# On the Astronomical Genius of Goldilocks

In honor of social distancing, I was going to begin this post with all of the letters separated by six feet, but I figured I’d lose your attention pretty quickly. That’ll probably happen anyway. Let’s jump right to it, shall we? The Drake equation:

N = R* × fp × ne × fl × fi × fc × L

In this equation,

• N is the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy
• R* is the rate at which new stars are created in our galaxy
• fp is the fraction of stars that have planets
• ne is the average number of planets per star that might support life
• fl is the fraction of life-supporting planets that actually develop life
• fi is the fraction of developed life that becomes intelligent
• fc is the the fraction of intelligent life that sends signals into space
• L is how long a signal-sending civilization survives and sends those signals

In the first post, we decided R* = 2 Sun-like stars added to the Milky Way galaxy per year. In the second post, we set fp = 0.99 to reflect our understanding that nearly all stars probably have one or more planets. Now we are on ne, the average number of planets per star that might support life. The little e stands for Earth, owing to that particular planet being the only one we know of that supports life.

We might consider ourselves very lucky to be on a world that supports life. But if you think about it, if Earth didn’t support life, we wouldn’t be here to be unlucky about it. Let that twist your noggin for a bit.

So how is Earth so conducive to life? To begin, let’s start with our distance from the Sun. Earth’s orbit is directly surrounded by the orbits of two other worlds: Mars and Venus. Mars is about 142 million miles from the Sun, Venus 67, and Earth 93. That difference alone is enough to lead, at least in part, to entirely different outcomes on these three planets. Mars is sufficiently farther away that it is much colder than Earth – and Venus is sufficiently closer that it is much hotter. In both cases, the situation has been exacerbated to an extreme. Mars has lost most of its atmosphere from being pummeled by solar radiation and particles – because in addition to being colder than Earth, it doesn’t have the protective magnetic field that Earth has. Meanwhile, Venus developed a runaway greenhouse effect (see this post for more on that phenomenon), leading to a surface temperature of well over 800 degrees Fahrenheit, and making it hotter than Mercury, the innermost planet (which doesn’t have an atmosphere at all).

To paraphrase the story of “Goldilocks and the Three Bears”, porridge on Venus is too hot, porridge on Mars is too cold, and porridge on Earth is just right. Our region of the solar system has therefore come to be known as the Goldilocks zone. Outside the zone, based on our understanding of the conditions necessary for life as we know it to develop, it can’t. So how big is this zone? The distance from Earth to the Sun (about 93 million miles) has come to be known as an Astronomical Unit (AU). Latest estimates suggest the Goldilocks zone for our Sun stretches from 0.99 AU to 1.7 AU. Had the Earth been formed in an orbit outside that range, we wouldn’t be here to lament it. And look at just how close we were to not being in the Goldilocks zone – about 1 percent closer to the Sun would have made the Earth too hot for life as we know it to survive. Also, doing the math, Mars is actually in the Goldilocks zone. And sure enough, there is still some reasonable debate over how much atmosphere and water Mars may have had in its past – and even whether it might at one point have harbored some form of life. But whatever happened there in the past, it has long since turned far too cold.

The single biggest reason that temperature determines whether a planet can support life is that temperature determines whether a planet can have liquid water – which is the substance within which life probably arose on Earth, and also the substance within which our cellular activities take place. By weight, most of your body is made of water. There are a handful of other major ingredients of life as we know it on Earth – and it seems the key to life forming here was that these other elements (carbon, nitrogen, and sulfur, as examples) were colocated with the liquid form of water, where they could dissolve and interact at their leisure over a period of many millions of years. There are two general types of planets: smaller, denser, rockier ones like Earth; and larger gas giants like Jupiter. It is much easier to get liquid water and other life-essential elements together on a rocky world like Earth than on a gas giant like Jupiter. So Earth has two things going for it: a good temperature to support liquid water and a nice rocky surface on which the magic of life can commence.

How many worlds have this good juju? Without looking any farther than our solar system, we could hazard a somewhat defensible guess that the average number of potentially habitable planets per solar system is 1. That would essentially be saying that our solar system is typical. But just how typical is it? For one thing, in our solar system, all of the denser, rockier planets ended up in the orbits closest to the Sun, increasing the likelihood that if a planet was going to be in the Goldilocks zone, it was also going to be a rocky planet. Is this common? There’s a line of thinking that denser planets with heavier elements are more likely to end up closer to a star as it forms, since gravity would tend to pull the heavier atoms closer to the star. But even a gas giant like Jupiter may have a rocky core at its center, and that core might still be bigger than Earth. And as far as we can tell, the arrangement of planets around other stars is all over the map.

For most of the exoplanets (planets orbiting other stars) that we have discovered, our most important tool has been NASA’s Kepler space telescope, which operated in orbit from 2009 to 2018. For more information on Kepler and exoplanets in general, you should definitely have a look at exoplanets.nasa.gov. Kepler confirmed over 2600 planets, and based on those observations, it is likely that 20 to 50 percent of the stars in our galaxy have rocky planets in the Goldilocks zone. Let’s split the difference and call that 35 percent, which means we are going to say that ne = 0.35. Now, ne was supposed to tell us how many habitable planets there are around a given star, and of course you can’t have 35 percent of a planet orbiting a star. But what this math tells us is that your chance of finding a habitable planet around a given star is 35 percent – or that a little over 1 in every 3 stars has such a world in its domain.

There’s one additional complicating factor that I didn’t take into account here. We’ve only been talking about planets that could support life. But a couple of the planets in our solar system have fairly large moons which might also be able to support life – Jupiter’s Europa and Saturn’s Titan are good examples. Europa is covered in ice, and there are indications that a vast ocean of liquid water could lie underneath. Titan looks a lot like what we think the early Earth might have. Because of its potential internal ocean, Europa looks like the stronger candidate at the moment – and if we were to make the incredible discovery of life there at some point, it would be an exception to the Goldilocks zone rule – although the fundamental reasoning behind the Goldilocks zone still applies – the formation of life is best served when liquid water can interact with other elements. Our 35 percent estimate for ne therefore might be a bit low – but we need to learn more about Europa, and NASA is planning the Europa Clipper mission to do just that sometime later in this decade. So for now, let’s leave our estimate for ne to be 0.35.

And thus progresses our version of the Drake equation:

N = 2 × 0.99 × 0.35 × fl × fi × fc × L

In the next post, we’ll dig into fl, the fraction of habitable worlds that actually harbor life. Up until now, we’ve had some pretty solid observations on a pretty grand scale to support our calculations. Since our world is the only one we know of where life has actually arisen, everything from here on out will be much more speculative. But taking a step back at what we’ve discussed so far, the chance for extraterrestrial life is looking pretty good – a couple of new stars a year, nearly all of which have planets, and a third of which have planets on which life could form. The early numbers are encouraging, as they say. “They” possibly being aliens.