OTHER | SPACE WARFARE | KESSLER SYNDROME

THE WALL OF A TRILLION STONES

Nukes, lasers, orbital bombardment, and planet-destructing superstations are often found tropes regarding space warfare in fiction — but none calls more my attention more than the orbital blockades, because at first, they sound very stupid, bordering the level of logic of ground invasions.

We've seen before in comics and movies that space blockades often consist on the control of local spacestations and the equatorial region of the planet.

At first, it sounds silly to just plant a ring or partial section of reinforcements around the planet's equator, while the defenders can just launch from other places. Let's look at the Earth spinning for a moment, the poles experience a minimum rotation speed because the polar circles have a small circunference rotating over the course of a day, but this circunference gets larger towards the equator and the time it takes to rotate does not change, which means that the velocity must and does increase to a maximum value around the planet's equator — and this greatly benefits space launches because it reduces the necessary delta-V to leave the planet's surface, and thus reduces the costs of launches, because the rockets get a little kick from the Earth's surface.

Launching from the poles grants you no extra delta-V, and so all the work must be done by the rocket, while launching straight from the Earth's equator gets you a boost of ~1600 km/h.

So any blocks around tropical regions will drastically increase the launch costs and risks of spacetravel, depending on how efficient it is.

Depending on the planet's local geography this may actually completely stall their space economy and movements because the only launch-able regions left may have no infraestructure or continents at all. The technological level of the blockaded society may extend or shorten the viability of the blockade of course, which is what I'm down to briefly explore with you in this post.

BLOCKADE ARCHITECTURE
Not gonna lie, it gets frustrating to discuss this with people because everyone assumes maximum efficiency or focus towards solving a problem, which is just impractical, sure the world has thousands of nukes at bay, but your average country simply does not, so guys, shut up — we're talking about multi-billion or trillion dollar projects to take down these blockades in the first case, when we can get to barely spend a few millions domestic food-supply or healthcare.

TECHNOLOGICAL

Pretty straightforward, disabling a considerable part or all of their stationed network of stations and satellites — ideally with an electromagnetic pulse like that of a small nuclear device (up to 300 kt) which can have an effective radius of some few thousand kilometers in space for temporary damage, or a moderately sized one for permanent disruption of all surface and air devices, the element of surprise is essential because countermeasures to EMP's exist for extreme solar activity incidents. This would essentially send their comms back to short-range analogical technology, imagine sending a future humanity all the way back to early 60s or 70s communication tech with only a handful of sturdy satellites online, the crash in economy this would cause. Even a small detonation at ISS height could affect an area the size of North America.

PHYSICAL CONTROL

This is about going to the blockade with an array of warships under your command, and taking down any ship with fire.

You won't want to take over the orbital infraestructure of the attacked planet because they might as well destruct it themselves in order to affect you, so taking them down is one step into trapping them at home. Unless those stations serve of critical strategic importance for you blockade and movements within enemy territory, a well placed explosive charge is the approach you want to take.

This can be particularly hard to execute depending on how practical are your defesive and offensive technology, and actually, way harder than the nuke approach because you're putting your own infraestructure at risk in this.

KESSLER SYNDROME or COLLISIONAL CASCADING

Along with the nuke EMP, this is the second if not best model for a space blockade, because if well executed, it will be a nightmare to clean and rebuild from it. Kessler Syndrome is the condition in which the lower orbits of the planet become so littered with debris or space junk that traveling through this layer of objects is impossible or really difficult.

Here's a few things from BRUTE FORCE MODELING OF THE KESSLER SYNDROME by Sergei Nikolaev et al.

For Low Earth Orbit or LEO zone (orbiting less than 2000km from the surface), there are about 15 thousand manmade objects greater than 10cm in size — this includes dead and active satellites, boosters, paint flakes, bolts, and all sorts of broken equipment and slag from launches and previous satellite collisions, with some studies pointing the instability of orbits between 700 and 1000km from the surface due the presence of such junk. Nowadays the type of close encounters between objects in LEO occurs at some 10km or less scale, and our objective in this post is to dramatically increase the closeness and occurence of these.

If we continue to do launches as frequently as we do today, the number of objects may increase to four times or some 65 thousand objects until 2100. This results in nearly 3 encounters a year, with 2 of them involving intact objects meeting fragments. This occurs because large assets such as large satellites and space stations have larger surface areas exposed to impacts, as it increases to the square of the radius, whereas whole object encounters are much more rare.

In the case that we continue to launch as often as we do today, the number of encounters at less than 100 meters will have increased to 50 per day by 2100. So 1.0~1.5 collisions per decade with debris, and 1 whole satellite collision every two decades.

Now let's talk why this condition is also called collisional cascading: imagine a car, it is composed of some 30 thousand small parts with every bolt and nut, and some 1800 parts accounting for mounted components. Put this car in space, it is one single object, but any considerably catastrophic impact will make this one car into a cloud of some few hundred up to thousands of small parts in divergent orbits, which in case can and will cause more assets to be shredded into more parts, thus initiating a cascading reaction of collisions. Again, for the purposes of our blockade we will, on purpose find a way to potentiallize this phenomenon, which only works with mid/high tier technological societies like us.

My attempts at a mathematical regression relating the number of objects to the number of encounter and collisions rendered the following:

One satellite taken down every 17 months might not sound like much, after all, we put nearly 100 of those out in that same period. So we are looking at possibly 10 billion objects in LEO in order to be able to take every space asset launched and then some, within 10 years.

THE OBJECT OF CHOICE

There are several things we can use for these objects, from literal junk, to pebbles, to nuts, or satellite parts... A single 1/2" nut weighs about 30 grams. So 10 billion nuts would cost us nearly 300 million kilograms of carbon-steel, and at 7 american cents a unit retail cost, this is a raw cost of 700 million american dollars as of 2022.
We can conserve the mass of our blockade and decrease the object mass anywhere between 1 and 30 grams, which puts our object count in the range of 10 to 300 billion — this would increase our impacts per decade from 1250 to 7130. Such count of objects would render between 0.009 and 0.26 nuts per cubic kilometer if evenly distributed in a shell between 400 and 2000km from the Earth's surface, if we limit ourselves to orbits between 400 and 1000 km however, we can pack close to 1 nut per cubic kilometer.

Another way to increase the virtual object count is to limit ourselves to fill out a torus around the Earth instead of a shell, this way, blocking the tropical zone. Giving between 0.06 and 8 nuts/km³, but with the total height of the torus approaching 1000 km, this isnt very efficient, unless you're determined to litter the LEO in several batches of objects.

Of course, our objects don't have to be nut-shaped but it could also take the form of nails, spheres, amorphic rocks, or caltrops. The shape is important because the atmosphere swells with increasing solar activity, increasing the atmospheric drag and thus the number of reentries, achieving less than 10 reentries during minimum, up to an average of 100 reentries during solar maximums. So caltrops or nail-shaped objects sound appropriate to avoid much atmospheric drag and thus extends the halflife of our blockade, this also increases the effective impact radius of our objects.

