Finding a Twin Earth – Part 2 – The Odds

Part Two

Image credit – ESAHubble, M. Kornmesser

In this blog and an earlier post, I’m discussing the process of finding a twin Earth. This is part of a lengthy series devoted to the following: How are humans going to power the ships that escape to other planets? How fast will they go? How long will it take to get there? What will we find when we get there?

As we learned in Prometheus Blue, the Earth is doomed to the fate of a rogue star and as I have proven, there’s no way to stop it. Our only option is to get out of Dodge. We’ve got to go about finding a new Earth and evacuate our poor planet well before the end comes in 2713.

Here’s where I keep a running tab on those challenges and our discussions:

Finding, Getting To and Living On a New Earth

• Where would we go? The ExoPlanet Search – Finding a new Earth;
• Finding a Twin Earth Part 1 – What are the conditions we must find in a candidate planet that will enable humanity to thrive?
• Finding a Twin Earth Part 2: The Odds – What are the odds that we will find a twin Earth among all the candidates found so far?
• Drive Technology – Developing transport technology to get there, including fuel type;
• Testing and Simulation – How to best prove out our theories? Start with Mars;
• Sustainability – Carrying and manufacturing enough food, water, air and fuel for the journey. Surviving cosmic radiation;
• Ship Design – What is the best design for long term travel? How to survive micro-collisions?
• Funding – Who is going to pay for it?
• Getting Around – Traveling around the local system when we get there – the fuel, engine type we used for long distance travel may not be suitable for in-system maneuvering;
• What if we’re wrong? Confirming we have the right place (when we get there). Can we detect all critical factors from Earth?
• Establishing a Home. Building a sustainable life once we get there – grow food, build shelter, manufacturing, technology, 3D printing, etc.;
• Who Goes and How Many? Considering skills, age, health, propagation and the gene pool. Attrition during voyage and after we get there.
• Back home – Closer to impact date, implementation of birth controls, long term managed selection process.

In the last entry, Finding a Twin Earth – Part One, I laid out 12 major factors that might affect the conditions for a thriving human colony. Many of them could be wildly wrong, but I estimate that our chances of finding a twin Earth, suitable for thriving human life and within our “local space” of 50 light-year radius is about one in 35,000.

Follow me on this epic journey of my twisted logic.

First, we have to determine the likelihood that all 12 of these factors line up. Let’s not forget that there are probably more factors out there that I’m missing, but stick with me.

As it turns out, a famous scientist name Frank Drake made a pretty good attempt at trying to determine the probability of finding intelligent life in our galaxy. It’s not quite what we’re trying to do here, but the methodology is useful.

First, a bit about Dr. Drake. He was the first person to attempt to create a map of the center of the galaxy. He coined the term ‘pulsar’. He was one of the founders of the SETI endeavor. Some of you might remember when SETI was the coolest screen saver in the early two thousands. You would sign up and receive a packet of radio telescope data. Your computer would crunch through it, looking for non-random patterns i.e. signs of intelligence. When your packet was fully analyzed, your computer would send it in and get another. The screen saver showed the data crunching in graphical ways to impress your friends. I had it on every computer I owned.

Anyway, Frank Drake invented the Drake Equation. His equation was actually meant to predict the presence of intelligence life on other planets, so not every one of his factors applies to a search for a planet that might support life. He took several factors of probability and multiplied them together to get a very tiny likelihood of finding intelligent life. He then multiplied that by the estimated number of planets in the galaxy to get his estimated number of planets supporting intelligent life. His end results are not really that important because the factors change so frequently and so his results were almost certainly wrong. But it’s his methodology that I’m interested in.

