In previous posts I have suggested that the Kalandan OUtpost Planet or K.O.P. probably had a larger diameter and lower mass that Kirk and Spock said.
I was able to take the "approximately the size of Earth's Moon" and a mass "similar to Earth's" as far as I though treasonable, and designed a world with twice the diameter and thus eight times the volume of the Moon, with a fifth of the mass of Earth.
That was about as far as I thought was resonable in interpreting Kirk and Spock's words, and produced a world with a surface gravity near the limit for human tolerance and a density low enough that the bulk of the K.O.P. could have been made of a mixture of iron with some of the heaviest naturally occuring elements known to science.
Suppose that we try to make the K.O.P. exactly fit the specificaitons that KIrk and Spock describe, with exactly the diameter of Earth's Moon and exactly the mass of Earth?
Such a K.O.P. would have 49.256958 times Earth's density of 5.414 grams per cubic centimeter, and thus 271.602549 grams per cubic centimeter (or gm/cm3 for short). And it would have a surface gravity which is 13.47 g (the surface gravity of Earth being 1 g), and escape velocity 1.9146254 of Earth's 11.186 kilometers per second - 21.417 kilometers per second (km/sec for short)..
And a surface gravity of 13.47 g would be unbearable and deadly for Kirk, McCoy, Sulu, and D'Amato. They would fall down to the ground as soon as they stopped transporting, and the Losira image wouldn't have to kill them as they starved to death without being able to move.
But maybe they wore anti-gravity equipment to keep the the gravity they felt about 1 g. Maybe the creators of the episode failed to show or mention that anti-gravity equipment but it was there in "real life" in the fictional universe of TOS.
But Losira was built like a human woman and looked like a native of a planet with a surface gravity of only 1 g, and not like some sort of mobile carpet shaped being from a planet with a surface gravity of 13.47 g. Why would the Kalandans build an outpost planet with a surface gravity so much higher than they were used to?
Possibly the Kalandans gave the K.O.P. a surface gravity of 13.47 g as a disguise. Maybe the hypothetical enemies of the Kalandans would see the K.O.P. and say: "Wow! That's an artifcial planet with a surface gravity of 13.47 g! Whoever built that must have an incredibly strange homewold." "Yes, but obviously those Klandans wouldn't build such a planet. They like normal gravity. Keep looking for Kalandans."
And meanwhile the Kalandans in the K.O.P. would be comfortable using anti-gravity in their hidden quarters.
So I can imagine that the Kalandans might come from a planet similar to Earth and have a reason to build the K.O.P. to be very different from their homeworld.
But would building such a world be possible for the Kalandans or anyone else?
The densest known element occurring naturally on Earth and in the Solar System is Osmium, with a density of 22.59 grams per cubic centimeter. The K.O.P. would have a density of 271.602549 grams per cubic centimeter, 12.023131 times as dense as Osmium.
Many of the heaviest elements are radioactive and decay into other elements and isotopes with half lives varying form millions of years to tiny fractions of a second. So all of those elements have decayed into other elements in the billions of years since the solar system was formed. Scientists have created many such elements in experiments.
And maybe the Kalandans could find such elements in young worlds in young solar sysems, or the clouds of dust and gas expelled by recent supernovae. Or maybe they would have to transmute other elements into heavy elements to build the K.O.P. Collecting gazillions of tons of naturally occuring matter to built the K.O.P. would be a very vast project, and transmuting gazillions of tons of other elements into the desired elements would make it much harder. But perhaps the Kalandans could do that.
But what elements would the Kalandans have to use to build the K.O.P. with its vast density?
The elements numbered between 93 and 118 have been produced in laboratories. Some have lower densities than Osmium, and some have higher densities. But most of those elements have been produced in such minuite quantities that their densities can not be measured, and figures for their densities are calculations based on their atomic structure.
Every atom of an element has the same number of protons in the nucleus. However, the number of neutrons in the nucleus can vary. Atoms with the same number of protons but different numbers of neutrans are isotopes of an element. The isotopes of elements calculated to have higher densities than Osmium can vary greatly in their half lives.
The isotope 270 Dubnium has a half life as high as about 1 hour, the longest of any isotope densier than Osmium. With 8,766 hours in a Julian calendar year, the amount of 270 Dubnium would decrease by half about 8,766 times in a Julian year, and so it would almost all be gone after only one year, let alone thousands. So if the K.O.P. was mostly made of 270 Dubnium, it would decay into less dense isotopes and swell up to a much larger size much sooner than within a single year.
The highest density calculated for a synthetic element is 40.7 grams per cubic centimeter for 108 Hassium, which is only 0.14985 of the required density of 271.602549 grams per cubic centimeter. The most stable isotope of Hasium is 277 Hassium which has a half life of 130 seconds. With 86,400 seconds in a day, it would decay into less dense substances by half 664.6 times in a day and if the K.O.P. was made of 277 Hassium it would thus swell up to a much larger size in less than a day.