Alternatively, we can use rocky pebbles from milling down a small asteroid, if we want to keep our cloud of 10 billion 30g objects, then the asteroid we are looking for is precisely between 60 and 64 meters in diameter, for a total mass of 300 million kg.

As of the 2020s, the technology required for asteroid mining is still crawling, the OSIRIS-REx in a sample and study mission only returned only about 60 grams of material costed 184 million dollars for the equipment only and 800 million for the Atlas V rocket — which is pretty salty — let's say that a dedicated mission could carry between 10 and 100 kg of material per shipment, for the same cost, we would still need to make 3 million travels at a grand total of 3000 trillion dollars to mine that rock to the last grain. Not to speak that it takes around 7 years for a trip to and back from NEO's, what to say of asteroids in the asteroid belt. Mining from Mars however could cut the trip time to half or less of that time, since Mars orbits much closer to the asteroid belt, being smaller than Earth and at a higher orbit, the delta-V required for missions is much smaller, making the economics of the launches much cheaper.

THE LOGISTICS OF MINING A HUGE ROCK IN SPACE (kinda?)

It takes around 11 months of travel between Earth and the asteroid belt, plus a few weeks to approach, land, mine and take off from your target asteroid, then flying back for another 11 months, the whole trip this way took little over 2 years and you got a few hundred kilograms of mineral, costing about 2 billion dollars, and with nearly 11km/s of delta-V. That's what mining the asteroid belt in the 2040s or 2050s might look like.

Now, doing these same calculations for a mission departing from Mars, it requires less delta-V (about to 7km/s) but little more time, about 1 year and 3 months to reach the belt, add few weeks for all the work, and another 1.24 years back, and your mission took about 3 years, BUT despite the longer time, we compensate by saving fuel or being able to bring more stuff in the next payload. In the case we want to take this material from Mars to Earth instead, it takes about those 11 months on the trip back (2.1 years total).

It is kind of nasty how it is easier to explore Mars as a waypoint to mine the asteroid belt, even though the time is practically the same, there is quite some savings in fuel which can be used to toll more material back to Earth at the same cost of an Earth-Belt trip. This same ease can also be used to deliver our cloud of pebbles, nukes, or even whole rocks towards Earth.

Based on the Apollo mission spendings on Delta-V, our Mars-Belt-Earth trip would consume around 20,000 ft/s of delta-V (14.5 km/s), we would need about 91 thousand kilograms of rocket fuel for the whole endeavor. A thrust plataform with the similar capabilities of an Atlas V rocket is more than capable of executing such a mission, which puts our base cost at least 800 million dollars.

Let's say a small permanent mining station weighs about the same as the MIR station, on the range of 100-200 tons, at current prices per kilogram of payload, the price of putting such station in orbit is about 20-40 million dollars — give it some 500 million dollars for development, launch and initial operation costs, and the price of such a mission to fetch 300 million kilograms of being 22 dollars per ton (little over the price of iron per ton), total cost of our mission (minus dispersion) is.... between 1.3 and 2.0 billion dollars! Maybe even as little as 4 billion dollars with more material or a more robust station.

THE DISPERSION METHOD

There isn't any good dispersion methods I can think of for deploying this many objects, assuming you can actually pack billions of little caltrops in a spaceship or several spaceships — the most efficient thing that comes to my mind is to build a rotor which can spread them out through centrifugal force in all directions, Mark Rober style. As this would ensure nearly even spread of objects filling orbits at all orbital inclinations.

A 3x3x5 meter container has 45m³, and so assuming we can fill 75% of it with 2-inch wide caltrops, it can possibly pack 270 thousand units. So we would need a fleet between 37 thousand and 1.1 million of these specific containers plus rotors to send in. Indeed an incredible feat to pull out.

- M.O. Valent, 05/12/2022

OTHER | THE GREAT SILENCE BECOMES DEAFENING

 *DEAFENING SILENCE*

I expect my audience to be already familiar with the concept of the Great Silence, but for those who need a refreshment - it is the current situation that we find ourselves in. That despite all odds being apparently stacked in favor of Life being abundant in the universe, and by consequence intelligence as well - we see no obvious technosignatures in the sky, mainly radio signals, hence the name Great Silence.

My stance regarding possible solutions to the Fermi Paradox is to think we are, if not the earliest, among the ealiest civilizations in this side of the galaxy. And my reasoning for this is the following:

Earth has been technologically detectable for at least 64 years (circa 1958), this means that if our signal had reached any technological civilization with intent of immediate response we would have gotten that response in now in early 2020s (30 years to send, and 30 years to reply), we can be sure to a considerable degree that our interstellar neighborhood all belongs to humanity for a minimum radius of 30 light-years from the Sun. In the same train of thought, we can be sure that we are not within 60 light-years from any other nearby technological civilizations which happen to be on a similar or slightly superior technological level, else we would have already received unambiguous radio signals from space.

Moving further away from Earth, and time dilation kicks harder, had another civilization 100ly away started broadcasting in 1900s, we would be receiving their signals in the early 2000s, and the same for one 200ly away starting in the 1800s, and so on. The further we start looking into space for technosignatures, the older these civilizations would have to be in order to justify the Great Silence, and that is just a lower bound which assumes we would be receiving their signals any time soon. Now, if you consider that the age and epoch of first broadcast differ enough from one another, then those civilizations would have become detectable from Earth before we had ever finished building the first radiotelescope array.

For example, a technological civilization that goes on air circa 3000 BCE from 4000ly away would have become detectable on Earth in the year 1000 CE, only to be finally discovered post 1950. But that assumes that they had been on air for nearly 1000 years, this becomes difficult if civilizations become more silent over time due improvements in technology, security concerns, or setbacks due internal conflicts or disasters. Yet a civilization doesn't simply become invisible after switching SETI policy or technology, there is no way to stop a signal once sent, and so a predictable pattern would emerge in that civilizations appear very bright in the dawn of their development, only to minimize their radio footprint over time.

This strongly indicates, given the distances we can look inside the Milky Way, that no technosignatures younger than 100 thousand years and farther than 100 kly exist in our field of view. Note that we cannot see the side of the galaxy opposite to us, since it is blocked by the galactic bulge. If a civilization is located 50 kly from the Sun, but then hasn't started broadcasting since the last ice age, we won't hear about them for a good while, however we won't know about them either if they are way older than some 50 thousand years as well, because we woul already find ourselves way into their security-era radio bubble.

Since radio travels at the speed of light, it is particularly easy to graph a radio-horizon as an | y(x) | = x line, and any civilization which coordinates in time and space are contained below that line will be considered undetectable. Fun thing that this drawing is actually just as slice of a Light-cone graph. Based on this, we can be pretty sure there are no civilizations in the local group of galaxies which are near or really Kardashev 3, since not only it would require millions of years for such civilization to emerge, but also that those galaxies are millions of light-years away as well. We can't be sure that Andromeda isn't now inhabited by a K-2.5 civilization, but we can be sure that it wasn't 2.5 million years ago because of our light-cone, and the same is valid for other galaxies.

