In my head cannon asteroid miners have brought a small asteroid into Earth orbit and are mining it at the time of "The Paradise Syndrome". So Spock meant that the asteroid in question was almost as large as the asteroid that was Earth's temporary second moon and not almost as large as Luna, Earth's permanent moon.
In the original special effects the asteroid in "Paradise Syndrome" appears to be almost sphere shaped but with large bumps and hollows. Measuring it's image on my computer screen indicates the largest diameter is about 1.333 times the smallest visible diameter.
The dimensions of asteroid 10 Hygiea are about 530 x 407 x 370 kilometers, so the largest dimension is about 1.4324 times the smallest dimension. Hygeia has a mass of about 8.67 times ten to the 19th power kilograms.
The dimensions of asteroid 4 Vesta, one of the largest asteroids, are 572.6 X 557.2 x 446.4 Kilometers, plus or minus 0.2 kilometers. Vesta has a mass of about 2.59076 times 10 to the 20th power kilograms. Thus the largest dimension of Vesta is 1.28 times the smallest dimension.
The dimensions of Hyperion, or Saturn VII, are 360.2 x 266 x 205.4 kilometers, or 223.8 x 165.3 x 127.6 miles, with a mass of about 5.6199 times ten to the 18th power kilograms. So the largest dimension of Hyperion is 1.75 times the smallest dimension.
Deimos, or Mars II, is about 15 x 12.2 x 11 kilometers and has a mass of about 1.4762 X 10 to the 15th power kilograms. It's largest dimension is about 1.3636 times its smallest dimension.
Thus bodies in our solar system with approximately the same shape as the asteroid in "The Paradise Syndrome" can vary in mass by at least 175,501.96 times. But the "bumpiness" of the asteroid in "The Paradise Syndrome" indicates it is on the smaller end of the spectrum, otherwise each bump could count as a mountain taller than any on Earth.
In the remastered episode the asteroid seems to have a narrower shape.
It's shape seems to resemble Asteroid 433 Eros more. Eros has dimensions of 34.4 x 11.2 Kilometers, or its largest dimension is about 3.0714 times it's smallest dimension. Eros has a mass of about 6.687 times 10 to the 15th power kilograms. I'm sure that asteroids of similar shape should range vastly in size and mass.
in the episode it looked like the Enterprise was very close to the asteroid and the asteroid was only a few times the size of the Enterprise.
But:
Did Spock mean the asteroid is almost as massive or almost as large in diameter as Earth's moon?
It is certainly possible for another solar system to have an object classified as as asteroid that is almost the size of Earth's moon. But the asteroid is small enough to be lumpy and irregular in shape.
Earth's moon, Luna, has a equatorial diameter of 3,476.2 kilometers and a polar diameter of 3,472 kilometers, thus being almost perfectly spherical.
Earth's moon has a mass of about 7.342 times 10 to the 22nd power kilograms.
Wikipedia says:
https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size
The moon's polar radius of about 1,736 kilometers is 8.68 to 17.36 times the cutoff boundary for roundness of 100 to 200 kilometers radius.
The moon's mass of about 7.342 times 10 to the 22nd power kilograms is about 73.42 times the mass sufficient to become spherical.
By "that asteroid is almost as large as your Earth's moon" Spock may have meant that it was about a tenth or a hundredth as large. Considering the vast range in size of solar system objects that would make it "almost as large as your Earth's moon" from a certain point of view. But would that be enough to make the asteroid as small as it looked in the episode?
So in my head cannon asteroid miners have brought a small asteroid into Earth orbit and are mining it at the time of "The Paradise Syndrome". So Spock meant that the asteroid in question was almost as large as the asteroid that was Earth's temporary second moon and not almost as large as Luna, Earth's permanent moon.
In the original special effects the asteroid in "Paradise Syndrome" appears to be almost sphere shaped but with large bumps and hollows. Measuring it's image on my computer screen indicates the largest diameter is about 1.333 times the smallest visible diameter.
