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The "Old Solar System" is our solar system as described in many space operas and planetary romances written before the space age.

https://www.solarsystemheritage.com/

In stories in the Old Solar System at least three worlds, Venus, Earth, and Mars, had life and often intelligent life, and often high civilizations.

And many old solar system stories had far more planets than that with life - in some stories all the 9 planets including Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto had life. And sometimes undiscoverd planets like Vulcan, the destroyed planet that the asteriods were fragments of, Planet X beyond Pluto, a counter Earth on the opposite side of the Sun from Earth, and so on, also had life.

And of course a number of other objects in the solar system often had life. Earth's Moon sometimes had present or past life. The four Galilean moons of Jupiter - Io, Europa, Ganymede, and Callisto - and Titan, the largest moon of Saturn, and Triton, the large moon of Neptune, often had life. And of course some of the smaller moons also had life. And some of the asteroids sometimes had life. There were a few stories with life on comets.

And some of those ideas about habitability seemed scientifically possible before the space age when space probes revealed the actual conditions on other worlds in the solar system. And many of them went far beyond what scientists could consider possible even at that time.

And I am thinking of a story series where a character might materialize in a number of star systems, including some which seem to be our solar system, but which they discover are actually copies of it around distant stars. And of course one of the main clues is the different species of intelligent beings on the different planets Mars, for example, in the different copies of our solar system.

Obviously alternate universes where Earth has similar history up to maybe the 20th century would not involve different species of aliens evolving on Venus, so those have to be separate star systems created by highly advanced beings as duplicates of our solar system, but not so much duplicates of the real solar system as the Old Solar System of old Earth science fiction stories. Thus the creators of those duplicate solar systems would probably be fans of old science ficiton stories who have gained great power.

But the fake solar systems have to have the orbits and sizes of the planets and moons as close as possible to what was known about them before the space age began. So the character from more or less the original Earth doesn't notice differences in the sizes and orbits of the planets from what they learned on their home Earth.

So the problem is how to make worlds in the replicat solar systems habitable that have the same sizes and distances from their Sun as their uninhabitable counterparts in our solar system.

I do not think that there is any way to make the giant planets Jupiter, Saturn, Uranus, and Neptune, have solid surfaces if they have the same diameters, masses, and densities as they were known to have even long before the space age.

But there may be ways to make the planets and moons much smaller than Earth habitable.

Those small worlds are largely without significant atmosphere because their escape velocities are not high enough compared to the average velocities of atoms in their exospheres where gases escape into space.

If their escape velocities are 4 times those of the gases in their exospheres, they can hold onto those gases for thousands of years. If their escape velocities are 5 times those of the gases in their exospheres, they can hold onto to those gases for about a hundred million years.

So if the escape velocities of those worlds can be increased to 4 to 5 times the velocities of the gases in their exospheres they can hold onto those gases for thousands or millions of years. And perhaps the powerful beings who created those solar systems did so recently, and so those small worlds would have high enough escape velocities if the creators increased their masses to several times what they are in our solar system.

I note that the best way to measure the masses of worlds is to measure their orbital speeds relative to other worlds. The mass of a world with smaller objects orbiting it can be calculated from their orbital speeds and distances. But in our solar system the masses of the orbiting bodies are usually too small compared to the bodies they orbit to affect the calculations much.

So moonless Mercury and the larger asteroids and the larger moons in the outer solar system, none of which had know objects orbitng them before the space age, had relatively little know masses and might have been considerably more massive than they actually are according to the knowledge of the time.

There is a problem with Mars, which was discovered to have two small moons in 1877 and thus had well known mass, surface gravity, and escape velocity in the time of the Old Solar System stories. Some other process instead of increasing the mass of Mars may be needed to enable Mars to retain a more or less breathable atmosphere. I note that I have read some more or less scientific discussions of life on Mars as late as the 1950s and early 1960s which were relatively hopeful about the possibility of life on Mars.

And there is the problem of giving the worlds at widely varying distances from the star in each system the right temperatures for liquid water using life.

So I would appreciate any ideas how to make various versions of the "Old Solar System" plausible.

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    $\begingroup$ Is all the text necessary? Can you condensate it? $\endgroup$
    – L.Dutch
    Jan 20 at 7:13
  • $\begingroup$ I didn't read the whole wall of text, but in regards to " planets like Vulcan, the destroyed planet that the asteriods were fragments of", it never existed and the orbital anomalies it was supposed to explain were instead explained by Einstein's theory of general relativity. Wikipedia $\endgroup$ Jan 20 at 22:58
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    $\begingroup$ this looks like a lot of different questions, under the umbrella of one, please break it up into the individual questions Ask about each specific individual world since answers are going ot be very different. A lot of it will come down to Clarkean magic. $\endgroup$
    – John
    Jan 30 at 3:23
  • $\begingroup$ There's many answers ! If you would focus on a single Old Solar System scenario, it would become story-based... But what if this question would be focused on a single planet, say Venus ? According to these Old Solar System SF writers, Venus was inhabitable, large beasts were roaming around there.. It's 10 days, let's put a title change. @M.A.Golding I've only changed the title.. please undo when you don't agree. $\endgroup$
    – Goodies
    Jan 30 at 12:42

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Someone is engineering entire planets and moons into a set that, at least in terms of sizes, resembles our entire solar system. I think that implies they can get at least a few places to qualify as habitable (for humans) without a space suit.

Let me take a stab at some of the easier ones.

