Spock claims that the planet has a size about equal to Earth's moon, and yet a mass about equal to the Earth itself. This allows one to calculate the surface gravity of the planet, and it comes out to 13.5 times Earth's own gravity. That would make the men on the surface weigh something like a ton each! To be fair, Kirk does respond to the size and mass figures by saying "that would be difficult to explain", so it may just be that this isn't so much a mistake as an example of just how weird and inexplicable this planet is.
When Kirk tries to bury D'Amato he phasers the ground and discovers a red rock that the phaser won't cut through. He then phasers another spot about ten feet away and they see the same red rock. McCoy then comments that the whole planet must be made of this stuff. Really, Doctor? From sampling two spots on the ground, both in close proximity, you generalise to the entire planet?! Hell, we SEE rocks sticking up out of the ground that aren't red like this stuff!
The landing party investigates the planet further, eventually locaing an underground control centre. The planet is artificial, created by an ancient and powerful race as a colony world. However the race, named the Kalandans, were destroyed in a vicious plague. The woman who has been appearing is an image of the leader of a team who served on the planet; an automated defence system has been projecting the image in an attempt to keep outsiders away from the base. With the system deactivated and the mystery solved, Kirk beams back to the Enterprise and proceeds on course to his next mission. On a peculiar planet, the Enterprise must face a woman who can kill with a single touch.
The idea of an artificial planet is an interesting one. The size of Earth's moon - 3,475 kilometres give or take, and massing as much as the Earth - 6 billion trillion tons or so, this is a seriously impressive project to take on. In volume terms alone it would be like building tens of trillions of ships like the Enterprise. As a minor nit, though, a planet with that size and mass would have a surface gravity more than thirteen times that of Earth. There's no way a Human being would be able to walk around in such a place, let alone do so with the ease that Kirk and company do. One might assume that the Kalandans have some sort of artificial gravity technology going on, which would again be a massively impressive feat of technology on something planetoid sized; it might be slightly more reasonable to assume that the Enterprise folk have some handy little doodad on the back of their belts that compensates for high gee worlds.
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