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

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.

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 enoughto bearable for Earth humans without antigravity technology.

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 degernate matter and normal matter at the surface.

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 and merge to form supermassive black holes.

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 of 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.

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 science fiction some advanced societies can genrate artifical 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 migth consider generated gravity acceptable.

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 samller worldssufficient gravity to hold onto their artifical atmospheres.

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 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. At least solving it in a fictional universe where mini black holes of the right masses or artifical gravity generators are available!

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.

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.

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.

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.

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.

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.

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 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!

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 and 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 of 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 science fiction some advanced societies can genrate artifical 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 migth 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 samller worldssufficient gravity 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 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. At least solving it in a fictional universe where mini black holes of the right masses or artifical gravity generators are available!