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