Venus. Remove the current atmosphere. Replace it with a comfortably breathable atmosphere that also retains less heat than Earth's. Perhaps keep those perpetual clouds (but not so thick), but make them more reflective, especially to the IR portion of the spectrum. Don't forget to spin the planet a bit to achieve a reasonable length day. Add plenty of water. Add plants that thrive in a cloudy environment, throw in some some dinosaurs, and then include near humans in a matriarchal society that enslaves male astronauts who land there. 1950'S B movie status achieved.

Mars. Heat the core and spin it to get a magnetic field. Add a thin, yet breathable atmosphere that's high in greenhouse gasses to keep the place warm enough. Throw in some water, but keep it dry. Steal life forms from the John Carter of Mars series. See which group starts digging canals first.

The Moon. Again, get a magnetic field added. If you want to keep the look of the original, keep the high oxygen atmosphere barely breathable at the surface and have nearly all life in deep caverns. Figure out some chemosynthetic plant replacements, or have some very convenient rocks that glow far too brightly for aeons while also not giving off lethal radiation.

Dinner time! Someone else can figure out the more exotic places.

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I am a little disappointed by the answers so far.

There are several hypothetical ways to make small worlds with low escape velocities have substantial atmospheres.

Habitable Planets for Man, Stephen H. Dole, 1964, discusses the requirements for human habitability.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

On page 35 Dole describes the escape velocity requirements for a world to retain a gas in its atmosphere. The ratio between the escape velocity of the world and the root-mean-square of the velocity of the gas particles in the exosphere, the outer atmosphere where particles escape from the planet, is vital.

According to table 5 on page 35, the e -1 life of an atmosphere will be zero if the ratio is 1 or 2, a few weeks if the ratio is 3, several thousand years if the ratio is 4, approximately a hundred million years if the ratio is 5, and approximately infinite if the ratio is 6 or higher.

The speed of gas particles in the exosphere is caused by their temperature, which is believed to be caused by ultraviolet radiation from the Sun. On page 54 Dole said that if the exosphere temperature of a habitable planet could be as low as 1000 degrees K, the root-mean-square velocity of atomic oxygen would be 1.25 kilometers per second and a world with and escape velocity 5 times that, or 6.25 kilometers per second, could retain oxygen for a long enough time.

Going back to figure 9, this may be seen to correspond to a planet with a mass of 0.195 Earth mass, a radius of 0.63 Earth radius, and a surface gravity of 0.49 g.

A radius of 0.63 Earth radius would be 4,013.73 kilometers or 2,494.044 miles. Such a radius would be greater than the radii of Mercury, Mars, Pluto, the largest asteroids, and the largest moons of the giant planets.

So it would seem to be impossible for them to retain atmospheres for long.

But the temperatures in the exospheres of the smaller worlds that are farther from the Sun than Earth would probably be lower due to receiving less solar radiation, and thus the root-mean-square velocities of gas particles in the exospheres would be lower, thus making 5 times the root-mean-square velocities a lower number than 6.25 kilometers per second.

Furthermore, the highly advanced people terraforming those worlds may not have cared whether the atmospheres would last as long as one hundred million years. Ten million years, or one million years, or one hundred thousand years, might have been long enough for their purposes. Thus they might have been satisfied with creating worlds that had escape velocities which were only 4.75, or 4.50, or 4.25, times the root-mean-square velocity of gas particles in their exospheres.

So the world builders would have to increase the masses of the smaller worlds in the solar systems they created considerably, but not necessarily enough to make them all at least 0.195 times the mass of Earth.

So the better the radii and diameters and volumes of those small worlds were known before the space age, the more dense the materials used by the world builders would have to be for their copycat worlds high enough escape velocities.

The smaller and less massive a world is, the less its core materials will be compressed by the weight of materials above them, and the more its average density will depend on the natural density of its materials.

The densest known naturally occurring element is osmium, with 22.59 grams per cubic centimeter. Unfortunately osmium reacts with oxygen to produce the highly toxic gas osmium tetroxide. So Osmium shouldn't be a major component of a planet with an oxygen rich atmosphere.

Iridium is almost as dense as osmium at 22.56 grams per cubic centimeter and is much less toxic. It would be safe to built most of a world out of iridium. Platinum has a density of 21.46 grams per cubic centimeters.

Of course osmium, iridium, and platinum are very rare, so the world builders would have to mine the gases of an exploding supernova and synthisize them.

Assuming that most of a constructed small world would be made of iridium, with thin layers of normal rocks, ground, and water on top, the volume, mass, surface gravity, and escape velocity can be calculated for various sizes.

Since Earth has an overall density of 5.514 grams per cubic centimeter, an iridium world would have 4.0914036 times the density of Earth. Here are links to the surface gravity and escape velocity calculators used: https://philip-p-ide.uk/doku.php/blog/articles/software/surface_gravity_calc https://www.omnicalculator.com/physics/escape-velocity

0.1 times the radius, 637.1 kilometers or 395.88 miles, would give 0.001 times the volume or 0.0040914036 times the mass. That gives a surface gravity of 0.41 g and an escape velocity of 2.2626 kilometers per second.

0.2 times the radius, 1,274.2 kilometers or 791.76 miles, would give a volume of 0.008 Earth and a mass of 0.0327312 Earth. That gives a surface gravity of 0.82 g and an escape velocity of 4.525 kilometers per second. That might be an adequate escape velocity for a body in the outer solar system to retain oxygen long enough.

I note that the outer solar system bodies Io, Europa, Ganymede, Callisto, Titan, and Triton had larger estimated radii before the space age, and so iridium worlds with their diameters should have been able to retain oxygen atmospheres for considerable periods of time

0.3 times the radius, 1,911.3 kilometers or 1,187.64 miles, would give a volume of 0.027 Earth and a mass of 0.1104678 Earth. That gives a surface gravity of 1.23 g and an escape velocity of 6.788 kilometers per second. That escape velocity is slightly more than necessary to retain oxygen for one hundred million years with surface temperatures similar to those of Earth.

