How many earth-like planets?
How Many Stars?
According to Wiki, near Sol it’s one per 0.004 cubic light years or 0.14 cubic parsecs (and this may not include lots of brown dwarfs). So that’s four stars in a 3D ten light year cube. In Traveller terms that would be a 3x3x3 parsec cube.
Assuming you want a 2D star map for convenience then you can hand wave the 2D map as a navigation projection, the space equivalent of a Mercator projection. I think this is a plausible sciency hand wave if your setting includes any kind of FTL subspace, jumpspace, hyperspace etc as it’s easy to imagine things like that involving strange geometry.
Either way this gives you four stars in a
- 10x10x10 light year cube
- 10×10 light year square
- 3x3x3 parsec cube
- 3×3 parsec square
or the equivalent in other sizes.
(The main point of the 2D hand wave is that four stars in a 3×3 parsec square is roughly 50% which fits the Traveller ratio making conversion easier.)
Types of Star
The current best guess is planets have to be in a star’s goldilocks zone – not too hot, not too cold – to start on the path to an earth-like planet. The goldilocks zone being where liquid water can exist.
(There are lots of possible exception to this like gas giant moons at just the right distance from the gas giant but goldilocks planets is maybe the default case.)
The goldilocks zone of a star varies depending on its type and at what stage it is in its cycle.
There are two base categories – stars that start out too big and those that don’t. The ones that start out giant apparently blow up too soon for planets to develop so they’re a bust (except as exotics).
The ones that don’t start off too big become main sequence stars. These burn a long time (billions of years) but change over time. As they gradually burn out to become red giants their goldilocks zone moves further out so a planet that might have been in the right zone for a few billion years can eventually find itself too hot or too cold.
Eventually main sequence stars flare up into red giants which would swallow up any previously habitable planets and then collapse into red dwarfs. Red Giants might have a habitable zone very far out from the star but although Red Dwarfs have a (very close) habitable zone I’d imagine any planets close enough would have been wrecked by the Red Giant phase (maybe exotic exceptions as always).
So for main sequence stars and maybe red giants, at any particular time there is likely to be a zone that has been in the habitable range for billions of years – long enough for the process of becoming earth-like to start if other conditions are correct.
(nb something that confused me for a while, if the time it takes to start the process is c. 3 billion years then older stars don’t necessarily have a greater chance because of the way the habitable zone moves over time. A star might have a lot of suitable planets in a neat row of orbits but depending on how fast the star it might not have enough time at each location to finish the process.)
Also a lot of systems have multiple stars. Roughly
- 50% single star
- 39% binary
- 8% triple
- 3% four
Binaries can be in close or far orbit with those in close orbit thought to make it harder for planets to form. If we assume
- binaries have a 50/50 chance of being close or far
- triples are a close pair and one far
- four are two close pairs
- close pairs complicate the goldilocks zone
- far single pairs with their own planets creates a double chance
- assume close pairs have 0.5 chance and distant singles have 1.0
then that gives
- 50 x 1 = 50
- 20 x 2 = 40
- 20 x 0.5 = 10
- 8 x 0.5 + 8 x 1 = 12
- 3 x 0.5 + 3 x 0.5 = 3
or 115% i.e. systems with distant binaries (c. 20%) and systems with triples (c. 8%) have a chance of two goldilocks zones thus increasing the chance of one of the zones having a suitable planet.
How Many Stars of Each Type?
- 3% F, blue to white
- 8% G, white to yellow
- 12% K, yellow to red
- 75% M, red
- rest, various giants
Assuming red dwarfs (too cold) and the bright giants (not enough time) and red giants (exotic exceptions) don’t have habitable planets and some of the F, G, K stars are too young (especially F) that gives us about 20% of those systems which have stars with a goldilocks zone that may have lasted 3+ billion years.
So in an 8×10 parsec section of space you’d have 40 star systems and c. 8 with stars with viable goldilocks zones – multiplied by the bonus from binary systems say 8-10.
How Many Planets?
Since 2011 (iirc) the Kepler telescope has been off looking for planets and apparently there are a lot more than originally thought to the extent that assuming 2-12 per system is plausible so if a star has a goldilocks zone then there’s likely to be at planet in it.
What other conditions are necessary?
The sciece of planetary formation is still largely guess work so I’m just going to go with what I find plausible from my reading.
I’m going to say that gravity is one of the core conditions which is a function of mass and density. Simply put say you need gravity in an earth-like range to hold the right size of atmosphere. Too low and the atmosphere is too thin and it’s too cold. Too high and the atmosphere is too dense and it’s too hot. So, say you can have
- small, medium and large planets
- low, medium and high density
and say the chances are all linear then the combinations of
- small size, high density
- large size, low density
- medium size, medium density
might all give gravity in a 0.75 to 1.25 g range.
(Effectively this would replace the “size” roll in the Traveller world gen with a “gravity” roll.).
On a 2d6 roll the gravity table might be something like:
- 2-5 = low gravity, either rock planet with no atmosphere or frozen atmosphere
- 6 = low earth gravity
- 7 = standard gravity
- 8 = high earth gravity
- 9-12 = high gravity, dense oven atmosphere
so rolls of 6, 7, 8 would have the right gravity to retain the original CO2, Methane, Nitrogen etc exotic type atmosphere and for that atmosphere not to be too hot or cold for life to start and for that life to gradually oxygenate the original atmosphere over time.