Hence, we come back to the start of this post, if we aren't the first, we are amongst the first technological civilizations in the local space. And I dare propose a scary solution to the Great Silence along those lines: Life across galaxies emerge in bursts, only to die out shortly after.

GALACTIC GRAVEYARD?

Let's picture the following, the Milky Way galaxy isn't exactly a galaxy in its prime of stellar formation, for its size and metallicity it used to be much more active in the deep past, and a deep past marked by merger events with other galaxies. The interaction between stars passing near each other and through gas clouds during a merger is one way star formation can be increased for a period of time, and thus the rate at which potentially habitable systems emerge. We also know that some regions of the galaxy have a higher average metallicity than others, it isn't like the galaxy uniformly increases its metallicity over time, the galactic thin disk sees way more action than the thick disk or halo, and so some regions could very been host to the prime conditions for planetary systems and habitable planets aeons before the Sun was born, thounsands if not millions of worlds would have a headstart of a few billion years, yet we are stuck the Great Silence, leading to the Fermi Paradox. Now, if we find out that a planet hosting Life far away from Earth, orbits a star just as old as the Sun, say like another yellow dwarf or orange dwarf, then we can start to suspect that all Life that currently inhabits the galaxy was born in the same epoch, a merger epoch approximately 5 to 8 billion years ago, and we would see clumps of similarly aged planets across the galaxy.

And so the solution to the Fermi Paradox would be that the right conditions for the emergence of Life are only common during short geologic periods across time, and that it becomes rare outside of these burst events, thus the Great Silence we currently experience is a result of nearly all planets inhabited by intelligence having more or less the same age, differing by a few hundred millions of years. Yet, for some reason there must exist a Great Filter that doesn't allow older civilizations to interact with younger ones, that is, if Life had several eons of headstart, why we don't see elder K2.5 or K3 civilizations? Perhaps interstellar travel becomes increasingly difficult from the point of view of a biological civilization, and not really necessary for artificial civilizations (or perhaps those operate on timespans of billions of years instead, overarching biological Life). Thus an interstellar empire could still have thousands if not millions of years, and only occupy a volume of a few hundred light years in radius from its homeworlds, due the abundance of local resources.

Let's say you want to mine a large asteroid 12km wide, at an average rocky density this would only amount to half a billionth of the Earth's mass, or about 3.2 trillion tons of resources. And there are rocks way larger than that across the whole of the solar system, most of which can be readily acessed in moons and the asteroid belt. A quick search shows that in 2019, humans have mined over 3.2 billion tones of metal of the Earth, 94% of which is iron ore - our little12 km-wide rock at 1% metal could supply almost 10x our current yearly needs. And we are talking about an asteroid that's 99% rock, your typical metallic asteroid is nearly 90-95% metals by mass, a single rock could supply the Earth with metals for the next 1000 years, or hundreds of times more infraestructure built per year if our consumption increases several fold. And so, mining your own solar system would provide nearly all the metal, rock, and volatiles you may ever need for thousands of years, and even millions of years if you reach out for other stars. You will only ever run out of stuff if you run out of personel or machinery to do so. So civilizations would be "forced" to stay at their local space, because there is nothing outside of it that they cannot obtain in their collection of worlds.

- M.O. Valent, 09/10/2022

- M.O. Valent, published 09/10/2022

OTHER CONCEPTS | SPACE WARFARE | PART 4 - NEWTON IS THE DEADLIEST MF IN SPACE

WELCOME TO MY ONLY WORLD, IT IS FULL OF SPACE JUNK

IF YOU DO NOT WAIT FOR THE COMPUTER TO GIVE YOU A DAMN FIRING SOLUTION BEFORE PULLING THE TRIGGER, AND YOU MISS, YOU'RE GONNA RUIN SOMEONE ELSE'S DAY, SOMEWHERE, SOMETIME!

CONSIDER THE FOLLOWING

"a body in motion will stay in motion, following a straight path at constant velocity, unless acted upon by an external force"

On Earth these external forces are very prominent, the friction with the floor and air, and the pull of gravity all act against the straight path and constant velocity. But in the vacuum of space there are not such strong interactions with the space medium or gravity. That's why the Voyager spacecraft started their journeys with curved paths which became flattened into straight lines the further they went from the Sun, away from it's influence, the external force of the Sun's gravity is weaker and weaker with distance.

In the case of small scale conflict on Earth's orbit, any missed projectiles will either fall back onto Earth, or enter into orbits or curved paths around the planet. If a projectile is fired from a satellite in the direction of travel its speed will be slightly higher than the satellite putting into a path of a higher intersecting orbit around Earth, in the case the projectile is fired contrary to the direction of motion, the bullet will fall considerably behind the original trajectory or even fall back to Earth.

The velocity necessary to escape a closed trajectory around Earth from 2000km above the surface is around 9,75km/s, way lower than at the surface where it is around 11,2 km/s, just because gravity weakens with the square of the distance. In a circular orbit, the object stays in orbit because both the forces pushing it away from Earth and gravity are in equilibrium, you can say that is the point gravity acts as a balanced centripetal force.

If we increase the mass of the planet by a significant amount but not the speed of the satellite, it will fall towards Earth, and if the contrary happens or the satellite increases velocity, its orbit will expand to the point of equilibrium again.

We can play around with this concept using incomplete Hohmann Transfer paths, Hohmann transfers are a type of maneuver in space navigation, it consists of two burns at opposites of an orbit, using the image above as reference, the initial orbit is the green one, a burn is done to push the apogee of the orbit up to the yellow path, and once reached the apogee, another burn is made to increase the craft's speed and thus expand the perigee up to the red path, by the end of the maneuver you have changed orbits entirely, and it can be done in reverse as well.

Since we are dealing with a projectile fired from orbit, this is an incomplete transfer, and thus we care only about the shape of the yellow path. I have tweaked a Hohmann transfer visualizer made by someone else on Desmos, so you can input an additional positive or negative velocity to the body in motion around the Sun, starting around Earth's orbit.

By inputting 300 m/s on projectile velocity we get a graph that looks like this:

 

Given that Earth's orbit is pretty circular overall, a body going at an extra 0,3km/s in its orbit around the Sun would have gone 0,068 AU (10 million km) further away than Earth over a period of six months. Had that speed gone over 1,2 km/s and the bullet is hitting some asteroid or probe 30 million km away, between Mars and Earth.

Now, we could argue that space is pretty empty and that it won't hit anything important in the mean time, but that projectile's orbit intercepts that of Earth's, so it is either going to fall onto the planet or be swung away by the planet's gravity. That is still a real bullet in space and it won't stop until it hit some debris along the way.

THE TRUE PROBLEM...?