Call it the New Earth Equation. Simply stated: what is the probability (P) that any one planet that we find will be suitable to sustain human life? Let’s take one example to illustrate the equation. Factor one – temperature profile (TP). Let’s say the possible ranges of temperature on a planet are from Mercury to Uranus or 427 degrees C. to minus 224 degrees C. That’s a 651 Celsius degree range. OK. Now what’s the practical range for humans to thrive? I would say 50 degrees C at the top end (and that would be very uncomfortable). And maybe minus 10? Of course, being a Canadian, I’ve lived in 40 below (hello Winnipeg), but humans and life can’t thrive in that climate. If the average is minus 10, we have to have a significant period where it’s above freezing for life-giving water to flow. So let’s say our outside range is 60 Celsius degrees. That means that our range for thriving life is only 9.2% of the possible. So we’ve already, with one factor alone, eliminated nearly 91% of our candidate planets.

See where I’m going with this?

Borrowing from Drake, we might get:

Probability P = TP x LW x LP x PS x SS x SSS x OZ x MS x MN x GR x DIV x JS

Here is the link to what each factor represents. e.g. TP = Temperature Profile, LW = Liquid Water, etc.

Clearly this is going to be a very small number. This is the likelihood that any single planet that we encounter (be it via TESS – the Transiting Exoplanets Survey Satellite – or while tripping through space in our beautiful new fusion rocket system) will provide a thriving, sustainable environment in which to live.

And it will be wrong, because after all, we can’t estimate all these factors for certain. For example, we can’t tell yet how many planets might have a magnetosphere.

But we have to start somewhere. I’m also going out on a limb by saying that most of the factors are likely even lower than 9.2%. The presence of liquid water for example, might be less than 1%. But I’m going to be pretty generous with the individual probability factors to see where that leaves us.

Let’s manipulate a bit. Let’s say finding a gravity range, having a Jupiter or Saturn, an ozone layer and a single star system are each 20 percent. Maybe predators on most planets would be very rare, so give it 99% probability that they don’t exist. Plus a few others.

Play around some more. Here’s a table:

This is the probability that any one planet that we find would have all the factors that would enable humans to thrive. We’re up to 7 X 10^-10. About 1 in 1.4 billion. Looking good!!

But that’s for the WHOLE GALAXY. So how many candidate planets might that work out to? Remember how big our galaxy is. Our home galaxy is something like a hundred and five thousand light-years across. So there’s got to be a lot of planets. Here’s a guess:

All right. In our galaxy, there might be 505 planets that could allow humans to thrive. If you believed all the math above, there might be 505 Twin Earths out there.

Here’s where the numbers get ugly, yet again. Our galaxy is a very, very big place. The Milky Way is around 105,000 light-years across, maybe 1,000 light-years deep with a 12,000 light-year bulge in the middle. I did the math (surprise!!). Here’s how big our galaxy is:

All right. Stay with me. Let’s say over the future centuries, humanity will be able to travel to the stars, despite the immense distances. But unless we invent some kind of warp drive, let’s imagine that our exploration radius over the next several hundred years is 50 light-years. So that’s a sub-set of the entire Milky Way obviously. How small? Well, only about a half million cubic light-years. I make that out to be only 1 part in 18 million. Local space indeed.

So if we look at what proportion of the galaxy our 100 light-year sphere of local space consists of, we divide the 2 volumes. Multiply that by our estimated number of target planets in local space, and viola! Our probability of finding an Earth twin in local space is…

That’s 0.000028. Or one in 35,000.

So in summary, given all the factors that might affect the nature of planetary conditions, of the 505 projected Twin Earths in the galaxy, humans have a one in a 35,000 chance of finding one of those Nirvana’s in our local space of 50 light-years radius, if you believe all the factors that I’ve laid out are right. Which they aren’t. Trust me. They’re wrong. Because we can’t know with this level of precision. But it’s a start. It’s a logic path.

Of course when the Earth finally is obliterated by Blake’s Fragment in 2713, humans will gladly resort to artificial life support. Maybe we would bury ourselves deep into Ganymede or Europa. OK. Call that Plan B. This post is about finding a thriving, happy, sun-filled life. That should be our first priority.

But hey, we might be able to increase our odds of being right as our ability to analyze the various factors improves. But for now, our industrious heroes of science and engineering will go with the Prometheus Estimate:

The odds of finding a planet upon which humans can thrive as a species without artificial support within a 50 light-year radius is about 1 in 35,000.

Follow me