intentional laser communications aimed at specific star systems, etc.
At a given level of technology it varies based on funding. E.g, the proposed Cyclops radio telescope system could supposedly detect 1000 megawatt beacons out to 1000 light-years or eavesdrop on the electromagnetic “garbage” of technical societies out to about 100 light-years: 24.2.5 - SETI: Yesterday and Today
The 100-meter-diameter Green Bank radio telescope and 64-meter Parkes dish in Australia are currently engaged in a 10-year search for extra-terrestrial signals. It’s detection capability is described as “If a civilization based around one of the 1,000 nearest stars transmits to us with the power of common aircraft radar, the GBT and the Parkes Telescope could detect it.”
100-meter Green Bank dish: https://public.nrao.edu/wp-content/uploads/2013/09/gallery-images-largeGBT_4_large.jpg
64-meter Parkes Australia dish: https://upload.wikimedia.org/wikipedia/commons/0/00/CSIRO_ScienceImage_4350_CSIROs_Parkes_Radio_Telescope_with_moon_in_the_background.jpg
The current Veritas optical search could detect extra-terrestrial laser communications using technology similar to ours out to about 1,400 light years: Breakthrough Listen's new search for alien lasers | Space | EarthSky
Re unintentional RF leakage signals from earth, there have been widely varying estimates of detection ranges by extra-terrestrials if using our own technology levels:
“Dr. Seti” (Dr. H. Paul Shuch) estimates 1,000 light years: Ask Dr. SETI: How far can we hear?
However Dr. Seth Shostak estimates only 1 light year: http://www.universetoday.com/10229/dr-seth-shostak-answers-your-questions-about-seti/
I don’t know why the wide range of estimates by people working in the field. One may be using unintentional TV signal leakage (so-called “I Love Lucy” case), and the other unintentional cold war radar. In the TV case, the AM TV signals were transmitted continuously using several thousand watts, and were mildly directional in a horizontal plane. IOW the radiation pattern was designed to not go into space.
In the case of cold war missile-detection radar systems, they were essentially beamed straight into space at extremely high power levels. The Cobra Dane radar transmitted at 15.4 megawatts peak, and similar radars had an approx. 3db beam width of 2 degrees. That is fairly broad vs a 100-meter steerable dish, but it’s still 42 db gain, which would equate to roughly 193 gigawatts peak effective radiated power.
I don’t know what the max RF input power is for Arecibo, but that 300-meter dish would produce about 71db gain at 1.4Ghz (21 cm hydrogen). If 15.4 megawatts input was used, the effective radiated power would be about 193 terawatts.
Another major difference in detection capability over the years is not the antenna or modulation but increasingly sophisticated techniques for extracting weak signals out of background noise, and over a wide range of frequencies. In the real world it’s very different than listening on headphones, as depicted in the movie “Contact”. It’s more like the Large Hadron Collider where oceans of data are produced, filtered and analyzed over long periods by supercomputers.
LHC computer room: https://cds.cern.ch/images/CERN-CO-1207154-01/file?size=large
Calulators:
https://www.satellite-calculations.com/Satellite/gain_bw.htm
http://www.sengpielaudio.com/calculator-amplification.htm
To be clear, in Contact, Dr. Arroway was not listening to the headphones for any scientific purpose. She was doing it because she felt like it, because she found the white noise relaxing. Until the day it turned out to not be white noise.
Earth has a buttload of satellites and assorted space-junk orbiting it. Could we look at a similar planet and think Hey, that’s not natural?
We cannot even see entire planets in other solar systems. (They have all been detected indirectly, not by imaging them.) We certainly could not see satellites around them.
I was thinking more along the lines of what the satellites blocked or reflected, like light from the star or natural radiation from the planet.
They’d have to be humongously bigger than any satellite we’ve ever launched. In other words, a megastructure. That was the wild speculation about Tabby’s star, but it’s since been shown to most likely be caused by dust.
Could we use spectroscopy to detect industrial pollution? Are things that are unlikely to be natural, CFCs for example, detectable at a distance?