And that size is smaller than the pre space age estimates of the diameters of Ganymede, Callisto, Titan, and Triton.

0.4 times the radius, 2,548.4 kilometers or 1,583.52 miles, would give a volume of 0.064 Earth and a mass of 0.2618498 Earth. That gives a surface gravity of 1.64 g and an escape velocity of 9.05 kilometers per second. A surface gravity of 1.64 g would probably be too uncomfortable for human settlers and humanoid aliens on such a planet would probably not look like Earth humans.

Lead is quite common. Although it is poisonous to humans, it would probably not cause problems locked away in a world's core separated from the surface by kilometers of other substances. Lead has a density of 11.342 grams pr cubic centimeter, or 2.0569459 times the overall density of Earth.

0.4 times the radius, 2,548.4 kilometers or 1,583.52 miles, gives 0.064 Earth volume and 0.1316445 Earth mass. That gives a surface gravity of 0.83 g and an escape velocity of 6.417 kilometers per second, slightly more than necessary to retain an oxygen atmosphere for one hundred million years with surface tempratures similar to Earth's.

0.5 times the radius, 3,185.5 kilometers or 1,979.4 miles, would give a volume of 0.125 Earth and a mass of 0.4443003 Earth. That gives a surface gravity of 1.03 g and an escape velocity of 8.021 kilometers per second.

0.6 times the radius, 3,822.6 kilometers or 2,375.28 miles, would give a volume of 0.216 Earth and a mass of 0.4443003 Earth. That gives a surface gravity of 1.23 g and an escape velocity of 9.626 kilometers per second.

0.7 times the radius, 4,459.7 kilometers or 2,771.16 miles, would give a volume of 0.343 Earth and a mass of 0.7055324 Earth. That gives a surface gravity of 1.44 g and an escape velocity of 11.23 kilometers per second, slightly higher than Earth's.

So it would seem theoretically possible to construct worlds the approximate sizes that Io, Europa, Ganymede, Callisto, Titan, and Triton were believed to be before the space age mostly out of Iridium or some other heavy elements, to have high enough escape velocities to retain oxygen atmospheres for thousands or millions of years.

Unfortunately, some Old Solar System stories put oxygen atmospheres and relatively Earth like life on even smaller solar system bodies.

For example, there were traces of an atmosphere and life on Amalthea, or Jupiter Five, in Arthur K. Barnes's "Satellite Five", Thrilling Wonder Stories, October 1938. Amalthea is only 250 by 146 by 125 kilometers, although before the space age it could be imagined to be a lot larger, though nowhere near the size of the Galilean moons.

https://www.solarsystemheritage.com/amalthea.html

There were a lot of stories with life and/or a breathable atmosphere on Titan, which is fairly plausible considering the titanic size of Titan. But I have read a story, "Schedule" by Harry Walton, Astounding science fiction June, 1945, where characters are involved in trade with the natives of Saturn's moon Rhea, who are not seen or described. http://www.isfdb.org/cgi-bin/title.cgi?45630

Rhea is now known to have a mean radius of 753.8 kilometers, although before the space age its size was not known very precisely. that makes it rather implausible for Rhea to have an oxygen atmosphere.

"A Matter of Size", by Harry Bates, Astounding Stories, April, 1934, mentioned that the protagonist had previously escaped from the Mutrantian Titans of Saturn's Satellite Three, who were ten times as tall as humans. I always assumed that the Titans came from Titan. http://www.isfdb.org/cgi-bin/title.cgi?47093

But maybe they wre called Titans because of their titanic size. I recently read a suggestion that the titans came from Thethys, the third satellite out from Saturn known before the space age. https://en.wikipedia.org/wiki/Saturn_in_fiction#Moons

Tethys has a mean diameter of only 1,062 kilometers and radius of 531 kilometers, so is unlikely to have breathable atmosphere, though before the space age it might have been imagined to be much larger.

And much the same goes for the moons of Uranus and various asteroids with life in Old Solar Ssytem type stories.

Either the world builders don't try to make such small worlds habitable or they have to find other ways to make them keep their atmospheres.

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Nucleation

Venus has an equilibrium temperature of 260 K - a little chilly, five degrees C above Earth. What makes our Venus hot is the mother of all greenhouse effects.

Your Venus will be very short on CO2, because its rampant plant life absorbs almost every molecule of the gas. But ... water is also a greenhouse gas! Your Venus might still be too hot, taking into account its thick, steamy atmosphere.

This is where looks are deceiving. Your Venus is, yes, covered by clouds, which conceal a watery surface dominated by foggy swamps and small seas. But looks are deceiving! The air is foggy with droplets of water, yes - but the vast majority of the planet's atmosphere is as dry as the air over the Sahara.

The trick? Nucleation. The plant life of Venus produces a tremendous number of small fertile particles, which we might loosely call spores, pollen, or airborne gametophytes, depending on how we choose to describe their reproductive processes in words. The spores take up a large amount of water, and use active metabolic processes to enhance the droplets they are bound to despite the dryness. They physically manipulate each and every water molecule like an enzyme binding a substrate.

