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?