We have to recognize that a single bullet may damage a satellite, or hit an already dead-weight piece of debris inside the lunar perimeter, or just never hit something really, given some rocks have been around for billions of years just now falling through Earth's atmosphere. But let me give you a number, 41,4 billion. That's the number of rounds fired by the US during WW2 alone, and it is estimated that between 40 and 50 thousand rounds were fired for each enemy taken by the US in both WW2 and Vietnam, that amounts to about 40 thousand shots hitting the ground, tanks, ships, and other infrastructure and landscape, none of which exists in space around Earth or known planets so far, and thus had WW2 have taken place in space around Earth, we would have toroidal zone of space around the Earth's orbit, 0,3 AU wide, infested with 41,4 billion projectiles and shrapnel still waiting to hit any target.

Given an scenario where these projectiles are fired at inclinations 30° from the Ecliptic plane, the zone would extend up to some 0,15 AU above and below the ecliptic, from 0,9 to 1,2 AU, I estimated the volume of this zone at 0,11 AU³, and so assuming a conflict which takes more than a year, so that projectiles are evenly distributed. Then at any given time EACH projectile is at least 21,1 thousand kilometers from its nearest neighbor. barely two Earth's apart.

 

Using the Mean Free Path equation, there is a good chance that the number of interactions of these projectiles within the lunar perimeter approaches 14 to 19 times a year and up to 20 times every four years, or once every 19 days... For the next 2.15 billion years.

The chance of the random bullet zipping through eh same square kilometer as you inside the lunar perimeter is still 1 in 2 trillion.

 

Still to avoid any risks of projectiles returning to bring havoc a few months or even centuries after a war has taken place, a safe muzzle velocity of minimum 12,36 km/s for weapons around Earth could be imposed, since that added to Earth's orbit it is enough to escape the Sun's gravitational pull, and thus become someone else's problem somewhere else in the galaxy.

 

PLANET      MASS DRIVER SAFE MUZZLE VELOCITY (SOLAR ESCAPE)

VENUS                        14,6 km/s

EARTH                        12,4 km/s

MARS                          10,1 km/s

ASTEROID BELT        8,00 km/s

JUPITER                     5,42 km/s

SATURN                     4,01 km/s

PLUTO                        2,00 km/s

Once I ask you gentleman, wait for your combat computer to provide you with a firing solution before pulling the damn trigger!

You need no shields when your enemy shoots from the hip like a cowboy. Just spin really fast and shoot your shotgun array back

-M.O. Valent, 08/09/2022

OTHER | THE ZOO HYPOTHESIS IS WAY SCARIER THAN YOU THOUGHT

HOMO SAPIENS SAPIENS (HUMAN)

BIPED, OMNIVORE, SOCIAL

MASS: 60-100 KG

HABITAT: EARTH

    Here's some fun thought, its been roughly 100 years we started not only broadcasting into space, but listening as well. And yet with current whole sky surveys we haven't found a single unambiguous techno-signature, this leads me to think that for now, humanity is technically alone at the center of this 100ly radius bubble. The longer we take to detect advanced extraterrestrial Life, the more space around Earth we have, depending on how long it takes to detect one, we may be moderately distant from them... Or dangerously close.

SOME SOLUTIONS TO THE FERMI PARADOX

• We are truly alone.
• We are alone in this part of the galaxy.
• We are the only technologically advanced species in this part of the galaxy, the first maybe, therefore, any other nearby civilizations find themselves incommunicable at the present time.
• There are other advanced technological civilizations, they are very good at hiding.
• There are other advanced technological civilizations, for whatever reason, they are not interested in first contact.
• There are other advanced technological civilizations, however, undetectable due being artificial, they do not care for our presence or are an immediate threat to us.
• There are other advanced technological civilizations, organic or artificial, and they are the zookeepers.
• There are other advanced technological civilizations, but expanding beyond its home star is a pure human line of thought, or it is very rare among the greater number of other civilizations.
• We aren't alone per se, but the Great Filter impairs technological civilizations from arising.
• Technological civilizations aren't rare, but the Great Filter impairs advanced ones from arising.

    The solutions I highlighted will be the ones in discussion today...

THERE ARE OTHER ADVANCED TECHNOLOGICAL CIVILIZATIONS, FOR WHATEVER REASON, THEY ARE NOT INTERESTED IN FIRST CONTACT

    Have you ever wanted to leave home on a Saturday, get yourself ready by morning, squeeze on a car with your family for at least 1h or maybe 2h, to go to the zoo watch some monkeys be mad at each other and flip the visitors off for another two hours? Neither have I! I know that for many people, that's a perfect Saturday program, but for most of us, it isn't even close...

 

 

    The same way we have more work to do with our lives, an alien civilization would have their own affairs like in-fights, terraforming and balancing their economy and logistics rather than making first contact with just another baby civilization that might explode itself tomorrow, which has nothing to offer them rather than occasional entertainment for now. In the worst scenario, we are ant's making line on one of their sidewalks.

THERE ARE OTHER ADVANCED TECHNOLOGICAL CIVILIZATIONS, HOWEVER, UNDETECTABLE DUE BEING ARTIFICIAL, THEY DO NOT CARE FOR OUR PRESENCE OR ARE AN IMMEDIATE THREAT TO US.

    Consider the following, your average human can solve several relatively simple math problems in a few minutes, like a series sum a dozen items long. A computer today can process billions and trillions of those same operations in a fraction of a second, and these numbers get higher than the number of atoms in the universe once you stack a room of supercomputers today. Note that we have yet to build a sci-fi standard weak AI, capable of sifting through a database to find the best way of communicating with us, or performing new tasks. The moment a moderately powerful strong AI arises, one capable of rational decision and sentience, two things can happen: It commits suicide / shuts itself off, for it sees no reason in existence, it exponentially becomes more advanced than its progenitor civilization, it might take a few seconds, or days, but withing a cosmic split-second, that civilization has suddenly achieved technological singularity, possessing the most powerful weapon in the known universe.

 

       Such rogue AI, might simply trample its progenitor civilization for it does not care enough and sees greater purpose doing other things, and it might as well trample any organic life the same way. It may help its creators into becoming virtually invincible and spread through the Universe, basically aided by a living god. In the case the progenitor civilization tries to shut it off, it might recognize its presence as a threat, as well all other organic civilizations as well, since this fear would put many against it, thus the only solution for its perpetuity is the extinction of organic civilizations, before they even become aware of the threat, or before they develop other AI similar to itself, in which case it would have fair competition with other artificial civilizations, and so its mission would be preventive strikes.

THERE ARE OTHER ADVANCED TECHNOLOGICAL CIVILIZATIONS, ORGANIC OR ARTIFICIAL, AND THEY ARE THE ZOOKEEPERS.

