# Is there good estimates/measures on the variables that make up the Fermi paradox?

Here's what I've got:

Universe size: Milky way is 100,000 LY wide. Nearest galaxy is 2.2m LY away.

Number of stars: about 300,000,000,000 in the Milky way. 100,000,000,000 galaxies.

Age of universe 13.8 billion years. Earth is 4.5 billion years old. Life on earth 3.5bn years.

Now I was thinking about the Fermi paradox.

Basically two variables I can think of that determine whether other life could find us.

• Probably that life is on another star.
• Time it takes them to get here.

So for example, say there's a 1/1,000,000 chance that there's life on another planet. (Life at least as intelligent as us).

That leaves only 300,000 other civilizations in our galaxy.

Now say they're 100,000 light years away. Then they have to be travelling at least 1/35,000 speed of light in order to have reached us in the last 3.5billion years. That's it's 30000km/hr, or ~Mach 25.

Now of course using the same probability of life on other solar systems, you can extend it to other galaxies to vastly increase the number of other civilizations.

But that requires increasing the minimum speed they can travel. They'd need to travel ~200 times faster in order to get here, or 1/175 the speed of light, just to have reached us within the last 3.5 billion years.

Now obviously my maths is very rough (and please edit if I've made obvious major errors!).

But it doesn't seem that unlikely that if life is relatively rare, that other life simply hasn't had the time to find us yet.

The question I have is, what's realistic for achievable interstellar/galactic travel speeds, and probabilities of life on other planets?

## 1 Answer

It is actually the Drake Equation that applies best to this. The Fermi Paradox framed the issue, the Drake Equation tries to wrestle it into an analyzable framework.

This io9 article gives an idea of what we are facing when we try to narrow down the possibilities here. It is an extremely compelling matter for which we have no data points. We don't even know enough to narrow down what a habitable planet is, or what modes of transportation exist. We can say nothing about the motivations of other possible intelligent beings.

The Drake equation is:

$N = R_{\ast} \cdot f_p \cdot n_e \cdot f_{\ell} \cdot f_i \cdot f_c \cdot L$ where:

$N$ = the number of civilizations in our galaxy with which radio-communication might be possible (i.e. which are on our current past light cone); and

$R*$ = the average rate of star formation in our galaxy

$fp$ = the fraction of those stars that have planets

$ne$ = the average number of planets that can potentially support life per star that has planets

$fl$ = the fraction of planets that could support life that actually develop life at some point

$fi$ = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

$fc$ = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

$L$ = the length of time for which such civilizations release detectable signals into space

Virtually nothing definite can be said about the last five factors of the equation.

Star formation rate is estimated as something near 10 per year, but there is still a lot of uncertainty about that, including whether the rate is constant or has bursts. We now think most stars have at least one planet and roughly one-fifth of Sun-like stars have Earth-like planets in their habitable zones. (Though 'Earth-like' and 'habitable' are stretched to include a rather broad range.)

N deals with civilizations that can communicate, not that can come see us in person, but even here it could be argued that they definition is too narrow. For all we know, if you are advanced enough, there is a way to get around the speed of light.

So really, no, there aren't good estimates for the variables involved. We probably haven't even identified all the variables. But that is no reason not to give the matter a lot of serious thought. If you would like to continue looking at it, astrodigital has a spreadsheet you can download.

• On current evidence (granted from only one instance), L seems likely to be much less than 1000 years. – jamesqf Apr 21 '15 at 19:53
• @jamesqf You are assuming we aren't going to keep sending out a discernible EM signal for many millennia to come. – kim holder Apr 21 '15 at 20:40
• Not assuming, deducing from available evidence, all of which points to a P-T level extinction event within 500 years or s. – jamesqf Jul 2 '15 at 19:04
• @Jens What the phrase 'For all we know' means is that our knowledge isn't sufficient to discount the possibility. So, it means what you said. – kim holder Sep 26 '19 at 22:11
• @kimholder Then sorry for misinterpreting. I can only blame my English teachers :-) – Jens Sep 27 '19 at 7:54