There is perhaps no more compelling question for mankind than, are we alone in the universe? Given the odds, with billions of stars in our galaxy similar to our sun and billions of planets orbiting them, it seems unlikely. But, as Fermi's paradox asks, if aliens do exist, why haven't we found any evidence of them yet? Astronomers at Cornell University have done the sums to provide an estimate of when we might expect a call from ET, but don't worry about marking the date on your calendar – they believe contact isn't likely for another 1,500 years.

Setting aside the theories that extraterrestrial life might commonly emerge but not thrive, or that maybe we should avoid making contact altogether, the idea of discovering life on other worlds is one our world is fascinated with. So why isn't our curiosity being reciprocated?

"We haven't heard from aliens yet, as space is a big place – but that doesn't mean no one is out there," says Evan Solomonides, a student at Cornell University. Solomindes, along with Professor of Astronomy, Yervant Terzian, deconstructed Fermi's paradox and coupled it with the mediocrity principle – which suggests that Earth isn't all that special in the universe – to arrive at the disappointing 1,500-year time frame.

One factor taken into consideration is the rate at which our broadcast signals are traveling through the Milky Way. For the last 80 years or so, we've been indirectly announcing our existence to the universe as a result of beaming TV and radio signals into space, meaning those signals have reached every star and planet within 80 light-years of Earth. That's around 8,531 stars and 3,555 Earth-like planets, and yet, we haven't heard any response.

And although that might sound like a lot of planets, it's barely a drop in the ocean. The Milky Way contains around 200 billion stars, with estimates there could also be billions of Earth-like planets. This is the mediocrity principle, which Carl Sagan once summed up in a beautiful but depressing thought: "We find that we live on an insignificant planet, of a humdrum star, lost in a galaxy, tucked away in some forgotten corner of a universe in which there are far more galaxies than people." With that in mind, it might just be that aliens can't find us. We need to give them time.

So why have the researchers penciled in humanity's first date with extraterrestrials for the middle of next millennium? By combining the Fermi paradox and the mediocrity principle, they calculated that we will most likely have a response by the time our radio signals have spread across half of the Milky Way, circa 3,500 CE.

"It's possible to hear any time at all, but it becomes likely we will have heard around 1,500 years from now," says Solomonides. "Until then, it is possible that we appear to be alone – even if we are not. But if we stop listening or looking, we may miss the signals. So we should keep looking."

Obviously, that isn't a hard-and-fast time limit, and the researchers are clear that even if ET stands us up on that date, it doesn't mean we'll be alone forever.

"We simply claim that it is somewhat unlikely that we will not hear anything before that time," Solomonides says.