Released above large stands or colonies of similar plants, the fogs initially served as a reproductive mechanism, and still do. At a low level, scarcely above the treetops, they became co-opted as a local sunscreen, and to some extent they still serve this role. Yet over time, as the air grew drier, the spores also evolved to fly much, much higher, stealing the water that would have gone to cumulus and stratus clouds, competing with one another to bring that water ever further up into the coldest fringes of the atmosphere. They compete to select out deleterious mutations they way human sperm do, but also collaborate to help select one another on a wider range of criteria, and to form effective colonies of multiple symbiotic plant cells. When they prepare for their return to the ground, they work together to choose a future shape (bushy or tall, woody or supple) and preferred environment. High in the sun, they enjoy the strongest energy source Venus can provide, yet they are dependent on the nutrients they were packaged with from the ground. So in the end, as yet tiny embryos, they adhere together in a regulated way to bring down raindrops on the drenched surface of the planet, and high humidity in the small zone beneath the lower level of protective fog.

In a page ripped from the Gaia hypothesis, these plant spores regulate the temperature of the entire planet with their high albedo and enforced dryness. The planet appears completely out of any sensible hydrological equilibrium, but it is in fact in a homeostatic equilibrium. And it is the very energy of the life-giving Sun that powers this biology and prevents the planet from developing a runaway greenhouse effect and becoming so hot that it would lose the hydrogen that makes its water possible.

---- Addendum ----

  1. Why didn't Venus get steam-sterilized before this evolved? Because the Sun was much fainter earlier in history. Earth was frozen almost all the way to the equator, and it takes some doing to explain how life managed here. Life had plenty of chance to evolve on Venus before this happened.

  2. Why isn't our Venus like this? Because life on Venus progressed to sentience nearly a billion years ago. While we can't know all the details, Venus is (or may have been) entirely resurfaced about a billion years ago. This event killed the biosystem, and all the CO2 in the plant life was released. The atmosphere became so hot that hydrogen atoms from the carefully conserved water poured out into space. Only a tiny subset of organisms that had crossed space on a natural asteroid or during the final doomed quest to colonize Earth remain, preserved in exile, firmly resolved to repeat their mistakes.

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Diverse environments

On earth, we find different forms of life in very diverse environments e.g.

  • Fish are found in the Mariana Trench 7 km below the ocean’s surface living in total darkness and at pressures 1,000 times more than at sea level.
  • Bacteria have been found living at high temperatures. P. fumarii could live at temperatures at 113 °C (235 °F). Strain 121 can grow at 121 °C and can even survive for two hours at 130 °C. There are bacteria living at 250 °C.
  • Methane-eating microbes have been found that help regulate Earth’s temperatures with remarkably high metabolic rates within seafloor carbonate rocks.

Your Life form

Your life form can live in

  • liquid methane or ethane as found in lakes of Titan.
  • Thick mixture of carbon dioxide and nitrogen at high temperature as found on Venus.
  • Thin mixture of carbon dioxide and nitrogen at low temperature as found on Mars.
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Another answer to my question.

In the "old Solar System" in old science fiction stories from the first 60 years of the 20th century, some of the other panets and/or moons in the solar system had life of their own, and in many cases were habitable for Earth humans, so that Earth humans could survive on their surfaces without any enviromental protection.

So I asked about ways which persons with advanced science and technology might have created a sort of a fake "old Solar System", when the other worlds appeared to the natives of the duplicate Earth - with their pre space age instruments - to be more or less similar to those worlds looked to people of our Earth before the space age, when it was still considered possible that some other worlds might possibly have native life on their surfaces.

The trick would be to built worlds which looked like the worlds in our solar system looked with pre space age astronomical instruments, but which were actually different enough from the real worlds to have oxygen rich atmospheres, for example.

In my previous post I discussed ways to get the smaller planets and larger moons to have much higher escape velocties than they actually have, so they can retain dense atmosphers for at the least the thousands or millions of years than the builders of those fictional "old solar systems" would want them to keep their atmospheres.

Since pre space age astronomers already had fairly good ideas about the diameters and volumes of those smaller planets and large moons, I tried giving them greater masses, densities, and escape velocities by making them mostly composed of super dense iridium or lead with thin surface layers of other materials necessary to support life.

And I found that objects with radii as low as 0.4 Earth radius, or 2,548.4 kilometers or 1,583.52 miles, could have a high enough escape velocity to retain substantial atmosphere for thousands or millions of years, which might be long enough for the purpose of their builders, if they were almost entirely made of iridium, or possibly lead in the case of Ganymede and Titan.

And even objects with radii as low as 0.2 Earth radius, or 1,274.2 kilometers or 791.76 miles, could have escape velocities as high as 4.525 kilometers per second, which might enable them to retain atmospheres long enough, if made almost entirely of iridium with thin surface layers of other materials.

We now know that beside the planets, the moons Ganymede, callisto, and Titan have radii over 1,911.3 kilometers, while Io, the Moon, Europa, and Triton have radii over 1,274.2 kilometers. That makes seven moons, in addition to the planets, which might possibly have had escape velocties high enough to retain substantial atmospheres if they were almost entirely made of Iridium.

However, there were a total of 31 moons known in the solar system before the space age started and many smaller moons were discovered. Earth had 1, Mars 2, Jupiter 12, Saturn 9, Uranus 5, and Neptune 2. The smaller moons on that list were still being discovered during the period of 1904-1951 when old solar system stories were being written, and some of them are described as having life and even as being habitable for humans in some stories, despite being much smaller than even 0.3 Earth radius.

There were also thousands of asteriods and comets known before the space age, all much smaller than 0.3 Earth radius,and some of them were described in fiction as having life and/or being habitable for humans.

An object with 0.001 of the mass of the Earth and a radius of 6.371 kilometers, 0.001 of Earth's radius, would have an escape velocity of 11.186 kilometers per second, similar to Earth's escape velocity. It would have 0.001 times Earth's mass in 0.000000001 if Earth's volume and so would be 1,000,000 times as dense as Earth. It would have a surface gravity of 1,002.06 g.

