Calc Mortal Engines - MEDUSA destroys Panzerstadt-Bayreuth

I've been hoping to find a way to quantify this for years, but wasn't sure how to. But no more!

Ghostly spheres of light detatched themselves from the glowing machine and drifted down over Circle Park like fire-balloons. Lightning danced around the spires of the Guildhall. The rushing, whining roar grew louder and louder, higher and higher, until even with her hands clapped over her ears Katherine felt she could not bear a moment more of it. Then, quite suddenly, a stream of incandescent energy burst from the cobra's hood and stretched northwards, a snarling, spitting cat-o'-ninetails lashing out to lick at the upper works of Panzerstadt-Bayreuth. The night split apart and went rushing away to hide in the corners of the sky. For a second Katherine saw the tiers of the distant conurbation limned in fire, and then it was gone. Apulse of brightness lifted from the earth, blinding white, then red, a pillar of fire rushing up in silence into the sky, and across the flame-lit snow the sound-wave came rolling, a low, long-drawn-out boom as if a great doo rhad slammed shut somewhere in the depths of the earth.

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Vambrace shakes his head. "Fires are still burning all over the wreck. But we circled as low as we dared and took photographs. The upper tiers have melted and collapsed on to the lower, and it looks as if all the boilers and fuel-stores exploded at the first touch of our energy beam."

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MEDUSA destroys the city of Panzerstadt-Bayreuth, and later self-destructs, taking London with it.

But the rest of what he had been planning to tell her died away in an astonished sob, because suddenly he could see the town below him and Airhaven and the approaching riders as clearly as if it were the middle of the day. He saw the stars fade; he saw Hester's face freeze in mid-shout with spittle trailing from the corners of her mouth; he saw his own wavering shadow dancing on the blood-soaked grass.
Above the crags, the night sky was filling with an unearthly light, as if a new sun had risen from the Out-Country, somewhere far away towards the north.

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When Tom and Hester are captured by Speedwell, Shrike is noted to be hundreds of miles away (by the omniscient narrator to boot).

Hundreds of miles away across the moonlit mud, Shrike spots something. He signals to the Engineer pilots, who nod and grumble as theysteer the Goshawk 90 down to land. "What now? How much longer are wegoing to keep flying back and forth along these track-marks before he'll admit the kids are dead?" But they grumble quietly: they are terrified of Shrike

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When in the Rustwater Marshes, Hester estimates that London is almost a thousand miles away by now.

"Then Wreyland and Anna Fang brought us much further south than I thought," whispered Hester to herself. "London must be almost a thousand miles away by now. It'll take months to catch it up again, and Shrike will beon my tail the whole way."

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As of two days before MEDUSAs self-destruction, London was 500 miles away from Batmunkh Gompa.

But his other officers were more ready to believe the Wind-Flower's report. "He's coming here, all right," said one, an aviatrix from Kerala, not much older than Tom. "I took a scout-ship west the day before yesterday, Feng Hua," she explained, with an adoring look at Miss Fang. "The barbarian city was less than five hundred miles away, and approaching fast. By tomorrow night MEDUSA could be within range."

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However, it takes at least three days for the Jenny Haviner to reach Batmunkh Gompa from the Sea of Khazak.

They flew for three days through a black-and-white world of snow and glaciers and the sheer dark rock of young mountains, where Tom or Hester sometimes had to mind the controls while Anna Fang took cat-naps in theseat beside them, afraid to risk leaving her flight-deck. And still they climbed, until at last they were skimming over the lower buttresses of great Zhan Shan, tallest of the earth's new mountains, whose snow-capped caldera jutted into the endless cold above the sky

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As thus, it takes a shorter period of time (at least a day and a half) to go 500 miles and back than for the Jenny Haviner to return from Batmunkh Gompa. So, we have a low end distance of 500 miles (804.67200km, or 804672m), and a high end distance of 1000 miles (1609344m).

The blast causes an explosion so bright it causes the stars to vanish from sight and is directly compared with the Sun. The luminousity of the Sun is 100,000 lux. The conversion factor from lux to apparent magnitude is -2.5 log I - 14.2.

L = -2.5 log I - 14.2
= -2.5 log 100,000 - 14.2
= -26.7

M(star) is the apparent magnitude of the light source
m= is the apparent magnitude of the sun (-26.73)
L(star) is the Luminosity
L= Luminosity of the sun (3.486*10^26)
d= Distance to the sun from earth (0.000004731537734207877 parsecs)
d(star)= distance to the light source

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(Low end)

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(804672))^2)

Going through this step by step...

(146000000000/(804672))^2) = 3.29206144e10
-26.7 - -26.73 = 3.29206144e10/((L/3.846*10^26)
0.03 = -2.5Log(3.29206144e10/((L/3.846*10^26))
0.03/-2.5 = (3.29206144e10/((L/3.846*10^26))
10^(-0.012) = (3.29206144e10/((L/3.846*10^26))
0.972747224 = (3.29206144e10/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 3.29206144e10
3.75869527e27/3.29206144e10 = 1.14174518e17 joules = 27.28836472275334657 megatons

(High end)

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(1609344))^2)

(146000000000/(1609344))^2) = 8.23015361e9
-26.7 - -26.73 = 8.23015361e9/((L/3.846*10^26)
0.03 = -2.5Log(8.23015361e9/((L/3.846*10^26))
0.03/-2.5 = (8.23015361e9/((L/3.846*10^26))
10^(-0.012) = (8.23015361e9/((L/3.846*10^26))
0.972747224 = (8.23015361e9/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 3.29206144e10
3.75869527e27/8.23015361e9 = 4.5669807e17 joules = 109.1534584130019141 megatons

Final Results
MEDUSA destroys Panzerstadt-Bayreuth (low end) = 27.288 megatons
MEDUSA destroys Panzerstadt-Bayreuth (high end) = 109.153 megatons