So the problem for people who want to interpret the Kalandan Outpost Planet (or K.O.P.) as having as much matter in as small a volume as Kirk and Spock say, is that it would have an average density of 271.602549 grams per cubic centimeter.
And that would be far denser than any known material in conditions familiar to us. Of course, under conditions of extreme pressure, like in the cores of large planets and in the cores of massive stars, or the cores of white dwarfs, or the coares of neutron stars, or within the event horizons of black holes, ordinary matter can be compressed to much greater densities than 271.602549 grams per cubic centimeter.
But such compression is a result of the weight of material higher up pressing down on material lower down, due to the gravitational interaction of all the matter within that astronomical object. If all the matter higher up is removed, the compressed matter would tend to decompress - possibly quite explosively. So the K.O.P. could not be built of such dense materials if it had merely the size of the Moon and merely the mass of Earth. It it was created in an instant by magic, its gravity would not be strong enough to keep it from decompressing rapidly.
The only form of normal but highly compressed matter that would not decompress would be matter within a black hole's event horizon. So one theoretical model for the K.O.P. would be world with the volume, mass, and density of Earth's Moon, with a tiny black hole with the mass of the Earthin side the Moon like object. One could hope that the Kalandans calculated that such a K.O.P. would last long enough for their unspecified purposes.
But there may be other and more exotic forms of matter. The last time I checked there many theoretical particles in particle physics, some of them confirmed by experiments. And atoms of matter could theoretically be built out of many of those exotic particles.
For example, there is antimatter, consisting of antiparticles otherwise similar to normal matter. Three is a possbility that antimatter might have reverse gravity, repelling other antimatter and normal matter. That would not help building a dense world. But it is considered almost certain that anti partiles have gravitational attraction to other antiparticles and normal matter. But that would not help in constructing a superdense world since the anti particles and normal particles which were pulled into contact with each other by their gravity would annihilate each other.
Mirror matter, also called shadow matter, and Alice Matter, is a hypothetical courterpart of ordinary matter. Most of the interactions of mirror matter, if it exists, with ordinary matter would be through gravitational interaction. So if there is a lot of mirror matter in the universe, it might be possible in Star Trek to cptpure and contain it using tractor beams and force shields if that they gravitationally based.
Thus a civilization might fill a world with a specific radius, volume, mass, and density or ordinary matter with a equal mass of mirror matter which woiuld fill the volume of the world and not interact with the ordinary matter except through gravity. So the mirror matter and the ordinary matter wouldn't exert any pressure on each other to fight against the doubled density. But the mirror matter might interact with other mirror matter through the atomic and electromagnetic forces mediated by mirror bosuns. In that case mirror matter oculd only be condensed as much as ordinary matter by gravity.
In that case tens or hundreds of different types of mirror matter would be needed to achieve the desnity of the K.O.P. . Each form of mirror matter could interact with ordinary matter and other forms of mirror matter by gravity, but couldn't interat with them via the electromagnetic and nuclear forces. And that could result in achieving the required density of the K.O.P. using ordinary matter and many different forms of mirror matter. What would be needed would be a physical theory reqiuring many different forms of mirror matter.
And there is this:
Parity can also be spontaneously broken depending on the
Higgs potential.
[9][10] While in the case of unbroken parity symmetry the masses of particles are the same as their mirror partners, in case of broken parity symmetry the mirror partners are lighter or heavier.
https://en.wikipedia.org/wiki/Mirror_matter
So maybe it might possibly be possible to create mirror particles many times more massive than their ordinary counterparts, massive enough to make the density of the
https://en.wikipedia.org/wiki/Mirror_matter possible.
Exotic atmos are atomswher eone or more particles has been replaced by a different particle which has the same charge. Since the replace particles usually decay very fast, exotic atoms, whatever their mass, do not seem like constructin material.
https://en.wikipedia.org/wiki/Exotic_atom
And then there is dark mattter.
Dark matter is a hypothetical form of
matter thought to account for approximately 85% of the matter in the
universe.
[1] 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. Various
astrophysical observations — including
gravitational effects which cannot be explained by currently accepted theories of
gravity 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.
[2]
In the standard
Lambda-CDM model of cosmology, the total
mass-energy content of the universe contains 5%
ordinary matter and
energy, 27% dark matter, and 68% of a form of energy known as
dark energy.
[6][7][8][9] Thus, dark matter constitutes 85%
[a] of the total mass/energy, while dark energy and dark matter constitute 95% of the total mass-energy content.
[10][11][12][13]
https://en.wikipedia.org/wiki/Dark_matter
Many different types of elementary particles have been proposed as constituting some or all of dark matter.
It is not believed that dark matter can form atoms and molecules and large objects. But I think that if a bunch of dark matter particles are close enough together, and have velcoties lower than the escape velocity of the bunch, they will stick together through their mutual gravity. So I suppose that if tractor beams and some types of force shields use gravity they can be used to gather a mass of dark matter particles into a small enough volume that they will be gravitationally gound to each other.
So possibly the K.O.P. could have been formed out of a relatively small mass of ordinary matter and an Earth sized mass of dark matter.
Thus constructing a world with the required density of the K.O.P. might seem a little bit more plausible, if the Kalandans could construct it out of a form of exotic matter with the right properties.
And I for one pe prefer to imagine that the K.O.P. was probably larger and less massive than Kirk and Spock said, and thus had a much more plausible density and could have been built out of more ordinary materials.