An object with 0.001 of the mass of the Earth and a radius of 63.71 kilometers, 0.01 of Earth's radius, would have an escape velocity of 3.537 kilometers per second, probably not large enough to retain an atmospehre. It would have 0.001 times Earth's mass in 0.000001 times Earth's volume and would have a density of 5,514 grams per cubic centimeter, or 1,000 times Earth's density. It would have a surface gravity of 10.02 g.

An object with 0.001 of the mass of the Earth and a radius of 31.855 kilometers, 0.005 of Earth's radius, would have an escape velocity of 5.002 kilometers per second, which might be enough to retain an atmosphere for long enough. Such an object would have 0.001 of Earth's mass in 0.000000125 of Earth's volume. Thus it would have a density of about 44,112 grams per cubic centimeter, about 8,000 times as dense as Earth. It would have a surface gravity of 40.08 g.

An object with 0.0001 the mass of Earth and a radius of 0.6371 kilometers, 0.0001 the radius of Earth, would have an escape velocity of 11.186 kilometers per second, similar to Earth's. It would have 0.0001 time the mass of Earth in 0.00000000001 the volume, and would be about 100,000,000 times as dense as Earth -551,400,000 grams per cubic centimeters. It would have a surface gravity of 10,020.66 g.

An object with 0.01 the mass of Earth, and a radius of 63.71 kilometers, 0.01 that of Earth, would have an escape velocity of 11.186 kilometers per second, similar to Earth's. It would have 0.01 of Earth's mass in 0.000001 of Earth's volume, and thus a density of 55,140 grams per cubic centimeter - 10,000 times that of Earth. It would have a surface gravity of 1,002.06 g.

An object with 0.1 the mass of Earth, and a radius of 637.1 kilometers, 0.1 that of Earth, would have an escape velocity of 11.186 kilometers per second, similar to Earth's. It would have 0.1 of Earth's mass in 0.001 of Earth's volume, and thus a density of 551.4 grams per cubic centimeter - 100 times that of Earth. It would have a surface gravity of 10.02 g.

An object with 0.05 the mass of Earth, and a radius of 637.1 kilometers, 0.1 that of Earth, would have an escape velocity of 7.91 kilometers per second, which should be enough to retain an atmosphere for millions of years. It would have 0.05 of Earth's mass in 0.001 of Earth's volume, and thus a density of 275.7 grams per cubic centimeter - 50 times that of Earth. It would have a surface gravity of 5.01 g.

An object with 0.02 the mass of Earth, and a radius of 637.1 kilometers, 0.1 that of Earth, would have an escape velocity of 5.002 kilometers per second, which might be enough to retain an atmosphere for millions of years. It would have 0.02 of Earth's mass in 0.001 of Earth's volume, and thus a density of 110.28 grams per cubic centimeter - 20 times that of Earth. It would have a surface gravity of 2 g.

An object with 0.015 the mass of Earth, and a radius of 637.1 kilometers, 0.1 that of Earth, would have an escape velocity of 4.322 kilometers per second, which might be enough to retain an atmosphere for millions of years. It would have 0.015 of Earth's mass in 0.001 of Earth's volume, and thus a density of 82.71 grams per cubic centimeter - 15 times that of Earth. It would have a surface gravity of 1.5 g, which might be low enough to be bearable for Earth humans without antigravity technology.

So using even denser materials than iridium, it might be possible for somewhat smaller worlds to have both a high enough escape velocity to retain an atmosphere and a low enough surface gravity for humans to visit. But it doesn't seem likely that any combination of mass and radius would work for objects with a radius much less than 650 kilometers, which leaves out a lot of small moons and all of the asteroids.

And what sort of material could have such high densities?

It might be possible to create artificial superheavy isotopes that don't rapidly decay. There is a theoretical "island of stabiity" predicted to exist among some superheavy elements. So possibly the builders of an artifical solar system might find a way to create massive amounts of superheavy elements in the "island of Stabiity" that might be dense enough and also last long enough to build worlds out of.

https://en.wikipedia.org/wiki/Island_of_stability

A white dwarf star is dense enough that most of its matter would be what is called degenerate matter. Degenerate matter is extremely dense. It would certainly be dense enough to give even small moons and aseroids high enough escape velocity.

https://en.wikipedia.org/wiki/Degenerate_matter

There is a famous story by Jack Vance, "I'll Build YOur deam Castle", where small amounts of degenerate matter from white dwarf stars are coated with normal matter to bring the surface gravity down to Earth normal and terraformed to be habitable.

http://www.isfdb.org/cgi-bin/title.cgi?57659

Unfortunately, the degenerate matter inside white dwarf stars is dense and degenerate because of the pressure of all the matter above and around it. If degenerate matter was removed somehow from a white dwarf star, the pressure would be removed and it would expand and become much less dense normal matter instead.

Neutron stars are even denser than white dwarfs, and the matter inside them is mostly neutrons formed by protons and electctrons being forced together, with shells of degenerate matter and normal matter at the surface.

https://en.wikipedia.org/wiki/Neutron_star

And the neutron star matter would also rabidly expand into normal matter if removed from the pressures in the neutron star.

To be continued.

Continued 01-24-2022.

Of course black holes are even denser than white dwarfs and neutron stars.

And nothig can get out of black holes - except for Hawking radiation.

Hawking radiation is thermal radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical argument for its existence in 1974.1

https://en.wikipedia.org/wiki/Hawking_radiation

Very massive stars can eventually collapse and form stellar mass black holes. And where stars, and thus stellar mass black holes are densely packed, like in the center of a galaxy, stellar mass black holes can merge to form supermassive black holes.