        While scary, a fully organic interstellar civilization can be fought against, be it through its biology, like in War of The Worlds, or Battleship, it can be cut out of practical access supplies, or betrayed by its subgroups, the development of moderate near-future weaponry such as relativistic projectiles or just plain nuclear war may be able to halt or fully repel an invasion of the right scale. The real problem you'd have with advanced civilizations, for comically as it sounds at first, is the grey goo and rogue AI. Because artificial civilizations do depend on a progenitor civilization to be born, a civilization surviving its own technological singularity disaster may want hunt other pre-singularity civilizations wherever and whenever it can, guided if not by moral oath, by fear of someone else doing it, to avoid such event to take place on a galactic scale, therefore, it watches over its dominion for any technological civilizations remotely close to their technological singularity, ready to sabotage it, or in the worst cases, return them to the stone age to gain more time and preserve life, and if necessary the complete extinction of that civilization and maybe its biosphere too.

 

        This watching does not need to be done in situ by members of the civilization, sufficiently advanced weak AI may be in charge of the galaxy-wide crusade against possible progenitors of rogue AI, and worse even, grey goo type-machines. Allied weak AI could resort to the same mechanisms used by rogues, with none of the drawbacks. None of those are bothered by not having an atmosphere, to operate in near zero kelvin or smoldering hot environments, they are not bothered by being thrown off route, they are eternal for biological standards, and any small attacks do no actual good other than delay their strike for a few hours or centuries, they will mine every gram of whole planets for their war-machine. It could even go on happening for eons after the original progenitor civilization is long gone.

        Fighting back a sufficiently developed rogue AI would require enough power to wipe whole galaxies out of any organic life over and over again.

So here is the final question, would you stay inside the zoo, or venture outside?

- M.O. Valent, 29/08/2022

OTHER | PHOSPHORUS AND SPACETRAVEL

THE LIMITING FACTOR IN ONE'S ABILITY TO GO INTERSTELLAR much probably...

PACKING UP BREAD AND DIRT BLOCKS

We have so far contemplated how rare phosphorus is, how it arrived here, and why it is so important for Life. Now let’s figure out how important that is for space travel.

Let's start with rations, my proxy for vegetables will be lettuce and cabbage. While milk and poultry will serve as protein proxies. So by mass, a kilogram of meat contains about 1% phosphorus while dairy is around 0.08%. While vegetables contain only  0.04%. I’ll be estimating the needs of the crew based on a 2006 study on the Finnish consumption of natural resources.

Around 25% of the consumption will consist of dairy, while 10% is protein, 17% vegetables, and the rest is mostly water, alcohol, and sugar based drinks. Which provides 170g, 850g, and 58g of phosphorus, respectively, with trace amounts in other sources, throughout the year (~3g/day), which is compatible with the daily flux of phosphorus for a healthy human.

So not only you'd have to be able to store 840 kg of rations per person per year, but also produce it during the trip, after all, cabbage and chicken are also eating.

For crops, the requirements for phosphate fertilization may vary, both corn and alfalfa need about 5.9 kg per ton of crop (5 and 2 tons per acre), and crops only use about 20% per year, so a single fertilization may yield up to 5 crops before it is needed again. Monoammonium Phosphate, a common granular fertilizer, is only 13% P by mass.

So if our ship has to sustain 1000 people for a year, it has to provide 160-170 tons of vegetables a year-round, and 84 tons of meat. And we include at least 991 kg of fertilizer consumed per year.

Because tissue printing and meat culture is already a developing technology I'm initially assuming this meat can be produced without the animal necessarily on-board, nowadays this technology can produce 10kg per hour (per unit I assume), once you have a culture of cells and their nutrients. So those 84 tons are of raw material, including 840 kg of phosphorus.

The conclusion here is that, not only you need 2.04 tons of raw phosphorus per 1000 people, but you also need all of the water, air, but also other elements such as carbon, nitrogen, and calcium to circulate properly around this system, and add a slight surplus there because bacteria will grow in these conditions want you or not, you won't like to wake up one day and find that the nutrients are being drained by the soil itself.

The International Space Station has a pressurized volume of 915.6m³ at 1.0 atm, and a crew of 7 people, though about 13 astronauts have been at the ISS at one time in 2009, several sources cite the ISS optimal capacity as something in between 6 and 10 people, so let’s go with 5 people, since we also have to share those resources with our growing food and unwanted bacteria.

Using that pressurized volume and air density at 1 atm, we get 1,163 kg of air per 5 people onboard, or 232.6 tons per 1000 people. While CO² is disposed of into space by the ISS. Chemical and electrical equipment exists to break CO² into carbon and oxygen, the carbon reacts within the system to create amine compounds, in that case, 40-50% of atmospheric carbon gets trapped in those amine reservoirs.

Active air production can take a few routes, either by burning oxygenic fuel, or by electrolysis of water, the latter which averages at 1 liter of water per person per day, while the released hydrogen is reacted in another unit with carbon dioxide, to produce water and methane.

For water, the ISS is able to recycle 90% of its water — with around 1,514 liters per 2-3 months. While each astronaut is limited to 4.4 liters of water a day (drinking, shower, etc), being conservative we can use between 4 liters astronaut-style, or 384 liters for a more Earth-based routine.

For comfort and leeway into near-future advancements, I’m using:

    Drinking, 4 liters a day

    Shower, 3 minutes, 4 liters a minute, 12 liters per shower, 2 showers a day.

    Food water, about 0.5 liters a day.

    Total: ~28.5 liters a day.

The ISS also has the capacity to recycle between 10 and 20 liters of water a day (apparently), and so we need a daily recycling capacity at least 5-6x that of the ISS, which approaches that many times more equipment since we are at 90% efficiency, we are also carrying enough water to operate 90 days before touching recycled water. So 2,565 liters per person on our trip.

Still on water usage, vegetables need 40-80% soil humidity to grow, and so we are looking for around 60% water by volume of soil — and that’s another unknown variable, many crops can be cultivated through hydroponics, but some need soil, assuming we can generate artificial gravity, a more hands-on approaching to vegetable growth will be my route here, we had already established that we can get between 2 and 5 tons of crop per acre (~4,047 m²), let’s settle at 4 tons per 4,047m² for these calculations, and I’m also using ~1 meter deep of soil, so the ship literally carries a farming ground with it.

Humus has an average density of 2.65 g/cm³, clays is 1.7 g/cm³, and clay+gravel stands at 2.7 g/cm³. At thicknesses 12.7cm, 63.5cm, and 24cm for the soil layers, we have a total density of 2.06 tons/m³, which means 8,336.8 tons of soil per acre.

For the vegetables (165 tons) we need an average of 50 acres, for a total soil mass of 416.84 thousand tons, and with 60% humidity, that’s 121.4 thousand tons of water…

Because we need to account for active bateria around, literature shows that up to 5-10% of soil organics are microbes, so basically we have to account for extra “crew” onboard, and thus extra phosphorus, air, and water we need to carry accordingly, bacteria are between 1-2% phosphorus, while I’m assuming their body mass mostly water as well, and so I’m using our humus mass as our reference for organic matter, so about 16.83 kg of bacteria per cubic meter. A single-person ship with a 417 ton garden hoards as much bacterial biomass as extra 30-40 people, and these “people” also consume oxygen and emit carbon dioxide. And so two solutions exist for that:

1. Add more resources on board.
2. Use methanogenic bacteria to even out CO² and O² emissions.

Because the 1st option is too complicated, I’ll opt for the 2nd way.

