How good is the Earth as a life-sustaining planet?

Over the past few days, I’ve been reading a lot of Asimov, partly to distract myself from exam work. That got me thinking: what if we find a planet which is better than the Earth to sustain life?

To measure this, of course, we’ll need a scale to measure planetary suitability for life-sustaining capacity. That sounds hard, so let me simplify it. We need a scale to measure how good a planet is at keeping stuff alive.

The factors of suitability seemed to be distance from the stara and temperature. Fortunately, there’s a formula for this:

T ∝ 1/√D (Temperature is inversely proportionate to the square root of distance)

This is what’s known as an inverse-square law, upon which gravity is also based. So, to simplify:

T2D = constant.

This is clearly not a universal constant, since the Sun’s temperature is the same whether you want to measure the ‘planetary constant’ (as I called it) of Mars or of the Earth. The Earth’s constant will come out to:

(5780 K)2 * 150 million km = 5011260000000000.

That isn’t very nice to look at, any more than 602300000000000000000000 is. (Avogadro’s Number). So, it’s simplified to 5.01126 x 1015 K2km.

First order of business: find a unit for planetary suitability. Square-kelvin-kilometres are a bit too difficult to use.

(This one’s still in progress, though I’m leaning towards ‘keplers’. On the other hand, ‘this planet has a suitability of 1.4 Senguptas’ has a certain ring to it…)

When I do find a suitable unit, the value of one of them will be set to “the suitability to sustain life of a planet 1 AU from a star whose effective temperature is 5780 K”.

This gives rise to the first question: what is the range of planetary suitability that is likely to create an atmosphere conducive to life?

In other words, how likely is another planet like Venus to allow life to be formed?

The way I see it, there are three zones for planetary suitability. There’s ‘unsuitable’, for the Mercurys and Plutos. There’s ‘possible’ or ‘dangerous’ for Venus- or Mars-like planets. And there’s ‘sustainable’ for the Earth.

Humans would like to think that Earth was ‘sustainable’, anyway. It’s possible that it was in the ‘dangerous’ zone, it was never likely to give rise to life, but it beat the odds, and did. Humans would not like the thought that they were almost not here.

Another factor in the calculation is how likely the planet is to have an atmosphere. This hasn’t yet been factored into the planetary suitability unit, but it will be once I figure it out. The Moon, or planets/moons like it, cannot have an atmosphere, because they don’t have enough mass to provide the necessary gravity to, well, ‘hold’ the atmosphere near the planet/moon. On the other hand, too much gravity means we won’t be able to live. I’ve estimated that a planet with a mass about 1.3 times that of the Earth would be, probably, the biggest planet on which we could survive.

Which brings me to the next three questions:

2. What’s the smallest planet on which humans could survive?

3. If we assume a fixed solar temperature, how much closer or further away towards/from the Sun could we get?

4. If we assume a fixed Earth-Sun distanceb, how much hotter or cooler can the Sun get to still sustain life?

One last thing to factor in; sustainability. It’s no use settling near a dying star, or one that’s REALLY hot and too far out. We need to be in the right zone there too, or we’ll have to move fast.

Hopefully, there won’t be a follow-up post on this for a couple of months, because that’ll mean bad exam results coming my way 🙂

a: Initially, I misunderstood the formula, and took it to mean the Earth’s surface temperature. I did discover my mistake, but not before finding out the interesting fact that the Earth’s surface is cooler than I thought: it’s only 14 degrees Celsius.

b: Although it isn’t fixed: because of the Earth’s moving around the sun in an elliptical (rather than circular) orbit, distance varies between 0.98 AU and 1.01 AU.