While some might take the total absence of contact from aliens as a rather bleak sign that our search for extraterrestrial life is all in vain, a new study explains why we shouldn't give up hope just yet – we just need to exercise a little patience.

Or maybe a lot of patience, because the sheer size of the Milky Way means it could be up to 1,500 years before we can reasonably expect to hear back from any extraterrestrials who've picked up our transmissions from Earth, say astronomers. In the meantime, we should probably all just chill out a little, and not jump to any hasty conclusions about being all alone in the dark.

"We haven't heard from aliens yet, as space is a big place – but that doesn't mean no one is out there. It's possible to hear any time at all, but it becomes likely we will have heard around 1,500 years from now," says astronomy student Evan Solomonides from Cornell University.

"Until then, it is possible that we appear to be alone – even if we are not," he adds. "But if we stop listening or looking, we may miss the signals. So we should keep looking."

Solomonides is co-author of a new paper being presented this week at a meeting of the American Astronomical Society in San Diego, California. The study is a probabilistic analysis of what's known as the Fermi paradox, using calculations to help shed some light on why we might never have received contact from alien civilisations.

Named after Italian physicist Enrico Fermi, the Fermi paradox highlights just how strange it is that we haven't yet heard from aliens. After all, scientists estimate there could be somewhere between 100 billion and 400 billion stars in the Milky Way, and it's highly probable that many of these stars would host Earth-like or habitable planets capable of sustaining life.

To extend the Fermi argument, it's also likely that some of these life forms might develop into intelligent or advanced species, capable of developing powerful communications technology or travelling into space, much like humankind has. If we accept these things, the paradox becomes clear.

"Even our mundane, typical spiral galaxy – not exceptionally large compared to other galaxies – is vast beyond imagination," says Solomonides. "Those numbers are what make the Fermi paradox so counterintuitive. We have reached so many stars and planets, surely we should have reached somebody by now, and in turn been reached … this demonstrates why we appear to be alone."

But the appearance of being alone isn't the same thing as being alone, the researchers suggest. After all, human broadcasts that are capable of being picked up throughout the Milky Way have only been transmitted for 80 years – in the form of TV and radio signals.

These signals would propagate outwards from Earth in the shape of a sphere, the researchers explain, and while they would travel at the speed of light, since they've only been broadcast for 80 years, that means our transmissions would have only reached a radius of 80 light-years from Earth. To put that in perspective, 1 light-year is around 9.5 trillion kilometres (5.88 trillion miles).

That might sound like a fair stretch to you and me, but the researchers' analysis indicates otherwise in terms of the overall expanse of the galaxy, suggesting that any signals we've sent into space would not have yet reached enough stars and planets such that we should expect an answer.

"[We] conclude that the Fermi paradox is not, in fact, unexpected. By the mediocrity principle [which suggests life would not be unique on Earth] and numerical modelling, it is actually unlikely that Earth would have been reached by extraterrestrial communication at this point," the authors write in their study. "We predict that under 1 percent of the galaxy has been reached at all thus far, and we do not anticipate to be reached until approximately half of the stars/planets have been reached."

Assuming the Milky Way contains 200 billion stars, the researchers calculate our signals have reached some 8,531 stars and 3,555 Earth-like planets so far, but they don't think that's enough to expect a response just yet. But within the next 1,500 years? Yep, that's more likely, they think.

"This is not to say that we must be reached by then or else we are, in fact, alone," said Solomonides. "We simply claim that it is somewhat unlikely that we will not hear anything before that time."

While 1,500 years might seem like an interminable period for humanity to have to wait, the positive spin is that, hey, at least if this research is sound, we might understand a little better why we haven't been contacted by advanced civilisations before now. And on the terms of this analysis, it's looking more likely that we'll hear from aliens someday, if not quite tomorrow.

"Though the Fermi paradox is undeniably counterintuitive, this paper is offered as an argument that it is not, in fact, unreasonable that we have thus far appeared to be alone," the authors write. "We may very well be reached someday. In fact, by the mediocrity principle, we should expect to be. But that day is not now, or any time in the immediate future."

The paper is now available on pre-print website arXiv.org ahead of being peer-reviewed for journal publication.