Calc A True Story calcs

...the Lachanopters made the left wing, and the aids were placed in the main battle as every man's fortune fell: the foot, which in number were about six thousand myriads, were disposed of in this manner: there are many spiders in those parts of mighty bigness, every one in quantity exceeding one of the Islands Cyclades: these were appointed to spin a web in the air between the Moon and the Morning Star, which was done in an instant, and made a plain champaign upon which the foot forces were planted, who had for their leader Nycterion, the son of Eudianax, and two other associates.

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There are many Spiders of Bigness, each bigger than an island of Cyclades, which weave a web so the Moon can go to war with the Sun. The smallest of the islands of Cyclades is Donousa, which has a width and length of 5km (or 5000m).
The huntsman spider, which is found in many varieties around the world, can grow up to 12cm across (or 0.12m) and can weight of up to 0.37 ounces (or 0.01048932kg).

M2 = (H2/H1)^3*M1
= (5000/0.12)^3*0.01048932
= 7.58776042e11kg

We have our weight...but how to find out speed. For an absolute low end minimum, the worlds fastest spider (the camel spider) can move at 16km/h (.

KE = (0.5)mv^2
= (0.5) X 7.58776042e11 X 4.44444444^2
= 7.49408435e12 joules
= 1.791129146749522 kilotons

This is a colossal lowball though, as we know they can move far faster than this. The web between the Moon and the Morningstar was spun in an instant, which while fast, is unfortunately vague. Thankfully, we have other methods we can use to find a minimum. A huntsman can move between 30 to 40 body lengths in a second.

L = 5km X 30
= 150km

T = 150km/1s
= 150000/340.29
= Mach 440.800494

KE = (0.5)mv^2
= (0.5) X 7.58776042e11 X 150000^2
= 8.53623047e21 joules
= 2.0402080473231358759 teratons

Otherwise, the badge huntsman can travel 16 times its own body length in a second.

L = 5km X 16
= 80km

T = 80km/1s
= 80000/340.29
= Mach 235.093597

KE = (0.5)mv^2
= (0.5) X 7.58776042e11 X 80000^2
= 2.42808333e21 joules
= 580.32584369024857551 gigatons

That's one method of finding our speed, but just in case, let's also go for another, using the distances of Ancient Greek cosmologists for the Solar System. Posidonius calculated the circumference of the Earth to be 38,647km.

R = π/C
= 38647/π
= 12301.7222/2
= 6150.8611km

According to Hipparchus, if 1 radii was a radius of the Earth, then the Moon was calculated to be 72 radii from the Earth at it's furthest, and 490 radii from the Sun.

For in Book 1 of "On Sizes and Distances" he takes the following observation: an eclipse of the sun, which in the regions around the Hellespont was an exact eclipse of the whole solar disc, such that no part of it was visible, but at Alexandria by Egypt approximately four-fifths of it was eclipsed. By means of this he shows in Book 1 that, in units of which the radius of the earth is one, the least distance of the moon is 71, and the greatest 83. Hence the mean is 77... Then again he himself in Book 2 of "On Sizes and Distances" shows from many considerations that, in units of which the radius of the earth is one, the least distance of the moon is 62, and the mean 671⁄3, and the distance of the sun 490. It is clear that the greatest distance of the moon is 722⁄3.

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L = 6150.8611km X 490
= 3013921.94km

L = 6150.8611km X 72
= 442861.999km

L = 3013921.94km - 442861.999km
= 2571059.94km

That's the distance, so how do we get a timeframe? Thankfully, A True Story gives us a timeframe to work with. Lucian says that he was taken alive back to the Sun as a prisoner the next day, meaning the entire main battle took place in a day. This gives us a timeframe of 24 hours.

As soon as this was done, news came to us by our scouts that the Nephelocentaurs were coming on, which indeed should have come to Phaethon before the fight. And when they drew so near unto us that we could take full view of them, it was a strange sight to behold such monsters, composed of flying horses and men: that part which resembled mankind, which was from the waist upwards, did equal in greatness the Rhodian Colossus, and that which was like a horse was as big as a great ship of burden: and of such multitude that I was fearful to set down their number lest it might be taken for a lie: and for their leader they had the Sagittarius out of the Zodiac. When they heard that their friends were foiled, they sent a messenger to Phaethon to renew the fight: whereupon they set themselves in array, and fell upon the Selenitans or the Moon soldiers that were troubled, and disordered in following the chase, and scattered in gathering the spoils, and put them all to flight, and pursued the king into his city, and killed the greatest part of his birds, overturned the trophies he had set up, and overcame the whole country that was spun by the spiders. Myself and two of my companions were taken alive. When Phaethon himself was come they set up other trophies in token of victory, and on the morrow we were carried prisoners into the Sun, our arms bound behind us with a piece of the cobweb: yet would they by no means lay any siege to the city, but returned and built up a wall in the midst of the air to keep the light of the Sun from falling upon the Moon, and they made it a double wall, wholly compact of clouds, so that a manifest eclipse of the Moon ensued, and all things detained in perpetual night: wherewith Endymion was so much oppressed that he sent ambassadors to entreat the demolishing of the building, and beseech him that he would not damn them to live in darkness, promising to pay him tribute, to be his friend and associate, and never after to stir against him. Phaethon's council twice assembled to consider upon this offer, and in their first meeting would remit nothing of their conceived displeasure, but on the morrow they altered their minds to these terms.