Theoretically, black holes with much less than stellar mass could have formed during the Big Bang (and maybe a superadvanced civilization might be able to create such mini black holes.

Hawking showed that the amount of energy and mass Black holes lose through Hawking radiation is inversely proportaional to their mass. The less massive a black hole is, the more energy it emits, and the more mass it loses. As it gets less massive, it loses mass faster, until a black hole with very little mass will finally explode into nothingness.

Mini black holes produced during the Big Bang will have evaporated unless their initial mass was more that about 5 times 10 to the 11th power grams - 500,000,000,000 grams. The mass of planet Earth is about 5.97237 times 10 to the 27th power kilograms or 5.97237 times 10 to the 30th power grams. So Earth has a mass about 1,194,4740,000,000,000,000 greater than the least massive primordial black hole which could survive to the present time.

So a small black hole inside a planet could give the planet a lot more mass and increase the surface gravity and escape velocity of the planet. But of course the black hole would absorb matter from the planet and grow more and moe massive. Eventually a time may come when what is left of the planet might suddenly collapse into the black hole.

Here is a link to a question asking how long a world would last if it had an Earth mass black hole inside it.

How long could a planet or moon survive if it had an Earth mass black hole within it?

The answer by Ash suggested that a world could last for billions or trillions of years with an Earth mass black hole at the center. So if Ash correctly accounted for all the factors, increasing the escape velocity of small worlds by putting natural or artificial black holes of the correct mass inside them shouldn't destroy those worlds anytime soon.

So that avoids the problem that degenerate matter or neutronium would expand to become matter of normal density if removed from white dwarf stars or neutron stars.

Physicists have imagined many forms of exotic matter. It is possible that some of those forms of exotic matter exist, or can be made, and can be stable when surrounded by "normal" matter, and some such forms of exotic matter might possibly be much denser than normal matter, and thus useful for increasing the escape velocities of small worlds.

Using such hypothetical forms of exotic matter would avoid the tendency of degererate matter and neutroomium to expand when removed from high pressures, and eliminate the problem of mini black holes slowly absorbing the matter of any worlds they might be inside.

One form of exotic matter which probably exists is dark matter.

Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe.1 Various astrophysical observations — including gravitational effects that accepted theories of gravity cannot explain unless more matter is present than can be seen — imply dark matter's presence. For this reason, most experts think that dark matter is abundant in the universe and has had a strong influence on its structure and evolution. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not absorb, reflect, or emit electromagnetic radiation (like light) and is, therefore, difficult to detect.2

https://en.wikipedia.org/wiki/Dark_matter

Dark matter is probably some as yet unknown type or types of subatomic particles. Since dark matter reacts to gravity, astronomical bodies might be able to capture dark matter to increase their mass, though dark matter is believed to avoid clumping together and forming larger objects. So presumably astronomical objects could not acquire or retain much thinly scattered dark matter.

I note that mini black holes could solve the problem of giving a world enough mass to have sufficient escape velocity to retain an atmosphere while also having a low enough surface gravity to be habitable for humans.

Imagine a world the size and density and mass of Earth's Moon, which acquires a mini black hole with many times that mass, so together the world and the black hole inside it have the same mass as Earth, with the radius of the Moon, 1,737.4 kilometers.

Such a world would have an escape velocity of 21.42 kilometers per second, and a surface gravity of 13.47 g.

If you reduced the mass to 0.2 times the mass of Earth, the escape velocity would go down to 9.58 kilometers per second, quite acceptable, and the surface gravity would go down to 2.69 g, less crushing but still dangerous for humans.

If you reduced the mass to 0.1 times the mass of Earth, the escape velocity would go down to 6.77 kilometers per second, which would probably be adequate to retain an atmosphere, and the surface gravity would go down to 1.35 g, which would be highly uncomfortable for long term human habituation.

If you reduced the mass to 0.08 times the mass of Earth, the escape velocity would go down to 6.059 kilometers per second, which would probably be adequate to retain an atmosphere, and the surface gravity would go down to 1.08 g, which would be tolerable for long term residence.

In the case of an object as large as the Moon, with a radius as large as 1,737.4 kilometers, it is possible to design a mass for that object that produces both a barely acceptable escape velocity and an acceptable surface gravity.

But with worlds smaller than that, the mass necessary for a large enough escape velocity will produce a dangerous and unbearable for humans surface gravity.

But if a small world of ordinary matter as a mini back hole at its center to increase the mass, it can also be orbited by a group of much less massive mini black holes. If those many less massive black holes orbit below the exosphere where the world's atmosphere escapes into space, their gravity will add to the other gravity and increase the escape velocity, enabling the world to retain atmosphere longer.

But the gravity of those mini black holes orbiting above the surface would pull upwards, and conteract the gravity of the world inself and the black hole inside it, and so could, in some configurations, reduce the surface gravity of the world to an acceptable level.

So if an advanced society can find or manufacture mini blackholes with the required masses, or perhaps stable, long lasting, high density forms of exotic matter, they might be able to give even the smallest planet, moon, oasteroid, or other world, both a high enough escape velocity and a low enough surface gravity to be habitable.