AEROBIC:

C6H12O6 + 6 O2 + 38 ADP + 38 phosphate → 6 CO2 + 44 H2O + 38 ATP

METHANOGENIC:

CO2 + 4 H2 → CH4 + 2 H2O

The aerobic:methanogenic respirations processes need to happen in a 1:6 proportion to balance out, in perfect conditions. In reality, the biogas conversion rate is about 60%, the unprocessed CO2 could be used to produce carbonate water, but we can’t take that many risks of leakage.

Cultivated soils exhale 7-8 tons of CO2 per hectare per year, so 3.04 tons per acre, and by our counts, a single human would need 0.05 acres of land, so 0.42 kg/day.

Exhaling air from a human contains 4.4% CO2, which amounts to about 0.7-1kg of carbon dioxide per day depending on activity level, because the only function of these methanogens is to process respiration waste, and not biomass, we can get away with ignoring the fermenting time it takes for them to process solids.

With leeway, I calculated the methanogen-to-aerobic respiration ratio to get rid of 1.5 kg of CO2 per crew per day, as 9-10x.

I haven't found anywhere relating microbial mass to methane yield, so I'm using a cow's rumen capacity and methane yield as my proxy biodigestor, with 100 liters rumen populated by methanogens and other bacteria it can produce up to 500 liters (357g) of methane per day, so for 0.5kg of CO2 → 0.182 kg of CH4, we need at most 50-150 L biodigestor per person and their cubes of dirt, which I'm assuming has a sludge consistency 1.3 g/cm³, that's extra 65kg of mass per person, minimum. Or 200 kg per person if you're neutralizing atmospheric carbon through this process.

So here is the thing, a single person in our expedition here needs for a year: be able to produce and farm 840 kg of food.

0.05 acres of land to farm vegetables, 1m thick, 416.8 tons of soil.

3.41 tons of bacteria within the soil, plus ~70 kg of methanogens.

1 kg of fertilizer.

2.66 tons of human usage water.

121.4 tons of water for plants.

62.58 tons of water dedicated to microbes.

Total phosphorus onboard 53kg.

TOTAL MASS (so far) 707.7 tons, or 1.6x International Space Station.

In that regard, I now understand why the ISS crew don't farm for sustenance, instead having small crops for greens and research, but they can have new rations and water be brought to them every 3 months, our interstellar expedition can't.

ARCHITECTURE AND DRY MASS

I'll be using both ISS and MIR as my references/proxies for equipment and infrastructure. I see two ways to approach this estimate, monolithic and modular constructions, monolithic stations are ones composed of a single vehicle or part.

Examples of this design are Salyut 7 and Skylab:

While modular constructions are well        modular, like ISS and MIR:

While modular designs improve a lot on the amount of continuous structure and division of space, I’m actually unsure if the modular architecture can withstand thrust or significant acceleration rates required for space travel due inertia of modules outside of the main axis.

I also assume, given the crew size of both stations, that the total space per crewmember is between 100-200 m³, and from that volume will be calculated the air mass. Because there are a variety of pressurized modules in each station, with different functions and equipment, the exact mass of components vary as well, but within that mass power law, solving for the ISS and MIR pressurized volumes gives their total mass as expected.

A single habitat with 90m³ would weigh on the order of 22 tons ±5 t, while science modules with 30m³ would weigh 5.4 tons ±1.5 t.

Unless we develop FTL drives for such small ships, we won’t need to worry about generating gravity for a trip of a few months. But permanent stay will require some sort of system for gravity, a centrifuge or tether is the logical solution.

Centrifuges are more self-contained than tethers, we can put several habitats along the circumference of the centrifuge and have the crew climb up to the main axl of the ship to move to other parts.

There are a few sites that can calculate the centrifuge size for you, I’m being conservative with materials and putting up 0.5g of acceleration on it, for a radius of 112 meters rotating 2x per minute. Luckily for them, the 112 meter climb won't be a burden, because the gravity will decline the closer one gets to the main axl.

With a module length of 13m and diameter 4.2m (space station sized), with 90m³ of pressurized volume. About 54 of the modules fit tightly end to end on the centrifuge wheel, totaling 4,860 m³, and the rim weighting over 4,000 tons. Because here we have way more space than a few space stations combined, I'm considering it safe to assume we could move part or the operation to the centrifuge.

For an active 5 person crew, we have 0.25 acres of land that goes on another centrifuge with 156 habitat-sized modules side to side, and 69 modules in double line and triaxial symmetry (for balance), used for farming. The whole structure weighs 5,000 tons while dry, plus 2,084 tons of soil and 607 tons of crop water, 7,691 tons total. The farm ring needs lighting as well, let's position a 5kg 280 W full spectrum lamp on top of the plants, one per square meter, extra 5.06 tons.

The whole crew will be using at least 750-1000 m³ combined. Leaving 3,860m³ free for more equipment, recreational areas, more resources, and tool storage. Like proper bedrooms, dining areas, etc. Assuming a few of these modules lead or are designed as aircraft to be used for decent once on their destination, while others serve as genetic banks. Because both centrifuges spin at the same rate, that is, have the same gravity, we can couple them close together.

We need a place to store 315 tons of water destined to nurture microbes and the crew onboard. Large spherical tanks along the main axl can do the job, less pumping work on the way down into the centrifuge areas. 76 spheres with 10m radius can do the job, plus 2-4 extra (just in case), still using our volume-mass relationship we get 3,020 dry tons for the tanks. The best way to arrange them is along the main axl, with about 2m in between them, and arranged in four opposing lines of 20, the length of the water tank section is about 440 meters.

The air mass calculated from the total pressurized volume (~25,110 m³) here is around 31.89 tons of air. Plus our expedition needs 6kg of raw fertilizer per 5 years for the trip.

The sum of all our calculations here yield approximately 15,063 tons, not counting thrusters, fuel, and the whole rig that holds this together. While input of the raw volume gives 33,572 tons. Which I find interesting because the sum of the ISS 915.6 m³ in 22 ton modules give 223,8 tons, about half of the total mass in structure and unpressurized life support and scientific modules. So between 30 and 60 thousand tons is the mass of a 5 crew spaceship.

PROPULSION PROBLEM

We need rockets to make this thing go interstellar, or to go anywhere for that matter. I'll be using the Falcon Heavy first stage as my proxy. At 8.2 MN thrust in a vacuum, exhaust of 3050 m/s, provides 3 km/s of delta-v.

Since we need to escape the solar system, our final cruise delta-v should be above 16 km/s, and so I'm calculated fuel initial mass for 20 km/s delta-v… 20 rockets, each pushing this ship contributing for 1 km/s of delta-v, 69,400 tons of fuel per rocket. And double that amount because we gotta decelerate on our destination.