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T = 60 X 60 X 24
= 86400s

T = 2571059.94km/86400s
= 29757.6382/340.29
= Mach 87.4478774

If that's not enough, we can also get the kinetic energy. Each Nephelocentaur's human parts equals the Colossus of Rhodes, which was 33m tall (they technically are centaurs, but I can't be bothered mathing that out; it will be higher than just a giant human in anycase). The average weight of a Greek Man is 88.1kg, with an average height of 177cm (1.77m).

As soon as this was done, news came to us by our scouts that the Nephelocentaurs were coming on, which indeed should have come to Phaethon before the fight. And when they drew so near unto us that we could take full view of them, it was a strange sight to behold such monsters, composed of flying horses and men: that part which resembled mankind, which was from the waist upwards, did equal in greatness the Rhodian Colossus, and that which was like a horse was as big as a great ship of burden: and of such multitude that I was fearful to set down their number lest it might be taken for a lie: and for their leader they had the Sagittarius out of the Zodiac.

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M2 = (H2/H1)^3*M1
= (33/1.77)^3*88.1
= 570949.805kg

KE = (0.5)mv^2
= (0.5) X 570949.805 X 29757.6382^2
= 2.52792888e14 joules
= >60.4189502868068828 kilotons

Alternatively, we can use the calculations of Aristarchus, that being 20 radii to the Moon from Earth and 380 radii from the Earth to the Sun.

L = 6150.8611km X 20
= 123017.222km

L = 6150.8611km X 380
= 2337327.22km

L = 2337327.22km - 123017.222km
= 2214310km

T = 2214310km/86400s
= 25628.588/340.29
= Mach 75.3139616

KE = (0.5)mv^2
= (0.5) X 570949.805 X 25628.588^2
= 1.87506917e14 joules
= >44.8152287284894868 kilotons

Finally...we know that the astrological distances of the Solar System are bigger than calculated back then (though ancient mathematicians and philosophers where surprisingly close). I don't think the Ancient Greeks would mind if we used modern values... The distance from Earth is 252170000km, while the distance from the Moon to the Earth is 384,000km, and the distance from the Sun to the Earth is 147620000km.

L = 252170000km - 384,000km
= 251786000km

T = 251786000km/86400s
= 2914189.81/340.29
= Mach 8563.84205

KE = (0.5)mv^2
= (0.5) X 7.58776042e11 X 2918634.26^2
= 3.23178876e24 joules
= 772.41605162523910622 teratons

L = 147620000km - 384,000km
= 147236000km/86400s
= 1704120.37/340.29
= Mach 5007.84734

KE = (0.5)mv^2
= (0.5) X 570949.805 X 1704120.37^2
= 8.29026606e17 joules
= 198.14211424474186174 megatons

Final Results
Giant spiders speed (low end) = Mach 235.094
Giant spiders speed (mid end) = Mach 440.800
Giant spiders speed (high end) = Mach 8563.842
Giant spiders kinetic energy (low low end) = 1.791 kilotons
Giant spiders kinetic energy (high low end) = 580.326 gigatons
Giant spiders kinetic energy (low high end) = 2.040 teratons
Giant spiders kinetic energy (high high end) = 772.416 teratons
Nephelocentaurs speed (low end) = Mach 75.314
Nephelocentaurs speed (mid end) = Mach 87.448
Nephelocentaurs speed (high end) = Mach 5007.847
Nephelocenaurs kinetic energy (low end) = >44.815 kilotons
Nephelocentaurs kinetic energy (low end) = >60.419 kilotons
Nephelocentaurs kinetic energy (high end) = >198.142 megatons

Hopefully I did all this right. A lot of the information is literally millenia old, but it shows even back then all of this was insanely impressive.