From episode 6.
The Fountain of Polaris bestows the power of the stars to a witch with hidden radiance. When Akko goes there for the first time, she sees how Chariot went there in the past like she did.
16:57, they enter the Fountain of Polaris, and at 19:26, we have our feat.
The stars embue Chariot with their power. Those stars increase in brightness.
You can see this with any of the stars, but highlighting one helps demonstrate this. The stars prior to this (and after) aren't shining as much).
Looking at Ampchu's Touhou luminousity calc and Endless Mikes luminousity revision calcs for help. We'll get our luminousity from the average brightness of a star increase to the brightest star. Given that this is the Fountain of Polaris, I'll be going with the values for Polaris, which has an apparent magnitude of 1.99 and is 430 lightyears (4.068e+18m). Now let's get the luminousity...
1.99 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(4.068e+18))^2)
Going through this step by step...
(146000000000/(4.068e+18))^2) = 1.28808292e-15
1.99 - -26.73 = 1.28808292e-15/((L/3.846*10^26)
28.72 = -2.5Log(1.28808292e-15/((L/3.846*10^26))
28.72/-2.5 = (1.28808292e-15/((L/3.846*10^26))
10^(-11.48800) = (1.28808292e-15/((L/3.846*10^26))
3.25087297e-12 = (1.28808292e-15/((L/3.846*10^26))
3.25087297e-12 X (3.864*10e26) = 1.28808292e-15
1.25613732e16/1.28808292e-15 = 9.75199112e30 joules
Polaris is 2500 times brighter than the Sun.
L = 3.84600e26 X 2500
= 9.61500e29 W
L = 9.75199112e30 - 9.61500e29
= 8.79049112e30
But that's not it! There are approximately 4548 visible in a hemsiphere of the Earth.
E = 8.79049112e30 X 4548
= 3.99791536e34 joules
= 9.5552470363288719568 yottatons
Let's also get the speed of which the magic of the stars crosses to Shiny Chariot.
5 seconds.
T = 4.068e+18m/5s
= 8.13600e17/299792458
= 2713877480 C
For a low end, we'll go with alpha centuri (4.367 light years away, or 41315009973760352m.
T = 41315009973760352m/5s
= 8.26300199e15/299792458
= 27562407.8 C
(146000000000/(8.26300199e15))^2) = 1.28808292e-15
1.99 - -26.73 = 3.12197914e-10/((L/3.846*10^26)
28.72 = -2.5Log(3.12197914e-10/((L/3.846*10^26))
28.72/-2.5 = (3.12197914e-10/((L/3.846*10^26))
10^(-11.48800) = (3.12197914e-10/((L/3.846*10^26))
3.25087297e-12 = (3.12197914e-10/((L/3.846*10^26))
3.25087297e-12 X (3.864*10e26) = 1.28808292e-15
1.25613732e16/3.12197914e-10 = 4.02352887e25 joules
Alpha Centari has a luminousity of 0.0017 L (L being the luminousity of the Sun).
L = 3.84600e26 X 0.0017
= 6.5382e23 W
L = 4.02352887e25 - 6.5382e23
= 3.95814687e25 W
E = 3.95814687e25 X 4548
= 1.8001652e29 joules
= 43.024980879541118384 exatons
Final Result
The stars embue Shiny Chariot with power (low end) = 43.025 exatons
The stars embue Shiny Chariot with power (high end) = 9.555 yottatons
Magic of the Stars (low end) = 27562407.8 C
Magic of the Stars (high end) = 2713877480 C
16:57, they enter the Fountain of Polaris, and at 19:26, we have our feat.
1.99 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(4.068e+18))^2)
Going through this step by step...
(146000000000/(4.068e+18))^2) = 1.28808292e-15
1.99 - -26.73 = 1.28808292e-15/((L/3.846*10^26)
28.72 = -2.5Log(1.28808292e-15/((L/3.846*10^26))
28.72/-2.5 = (1.28808292e-15/((L/3.846*10^26))
10^(-11.48800) = (1.28808292e-15/((L/3.846*10^26))
3.25087297e-12 = (1.28808292e-15/((L/3.846*10^26))
3.25087297e-12 X (3.864*10e26) = 1.28808292e-15
1.25613732e16/1.28808292e-15 = 9.75199112e30 joules
Polaris is 2500 times brighter than the Sun.
L = 3.84600e26 X 2500
= 9.61500e29 W
L = 9.75199112e30 - 9.61500e29
= 8.79049112e30
But that's not it! There are approximately 4548 visible in a hemsiphere of the Earth.
E = 8.79049112e30 X 4548
= 3.99791536e34 joules
= 9.5552470363288719568 yottatons
Let's also get the speed of which the magic of the stars crosses to Shiny Chariot.
T = 4.068e+18m/5s
= 8.13600e17/299792458
= 2713877480 C
For a low end, we'll go with alpha centuri (4.367 light years away, or 41315009973760352m.
T = 41315009973760352m/5s
= 8.26300199e15/299792458
= 27562407.8 C
(146000000000/(8.26300199e15))^2) = 1.28808292e-15
1.99 - -26.73 = 3.12197914e-10/((L/3.846*10^26)
28.72 = -2.5Log(3.12197914e-10/((L/3.846*10^26))
28.72/-2.5 = (3.12197914e-10/((L/3.846*10^26))
10^(-11.48800) = (3.12197914e-10/((L/3.846*10^26))
3.25087297e-12 = (3.12197914e-10/((L/3.846*10^26))
3.25087297e-12 X (3.864*10e26) = 1.28808292e-15
1.25613732e16/3.12197914e-10 = 4.02352887e25 joules
Alpha Centari has a luminousity of 0.0017 L (L being the luminousity of the Sun).
L = 3.84600e26 X 0.0017
= 6.5382e23 W
L = 4.02352887e25 - 6.5382e23
= 3.95814687e25 W
E = 3.95814687e25 X 4548
= 1.8001652e29 joules
= 43.024980879541118384 exatons
Final Result
The stars embue Shiny Chariot with power (low end) = 43.025 exatons
The stars embue Shiny Chariot with power (high end) = 9.555 yottatons
Magic of the Stars (low end) = 27562407.8 C
Magic of the Stars (high end) = 2713877480 C