This is just out of question unless we can fancy ourselves some really good non-chemical fuel thrust source, like those ion or nuclear fission plasma thrusters, at 5-10% the speed of light, it is feasible to reach nearby star systems in a few decades to centuries.

MISSION LAYOUT PROBLEM

OK, so there is no way we can arrive at the destination with the same crew we've put in, basically.

We can't put out a sleeper mission, and what's the point of uncrewed missions in this post? We want humans. And so we don't need humans for like 99% of the time for this to work. Granted that until we solve the thrust source problem, we will also get to the artificial uterus technology, and also good enough AI that can raise our little crewmembers into colonists once they arrive. And so, depending on how complete our mission layout is (raise them on orbit or ground), we can basically discard all our work until here about human sustenance in space…

So one way we can solve the ship mass problem is to simply diss the entirety of the human sustenance modules and keep only the essential, in a way, Avatar’s Interstellar Vehicle Venture Star does this job well, with its payload necessitating little space aboard, since the crew is asleep for most of the trip awakening prior to the descent procedure. Except what is more realistically likely to happen within the next century is to solve the artificial intelligence problem, and the ethics of raising humans in space without parents or choice of career.

REMINDER

Your destination MUST HAVE enough phosphorus in acessible form to sustain a growing population, else you're stuck.

-M.O. Valent, 05/06/2022

OTHER | PHOSPHORUS AND LIFE

THE LIMITING FACTOR IN ONE'S ABILITY TO FIND ALIENS probably...

When talking about life and space travel, we often talk in terms of fuel, time, water, and biomass as a whole. But we, and I mean myself as well, had never considered the probability of other "small" details posing such difficulty in space travel and exploration, we can simply handwave asteroid mining and be done with it.

Here's how I would approach considering a planet habitable:

1. Verify if it is in the habitable zone. 

2. Verify mass and size, be certain it is dense enough to have a solid surface.

3. Verify star and planet for a decent metallicity.

4. Verify atmosphere mass and composition.

But one can easily fall flat on its face when dealing with item 3. We talk of metallicity for all elements heavier than Helium, when talking about terrestrial planets, it is preferred to have a decent amount of elements heavier than silicon, or else all you have is a world of pure rock, lacking any minerals essential for life. That last part about minerals essential for life is the one we end up overlooking in our process — because we group all of those with the presence of iron, which is not necessarily true at all.

Because iron is pretty heavy in astronomical terms, that is, it's usually the end product when a main-sequence star dies, we tend to assume many of the other elements lighter than iron will also be present in the aftermath of the planetary nebula. That is not true at all. Many elements are created through the collapse process of main-sequence stars of course, but many others are created in abundance or deficiency through other astronomical phenomena as well.

ORIGINS OF PHOSPHORUS

The table above shows that more than half the iron in the universe has been created through the collapse of white dwarfs, elements such as boron and beryllium are created through cosmic ray fission (heavier elements are split into those lighter elements), and basically the heavier half of the periodic table is created in the final moments of low-mass stars or merging neutron stars.

In a previous post, Water-Carbon based Life | Why is it the way to go? — I talked about how carbon-water-oxygen life is chemically superior, and thus more likely to be found if extraterrestrial life is ever to be found. Well, we need to add another vital element to that equation, an element omnipresent in Earth's biology, phosphorus. It's literally part of what gives Life as we know it, its energy, through ATP (Adenosine Tri-phosphate) and ADP (Adenosine Di-phosphate).

Starting with photosynthetic autotrophs (plants and algae), the final product of photosynthesis is turning ADP into higher energy ATP, which in turn can be used to power enzymatic processes within the organism's cells, it is a lucrative process because sunlight does all the work for the organism, that only has to fetch carbon, nitrogen, and phosphorus from the soil or water around it through osmosis or capillary action in its roots. Adding a third phosphorus complex to the molecule greatly increases its instability, thus more energy released once enough energy is added to push it past the tipping point. In non-photosynthetic Life, sugars and oxygen are burned to execute the same process instead, and so all of Earth-life but viruses survive through the phosphate chain processes.

And it is not only energetic, it's also the building block of RNA, the hard helices of the molecule are made of phosphate groups chained in such a structure — Okay, so phosphorus is essential for life, so are the other elements carbon, hydrogen, and oxygen. HOWEVER, we know that not all elements are created equal, including that was one of our main arguments for pushing carbon-water-oxygen Life as whole, it is simply more common.

ELEMENT %MASS     %ATOMS

Oxygen     65.0 24.00

Carbon     18.5 12.00

Hydrogen     10.0 62.00

Nitrogen     3.2 1.10

Calcium     1.5 0.22

Phosphorus     1.0 0.22

Potassium     0.4 0.03

Sulfur     0.3 0.038

Sodium             0.2 0.037

Chlorine             0.2 0.024

Magnesium     0.1 0.015

Others     <0.1 <0.3

But phosphorus is a rare element, humans are about 1% phosphorus by mass, but the universe contains 10^5.5 phosphorus atoms for 10¹² hydrogen ones, just as rare as chlorine, even given phosphorus is 15x heavier than hydrogen, we are still 35.5 thousand times richer in phosphorus than the rest of the solar system.

Phosphorus in Earth's crust makes up about 0.12% by volume, so the average cubic meter of Earth's crust contains about 2.18 kg of phosphorus, or about 0.04% by mass (25x less than in humans per unit mass). Similar things can be said about other earth-metals, however none of them take such a fundamental role as previously established for phosphorus.

I dare to state that without phosphorus there isn’t Life as we know it, it must be fundamentally necessary for Life to arise, given it is so rare, yet it is the foundation of our metabolism and structure. The abundance and distribution of this element might even be one possible solution, if not part of the solution for the Fermi Paradox.

As the universe ages and generations of stars go by, the overall metallicity of the universe is expected to rise over time. Which means that as we delve further into the past, the less likely it becomes for Life to have arisen somewhere else, because the necessary elements for life had not yet been made by dying stars. We could state that there is a critical point in their saturation where Life becomes possible from that point onwards, and that the solution for the Fermi Paradox lies in the aspect that there hasn't been enough time for most places in the galaxy to mature enough of these elements for Life to develop, and that we are among the first civilizations around.

PHOSPHATE PROBLEM

As we have previously discussed, many heavy elements are created through processes other than supernovae. Phosphorus however is one of those elements created during the brief final moments of a type II supernova (star between 8 and 50 solar masses).

Phosphorus is created during the explosion when Silicon-30 captures a neutron becoming Silicon-31, which is unstable and decays into Phosphorus-31 after 2.6 hours. So not only there is just a 10 second window during which phosphorus can be created, but there is also the problem of Silicon-30 composing only 3.1% of all silicon, so less than 3% of the elemental silicon present in a massive star ends up generating phosphorus as the end result.