And of course if a society has advanced enough science and technology, natural gravity produced by the presence of mass would not be necessary. In some science fiction stories some advanced societies can generate artificial gravity without the presence of mass. And some writers might consider generated gravity to be too way out for the hardness level of their science fiction story, and other writers might consider generated gravity acceptable.

https://tvtropes.org/pmwiki/pmwiki.php/SlidingScale/MohsScaleOfScienceFictionHardness

The Legion of Space is a science fiction novel by the American writer Jack Williamson. It was originally serialized in Astounding Stories in 1934, then published in book form (with some revisions) by Fantasy Press in 1947 in an edition of 2,970 copies. A magazine-sized reprint was issued by Galaxy in 1950, with a standard paperback following from Pyramid Books in 1967.

https://en.wikipedia.org/wiki/The_Legion_of_Space

As planetary en- gineers, the Ulnars contributed a full share to that new science, which, with gravity generators, synthetic at- mospheres, and climate-controls, could finally transform a frozen, stony asteroid into a tiny paradise.

Page 12.

The tiny inner moon of Mars, a bit of rock not twenty miles in . diameter, had always been held by the Ulnars, by right of reclamation. Equipping the barren, stony mass I with an artificial gravity system, synthetic atmosphere, and "seas” of man-made water, planting forests and gardens in soil manufactured from chemicals and disintegrated; stone, the planetary engineers had' transformed into a splendid private estate.

p. 38

https://archive.org/details/Galaxy_Science_Fiction_Novel_02_Jack_Williamson_The_Legion_Of_Space_1935/page/n35/mode/2up

So in the fictional universe of The Legion of Space tens, hundreds, and maybe thousands of worlds in the solar system had been terraformed to be habitable for humans. Since most of them were too small to have sufficient escape velocity, especially if worlds as small as Phobos were commonly terraformed, the gravity generators must have been used to give the smaller worlds sufficient escape velocity to hold onto their artifical atmospheres.

And of course the problem with using the artifical gravity generators is that the amount of generated gravity necessary to give a world of a specific size a sufficiently high escape velocity would probably be far too much to give it a surface gravity low enough to be endurable.

Jack Williamson lived until 2006, and I wonder if he ever realized the difference between surface gravity and escape velocity and realized that there was a flaw in the description of terraforming in The Legion of Space (1934, 1947).

And possibly the way to avoid that flaw with generated gravity would be to dig a shaft to the center of a small world and build a big artificial gravity generator in the center, that would generate enough gravity to create sufficient escape velocity, and to also position smaller gravity generators in low orbit around the small world. The gravity generated by the smaller orbital generators would add to the gravity in the exosphere above them, and increase the escape velocity of the world, while it would reduce the surface gravity below them on the surface, to comfortable levels.

And I have to say that I am a little proud of having identified the problem of conflicting escape velocity and surface gravity requirements and then solving it, yesterday, January 24, 2022.

well, at least I solved it in a fictional universe where mini black holes of the right masses or artifical gravity generators are available!

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Tues. January 25, 2022.

My own question is about arificially constructing a solar system where many or all of the planets, moons, etc. are habitable, sometimes even habitable for Humans, despite the distances of those objects from their very Sun-like star and the diameters abd masses of those objects being the same as was known by astronomers before the space age, back when science fiction stories set in the "Old Solar System" were being written.

In many cases the diameters and masses of those planets, moons, and other objects were not known very precisesly when "Old Solar System" type stories were being written before the space age, so that leaves a significant range of possible values to choose from.

But even allowing for such uncertainty, it was clear that there were and are thousands of objects in our solar system which do not have sufficient diameter, mass, or density to have sufficient escape velocity to retain atmospheres for billions, millions, or thousands of years. There are millions of objects which could only retain an atmosphere for seconds.

So it would not be worthwhile for an advanced society to terraform those worlds and give them breathable atmospheres if those atmospheres would not last long enough.

So in my previous two answers to my own question, I discussed various more or less plausible, and even more or less possible, methods of increasing the masses and densities of small solar system objects to increase their escape velocities and enable them to retain atmospheres long enough for the purposes of the people who give them those atmospheres.

And I suggested that in some science fiction stories it would be possible to use artifical gravity generators to give a world far more gravity than the world's actual mass would give it.

And I suggested ways to get around the problem that for many diameters of worlds the amount of natural or artificially generated gravity necessary to give them sufficient escape velocity to retain atmospheres for long enough would also give them surface gravities many times stronger than human characters could survive.

And now in this answer to my own question I suggest a simpler method of giving small worlds the ability to retain an artificial atmosphere for long enough times.

I now quote my answer from another question:

How long can this planet hold its atmosphere?

Part One of Six.

Here is another answer to the question about how long a planet - a planet with a radius of 2,142 kilometers, mass of 6.594 X 10 the 23rd power kilograms or 0.1104084 the mass of Earth, and thus a surface gravity of 0.98 g and an escape velocity of 6.41 kilometers or 3.983 miles per second - could retain its atmosphere.

In my previous answer I wrote that if the oxygen in the exosphere of the planet's atmosphere, where gases escape into space, had a temperature of 1000 degees K or less, and a root-mean-square speed of 1.25 kilometers per second or slower, the planet could hold an oxygen atmosphere for about a hundred million years if it had an escape velocity of at least 6.25 kilometers per second.

Since your planet has an escape velocity of 6.41 kilometers per second, it may be able to hold on to an oxygen atmosphere for a hundred million years.

My previous answer also said that with the radius and mass specified in the question, the planet has an overall density of 16.018949 grams per cubic centimeter, which is a lot denser than most naturally occuring elements. Your planet would have to be composed almost entirely out of one of the densest known elements, which would be rather unlikely to happen naturally.

So perhaps I should suggest an alternate method of enabling a small planet with a radius of only 2,142 kilometers to retain its artifically produced atmosphere for long periods of time, without giving that planet extra mass requiring an improbable density.

Part Two: Percival Lowell's Main Error.

What was Percival Lowell's big error in his theory of the Martian canals?