The dimensions of asteroid 10 Hygiea are about 530 x 407 x 370 kilometers, so the largest dimension is about 1.4324 times the smallest dimension. Hygeia has a mass of about 8.67 times ten to the 19th power kilograms.
The dimensions of asteroid 4 Vesta, one of the largest asteroids, are 572.6 X 557.2 x 446.4 Kilometers, plus or minus 0.2 kilometers. Vesta has a mass of about 2.59076 times 10 to the 20th power kilograms. Thus the largest dimension of Vesta is 1.28 times the smallest dimension.
The dimensions of Hyperion, or Saturn VII, are 360.2 x 266 x 205.4 kilometers, or 223.8 x 165.3 x 127.6 miles, with a mass of about 5.6199 times ten to the 18th power kilograms. So the largest dimension of Hyperion is 1.75 times the smallest dimension.
Deimos, or Mars II, is about 15 x 12.2 x 11 kilometers and has a mass of about 1.4762 X 10 to the 15th power kilograms. It's largest dimension is about 1.3636 times its smallest dimension.
Thus bodies in our solar system with approximately the same shape as the asteroid in "The Paradise Syndrome" can vary in mass by at least 175,501.96 times. But the "bumpiness" of the asteroid in "The Paradise Syndrome" indicates it is on the smaller end of the spectrum, otherwise each bump could count as a mountain taller than any on Earth.
In the remastered episode the asteroid seems to have a narrower shape.
It's shape seems to resemble Asteroid 433 Eros more. Eros has dimensions of 34.4 x 11.2 Kilometers, or its largest dimension is about 3.0714 times it's smallest dimension. Eros has a mass of about 6.687 times 10 to the 15th power kilograms. I'm sure that asteroids of similar shape should range vastly in size and mass.
in the episode it looked like the Enterprise was very close to the asteroid and the asteroid was only a few times the size of the Enterprise.
But:
SPOCK: Doctor, that asteroid is almost as large as your Earth's moon. Far enough away, the angle necessary to divert it enough to avoid destruction is minute, but as the asteroid approaches this planet, the angle becomes so great that even the power of a starship
Did Spock mean the asteroid is almost as massive or almost as large in diameter as Earth's moon?
It is certainly possible for another solar system to have an object classified as as asteroid that is almost the size of Earth's moon. But the asteroid is small enough to be lumpy and irregular in shape.
Earth's moon, Luna, has a equatorial diameter of 3,476.2 kilometers and a polar diameter of 3,472 kilometers, thus being almost perfectly spherical.
Earth's moon has a mass of about 7.342 times 10 to the 22nd power kilograms.
Wikipedia says:
Solar System objects more massive than 10 to the 21st power kilograms (one yottagram [Yg]) are known or expected to be approximately spherical. Astronomical bodies relax into rounded shapes (ellipsoids), achieving hydrostatic equilibrium, when the gravity of their mass is sufficient to overcome the structural strength of their material. Objects made of ice become round more easily than those made of rock, and many icy objects are spheroidal at far lower sizes. The cutoff boundary for roundness is somewhere between 100 km and 200 km in radius.[1]
https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size
The moon's polar radius of about 1,736 kilometers is 8.68 to 17.36 times the cutoff boundary for roundness of 100 to 200 kilometers radius.
The moon's mass of about 7.342 times 10 to the 22nd power kilograms is about 73.42 times the mass sufficient to become spherical.
By "that asteroid is almost as large as your Earth's moon" Spock may have meant that it was about a tenth or a hundredth as large. Considering the vast range in size of solar system objects that would make it "almost as large as your Earth's moon" from a certain point of view. But would that be enough to make the asteroid as small as it looked in the episode?
So in my head cannon asteroid miners have brought a small asteroid into Earth orbit and are mining it at the time of "The Paradise Syndrome". So Spock meant that the asteroid in question was almost as large as the asteroid that was Earth's temporary second moon and not almost as large as Luna, Earth's permanent moon.
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