So of the 8-10 systems with planets in the goldilocks zones of the right kind of star that’s roughly 50% with gravity within the right range to retain an atmosphere i.e. 4-5 per 8×10 parsec area.
Using the above table you’d then specify the 2-5 rolls as trace atmosphere, 9-12 as exotic and only roll for the atmosphere of the 6-8 gravity planets.
Following the current theory of how the atmosphere developed on earth, this atmosphere roll would really be about how long the original exotic atmosphere has been transforming itself.
The general idea is life starts at the bottom of the sea where microbes develop to feed off stuff coming out of volcanic vents and these microbial organisms excrete oxygen. So the four stages of “earth-like” planet are
- stage one: exotic atmosphere, very high radiation (no ozone), dead land, exotic sea, microbe life at bottom of sea
- stage two: exotic atmosphere, high radiation, dead land, oxygenated sea, sea life
- stage three: thin breathable atmosphere at low altitude, exotic elsewhere, medium radiation, teeming sea life
- stage four: standard atmosphere at low altitude, thin elsewhere, low radiation, life starting on land
- stage five: standard atmosphere, background radiation, life everywhere
Say the table is (2d6)
- 2-3 stage one
- 4-5 stage two
- 6-7 stage three
- 8-10 stage four
- 11-12 stage five
A planets at stage one is are not much better than a lifeless rock. Stage two and three are not great but preferable for a stepping stone colony than bare rock. Stage 4 and 5 would be the prime we the prime colony sites.
The current theory of how a breathable atmosphere arose on earth starts with the right amount of gravity and lots of liquid (hence the importance of the goldilocks temperature range so the liquid doesn’t freeze or evaporate).With the atmosphere being mostly CO2 the liquid is initially carbonic acid which eventually leads to underwater microbes who oxygenate into water. If we follow this theory it means that if we assume a breathable atmosphere it must have water (or must have had water in the past).
So the hydrography percentage means different things depending on the previous gravity/atmosphere rolls.
Roll 2d6-2 (x10) = 0% to 100%
- for the planets with low gravity and trace atmosphere the percentage is frozen vs rock
- for the planets with too high gravity and exotic atmosphere the percentage is liquid something – the something depending on the type of atmosphere
for the planets with standard gravity
- for planets with stage one atmosphere it’s the percentage of exotic liquid. if 0-2 then life may have stalled or slowed
- for planets with stage two atmosphere, assuming the process requires water, it’s either the percentage of water or the percentage that has been oxygenated. if low, say oxygenation has only happened around the edge of tectonic plates (volcanic areas)
- for planets stage 3 or above it’s the percentage of water. if 0-2, assume planet terra-formed itself too slowly and the star’s goldilocks zone is moving past them so the planet is becoming too hot. (given the default theory this would be how a tattooine type planet developed i.e. it *had* oceans in the past to oxygenate the atmosphere which have since dried up
The end result of thinking this through again is close to what I had before except
- I thought I probably had too many “earth-like” planets but with the Kepler data I think that number is quite plausible (where “earth-like” doesn’t mean like earth now but planets that are part way through the terraforming process)
- I think i had too many planets that had reached the final stage because i was thinking if a star has been around 10 billion years and we’re assuming it takes 3+ billion years for a planet to go through the process then old stars should have more chance of an earth-like planet but this isn’t the case if the goldilocks zone moves – if it moves then the age of the star is maybe not as important.
So, more part way earth-like planets but fewer late stage earth-like planets.
The argument against lots of planets with life is the Fermi Paradox. Given the huge number of stars and (now known) the even huger number of planets, to explain it you (mostly) either need a single great filter or a long chain of small filters (collectively making a great filter) that make life a one in a trillion outside chance.
This would make space 99% airless rocks – not fun.
However I think a plausible great filter is the shifting goldilocks zones – say a system where the second planet out is in the goldilocks zone for 3 billion years but in the time it took to get near life on land the goldilocks zone has moved and the planet gets too hot. Then the 3rd planet out starts to develop life but after 3 billion years but just as it nears life the zone has moved on again and then the 4th planet and then the 5th. So after 12 billion years the star system may have *almost* completed the process of developing an earth-like planet 4 times. And then the star blows up.
What this would mean is the first species to get into space could find lots of planets that are *partway* earth-like and they could speed up the process (and maybe eventually slow down the sun so the goldilocks zone didn’t move again).
So not all airless rocks – although even the part way terraformed ones might still be mostly lifeless except under water. In a lot of cases colonists would need to bring their own flora and fauna.
Gas Giant Moons
As well as standard planets a potential second possibility for “earth-like” are large moons around gas giants.
Gas giant moons are apparently liable to be warmed by tidal warming which might mean they could exist not just in the goldilocks zone but possibly out some way into the otherwise too cold zone.
The gas giants we know about have lots of moons.
Tidal warming is proportional to how close the moon orbits the gas giant so if they were in the warmer part of the goldilocks zone they’d need to orbit far from the gas giant and if further away from the star they’d need to orbit closer.
Assuming an average size smaller than standard planets and
- size is small or medium
- density is low, medium and high
and out of the various combinations only
- small size + high density or medium size + medium density
gives standard gravity then the chance is lower than standard planets (which had the large size + low density option also.)
Then we have:
- lots of moons
- some of the right size
- needing to be in the right orbit of their gas giant
- their goldilocks zone possibly extending past the star’s goldilocks zone into the too cold zone
so a second chance at an earth-like planet in a suitable system and a small chance of both.