Lowell believed that the planet Mars was slowly losing its water. Molecules of water vapor in the upper atmosphere would have been broken up by ultra violent ultraviolet rays into atoms of hydrogen and oxygen. The ultra light hygrogen would move too fast compared to the escape velocity of Mars and would escape from the planet, never again to combine with oxygen to make more water.

This process happens in Earth's atmosphere, and probably was a main cause of the actual lack of water on Venus and Mars.

So Lowell believed the hypothetical Martians would make the best of it by using their dwindling water supplies efficiently, distributing snow melt water from the polar caps all over the planet with a system of canals, delaying their inevitable doom.

And apparently Lowell never thought that a better method for the Martians would be to keep the water from being lost from Mars by stopping the breaking up of water molecules and the escape of hydrogen from Mars.

How could the Martians do that?

How would humans living in hypothetical Moon bases prevent their air and water from escaping into outer space? By building totally enclosed Moon bases where air and water could not get out and would be endlessly recycled.

So the hypothetical Martians could have solved the problem of Mars slowly losing water by building larger and larger totally self contained "Moon bases" on Mars, perhaps eventually totally covering all of Mars with an airtight roof to prevent air, especially the hydrogen necessary for water, from escaping.

Astronomers in Lowell's time didn't have very good views of Mars. There was no way they could have been able to tell if they were seeing the actual natural surface of Mars or a planet wide roof made of more or less transparent or opaque material covering all of Mars and holding the atmosphere in.

Part Three: The Roof of the World.

So possibly the humans in your story decide to terraform a small planet with a radius of 2,142 kilometers which doesn't have the extreme density you ask for. 2,142 kilometers is a little less than the radius of Callisto (2,410 kilometers), which has an escape velocity of 2.440 kilometers per second. But Callisto has a very low density compared to Earth. Mercury is a bit larger (2,439 kilometers) but has a density much closer to Earth's density and has an escape velocity of 4.25 kilometers per second.

So it might be possible for your humans to find a planet with a radius of 2,142 kilometers which is massive and dense enough to have an escape velocity of about 4.00 kilometers per second, without the planet having a core made out of gold or some other rare element. And that might not be a high enough escape velocity to retain the artificial oxygen rich atmosphere they plan to produce when they terraform that planet for long enough.

So they could build a roof over the entire planet, with giant airlocks to allow spaceships to land. And fill the space below the roof with the artifical atmosphere they produce. That would be a massive project, but terraforming a planet is a massive project.

Part Four: A Roof of Nano Machines.

I remember once looking at, but not reading, a science fiction novel by Arthur C. Clarke and a collaborator. That might be the one that mentioned life forms in space which evolve to attack and consume parts of spacecraft. Anyway, in that story the Moon had been terraformed and given a breathable atmosphere. To prevent the atmosphere from escaping into space a sort of a roof made of gazillions of nano macheines was built over the moon. Each of the tiny nano machines was linked to its neighbors, and the spaces between were smaller than molecules. So air particles which hit the "roof" were bounced backed instead of escaping into space.

According to Wikipedia's list of theoretical megastructures:

Part Five: Planetary Roofs Supported by Air Pressure.

Shellworlds or paraterraforming are inflated shells holding high pressure air around an otherwise airless world to create a breathable atmosphere.[8] The pressure of the contained air supports the weight of the shell.

https://en.wikipedia.org/wiki/Megastructure#Planetary_scale

A shellworld13 is any of several types of hypothetical megastructures:

A planet or a planetoid turned into series of concentric matryoshka doll-like layers supported by massive pillars. A shellworld of this type features prominently in Ian M. Banks' novel Matter.

A megastructure consisting of multiple layers of shells suspended above each other by orbital rings supported by hypothetical mass stream technology. This type of shellworld can be theoretically suspended above any type of stellar body, including planets, gas giants, stars and black holes. The most massive type of shellworld could be built around supermassive black holes at the center of galaxies.

An inflated canopy holding high pressure air around an otherwise airless world to create a breathable atmosphere.4 The pressure of the contained air supports the weight of the shell.

Completely hollow shell worlds can also be created on a planetary or larger scale by contained gas alone, also called bubbleworlds or gravitational balloons, as long as the outward pressure from the contained gas balances the gravitational contraction of the entire structure, resulting in no net force on the shell. The scale is limited only by the mass of gas enclosed; the shell can be made of any mundane material. The shell can have an additional atmosphere on the outside.[5][6]

https://en.wikipedia.org/wiki/Shellworld

Having the roof of a shell world supported by air pressure is not some wild fantasy.

An air-supported (or air-inflated) structure is any building that derives its structural integrity from the use of internal pressurized air to inflate a pliable material (i.e. structural fabric) envelope, so that air is the main support of the structure, and where access is via airlocks.

https://en.wikipedia.org/wiki/Air-supported_structure

Some quite large structures are air supported, although they are much smaller than air supoorted shells around an entire asteroid or around an entire planet. But any story involving terraforming a planet involves mega projects.

Part Six: Force Fields.

In some science ficitons stories force fields of various types might have various practical uses. Perhaps in some stories force fields could keep the molecules of gas from escaping from tiny worlds which don't have enough escape velocity.

Those force shields might make it impossible for spaceships to land or take off. Or there might be giant air locks which stick up through the force shields that spaceships can take off and land in. Or maybe the force fields stop particles moving at the velocities of atmospheric gases, but let spaceships land and take off if they travel faster or slower than atmosphereic gases. For example, the classic Isaac Asimov story "Not Final!", Astounding Science Fiction, October 1941, involves a force field that can hold in air molecules.

https://archive.org/details/Astounding_v28n02_1941-10/page/n47/mode/2up?view=theater

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