So the K.O.P. could not be made out of any known chemical element. Science fiction stories are full of fictional elements which have all sorts of interesting properties and which are stable for long periods of time, thus either being non radioactive or else having very long half lives. The Diburium which is alloyed with Osium in the outer shell of the K.O.P. is one such fictional element.
And it is considered to be theoretically possible that there might possibly be some stable heavy elements.
In
nuclear physics, the
island of stability is a predicted set of
isotopes of
superheavy elements that may have considerably longer
half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the
chart of nuclides, separated from known
stable and long-lived
primordial radionuclides. Its theoretical existence is attributed to stabilizing effects of predicted "
magic numbers" of
protons and
neutrons in the superheavy mass region.
[1][2]
Several predictions have been made regarding the exact location of the island of stability, though it is generally thought to center near
copernicium and
flerovium isotopes in the vicinity of the predicted closed neutron
shell at
N = 184.
[4] These models strongly suggest that the closed shell will confer further stability towards
fission and
alpha decay. While these effects are expected to be greatest near
atomic number Z = 114 and
N = 184, the region of increased stability is expected to encompass several neighboring elements, and there may also be additional islands of stability around heavier nuclei that are
doubly magic (having magic numbers of both protons and neutrons). Estimates of the stability of the elements on the island are usually around a half-life of minutes or days; some estimates predict half-lives of millions of years.
[5]
Even if hypothetical elements in the island of stability can be harvested from recent supernovaa remnants or transmuted in the laboratory, they would seem to have little practical use unless their half lives were milliions of years, or at least thousands of yeaars, instead of mere days or minutes.
The memory Alpha article on Diburnium says that it is given an atomic weight of 377 and an atomic number of 122 in the S
tarfleet Medical Reference Manual. And if calculations suggest that such an element would not be stable, maybe diburium has a different atomic number and atomic weight than given in that non canon source.
But can an element in any hypothetical island of stabiity have a density of 271.602549 grams per cubic centimeters? Maybe, maybe not.
So whether it would be theoretically possible for an as yet undiscovered element to have a density of 271.602549 grams per cubic centimeter, and also last long enough to be useful, is uncertain.
But there is a way for ordinary elements to become super dense. Matter in the cores of white dwarf stars becomes compressed so much that it becomes degenerate. Electrons are stripped from their atomic nuclear which are pressed closer together than when the atoms or whole.
Typical values for the density of degenerate gas in white dwarf stars are about 10,000 kilograms per cubic centimeter, which is about 36,818.5 times the density needed for the K.O.P. A relatively small proportion of white star matter surrounded by ordinary matter whould be enough to give the K.O.P. the required density.
Unfortunately, when white star matter is removed from the tremendous pressures within a white star, it reverts to being normal matter and expands to a normal density.
Neutron stars are more massive than white dwarfs and their collapse under their gravity can't be stopped by becoming electron degenerate matter as in the cores of white dwarfs. They continue to collapse until their electrons in the core are driven into the protons to form neutrons. Neutron stars contain cores of this hyper dense neutron degenerate matter surrounded by layers of white star matter surrounded by top layers of ordinary matter. And if that neutron degenerate matter is removed from the intense pressures at the core of a neutron star it will rapidly expand to white star matter and then to normal matter.
Possibly the Kalandans could hold dense white dwarf or neutron star matter within the core of the K.O.P. using a powerfull force field to keep it from expanding. And possibly they have some way to use energy released by the dense matter to power the force field so they don't have to generate all the tremendous amounts of energy necessary. In that case the K.O.P. would last until the dense matter at its core stops producing energy to power the force field, which will collapse, allowing the dense matter to rapidly expand and assume a normal density.
Matter within the escape horizon of a black hole cannot escape, no matter if there is any outside pressure upon the escape horizon, and so it will remain compressed as long as the black hole endures. All known black holes are formed from the collapse of massive stars and thus have several times the mass of the Sun, and thus thousnds or millions of times the mass of the Earth required for the K.O.P. But primordial blakc holes formed during the Big Bang, if they exist, could have any mass, including a mass equal to that of Earth.
So perhaps the Kalandans coulde have found or made out of ordinary matter a planet the size, mass, and density of the Moon, and taken a black hole with the mass of Earth which they found - or perhaps created, like the artificial singularities of the Romulans - and put that black hole within the Moon like planet. And thus they would have created a planet with the size of the Moon and the mass of the Earth.
But how long would such a planet last before the black hole inside began to swallow significant amounts of it? I think that there would be many factors to be considered when calculating how long the planet would last, and if someone omitts an important factor their calculations might be in error. But I did ask a question about how long it would take for an Earth mass black hole to swallow a planet that it was inside.
https://worldbuilding.stackexchange...vive-if-it-had-an-earth-mass-black-hole-withi
And one answer says it would take billions of years. So if that answer is anywhere near correct the K.O.P. should last for the thosuands or millions of years the Kalandans may have intended to use it.
So there is at least one method of giving the K.O.P. the required density of 271.602549 grams per cupic centimeter which doesn't seem to violate any know scientfic laws and which might be possible,though a very,very big megaproject.