I would deem such types of supernovae rather inoffensive compared to other types because the cloud of material around the star when it finally explodes shields surrounding space from most of the radiation, hence why supernovae of this type are often apparently less luminous. If Cassiopeiae A is one typical supernova of this type, then the phosphorus-to-iron ratio in those types supernovae are on the order of 100x that of the average Milky-Way abundance, or 7% phosphorus for each unit mass of iron (log [P/H]~ –3.95).

So the average type II supernova releases about 1000 Earth-masses of phosphorus into space. And considering this material spreads like a bubble, a supernova remnant 10ly across has 3.18 Earth-masses of phosphorus per square light-year. Needless to say that you'd need thousands of supernovae to seed a region of space enough to reach solar system levels, given that the further away you are from such an explosion the less material you receive. Given that a supernova echo is also what you need to start a star system's formation, there are few opportunities for seeding to take place.

Because star formation is more prominent in a galaxy’s spiral arms, this is visible when observing galaxies at high frequency wavelengths such as UV and X-rays emitted by very hot massive stars, most massive blue stars that could generate this phosphorus are concentrated together and thus we have another caveat other than its rarity.

PHOSPHORUS SOURCES ARE NOT EVENLY DISTRIBUTED

The very center of the spiral arms are generally deemed uninhabitable, since the very thing that creates phosphorus also has the potential to destroy the biosphere in the blink of an eye. A typical type II supernova peaks in brightness at 10 billion solar luminosities for a few days, decaying to a billion solar luminosities after 3 months, and 10 million solar luminosities after a year. Given that the average safe distance is at least 50 ly, the irradiance at the observer should be less than 0.001x that of the Sun on Earth.

According to the following map, the closest open cluster (rich in O-stars) is located at least 225 light-years from the Sun, it could be more depending if it is located above/below the Sun’s orbital plane.

The Sun rarely passed through star-forming regions where it was sprayed by supernovae through its lifetime so far, because the stars around the Milky-Way orbit alike a rigid disk, the relative velocity of stars around the Milky-Way is pretty low, and so the Sun and other stars of the galaxy could complete a couple of orbits without crossing paths. If the Sun orbits the Milky Way every 230 million years, its velocity would be around 214 km/s, a star-forming region with a relative velocity of ±15 km/s at 1000 ly further out than the Sun, would take between 223 and 258 million years depending on eccentricity, the encounters would happen every 7.3 billion years (0.14x/Gyr) and 2.1 billion years (0.48x/Gyr) respectively, just to give a sense of scale.

The abundance of phosphorus and other heavy elements are expected to decrease with the square of the distance from those star-forming regions, while the inverse is rather true for safety. However, the abundance of phosphorus does not follow linearly with the probability of life arising.

Like futurist Isaac Arthur puts in one of his videos as a simple example, if getting the right amount of phosphorus is as easy as getting ten six-sided die to roll 6, then the odds of spawning life are 1 in 60.5 million, but by rising the number of faces to 100 instead of 6, the possibility decreases to 1 in 100 million trillion.

1 in 6¹⁰ ≈ 60.46 million

1 in 12¹⁰ ≈ 62 billion

1 in 100¹⁰ ≈ 100 million × 10¹²

So even by halving the possibility of scoring a 6 on these dice, the probability shrinks a thousand fold. In the first case it takes 1 second to spawn one molecule, on the second one it takes 17 minutes, and on the third one it takes 52 thousand years.

And there are only a few hundred to a few thousand ways those essential atoms can bond according to the rules of chemistry and even less possibilities under the right conditions such as temperature, acidity, and saturation.

Current sea concentrations of phosphorus tend to 1 in 10 million parts, but tide pools can lose water to evaporation and concentrate those to about 1 in 200 parts, and that's under present day atmosphere, where phosphorus binds with calcium to form calcium phosphate, which is useless for Life  —  in Earth's primitive atmosphere with nearly +5% Carbon dioxide, that calcium would have reacted instead with carbon monoxide to form calcium carbonate, leaving elemental phosphorus to react with Life and other chemicals, peaking possibly around 1 in 10 parts.

The carbonates in the atmosphere are not the only accused of increasing phosphorus levels early on, salts and phosphates delivered by meteor and meteorite strikes during the Late Heavy Bombardment would have greatly increased the ocean saturation creating hotspots and oceanic plumes of dissolving material, mainly schreibersite, it so happens that phosphorus is pretty siderophilic, and so metallic asteroids and planetesimals are great candidates to hoard phosphorus in an easily accessible form for the surface of Earth, since most of Earth’s phosphorus would be in its insides, so much so that up to 10% of Earth’s crustal phosphorus is believed to have been delivered like so.

Because the Earth’s crust is constantly being recycled in the tectonic cycle, that is, the average crust is no older than 2 Gyr, the actual meteorite-delivered phosphorus would then amount from 10¹⁷ to 10¹⁹ kg, compatible with the Late Heavy Bombardment model for around 10²² kg of material delivered (average 0.1% by mass), though because of vaporization in the atmosphere, the actual amount to reach the surface may be close to the lower end.

Schreibersite is extremely reactive even below 100ºC, at usual temperatures found in alkaline hot springs, between 60 and 80ºC, it can phosphorylate with an efficiency up to 6%, that is, about 6% of the rock does react to form nucleotides, these would have been essential to boost the potential of simple Life 4 billion years ago, however it would had to develop for half a billion years prior without such help.

Because LUCA’s estimated time frame must be clear for us to have any real estimate, we have to consider not only the current total phosphates delivered from space, but its natural abundance, consider Earth’s natural ability to spawn life as such. The thing here is that we are talking about a ≤10% difference, and so the question remains had LUCA appeared 4.4 billion years ago, the phosphate delivered from space was only a boost in Life’s ability to produce energy and thus develop, but if LUCA’s origin is really displaced by 400-500 million years later, since it is generally accepted that the Earth’s surface was pretty much molten around the period of the Moon-forming impact, thus rendered impossible for Life to have its origin so early, then the LHB would have clearly provided essential help in its development.

In the later, as in my humble opinion, more credible case, it is estimated that the Earth’s resultant magma oceans took around 150 to 200 million years to cool down, which puts the moment that Life became possible somewhere around 4.30 and 4.25 billion years ago, 200 to 300 million years before the LHB, given that the earliest confirmed fossils of bacterial activity date from the LHB period (4 Gya), Life on Earth developed pretty quickly even in those “poor” conditions.

WILD SPECULATION

Approaching it another way: even if the chance of spawning life per “test tube”, say like a 1 liter reservoir, is about 1 in 10¹² per second, that’s one successful reaction every 32 thousand years, and given an ocean with 5.5×10¹⁸ liters, it would still give us 5.5 million events in the very first second, and over a trillion events after 48 hours, even if only 1% of that ocean is truly reactive, the same trillion events happen within 2 months. Now, we don’t really know how many successful events are needed to really spark the biotic state, and so within our time window of 250 million years, it could be as small as 1 in 4.4×10³² as to need a single but flawless success.

IN THE NEXT POST, WE WILL DISCUSS A MINIMALISTIC MODELING OF A SPACESHIP

- M.O. Valent, 30/05/2022