An infamous feat, but I feel justified in giving it a calc (especially given the events of Kill La Kill If and all the cosmic shenanigans within). Let's go!
(http://imgur.com/Q1PbLEU)
Ryuko and Ragyo fight across space, passing by different celestial bodies as they go. There was a lot of controversy over the past due to Kill La Kills wonky visuals, and that said visuals might not actually be a proper portrayal or not of what is happening. However, it should be noted to the contrary, that most of the wonky visuals in Kill La Kill have outright been directly noted to be canon. Gamagoori changing size is due to his emotions...
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Satsuki, Ragyo & Goku Uniforms being noted to shine and emit light.
Nui's multiple 4th wall breaks.
(http://imgur.com/MRwPgr7)
As such, I believe it's fair to say that if all of the other visuals are explicitly canon, so should this be too. However, even if the visuals are canon, it could still be troublesome finding a way to actually quantify it. Thankfully though, I've found a way. Take note of Ragyo's dialogue during this sequence.
(http://imgur.com/kWYl8LW)
As such, Ragyo and Ryuko would have had to have moved a distance to allow the Sun to be visible during their fight. As such, we can confirm that they did indeed move during the fight. We'll go with a low end using the distance to the Sun, and a high end of the distance to one of the galaxies. The diameter of the Sun is 1391000km.
= 0.773094324 rad
= 44.2950419308293064 degrees
Put that through the angscaler and we have a distance of 1708700km. The distance from the Earth to the Sun is 149,597,870km.
L = 149,597,870km - 1708700km
= 147889170km
Next for our timeframe.
Timeframe is 19 frames.
T = 1s/24
= 41.6666667ms X 19
= 0.791666667s
Let's get our speed.
T = 149,597,870km/0.791666667s
= 1.8896573e11/299792458
= 630.321828 C
Now for our high end using a galaxy. I can't find reference for a galaxy with an Active Galactic Nucleus like we see, so I will just go with the Andromedra Galaxy for now, as it's the closest major galaxy to the Milky Way. The Andromeda Galaxy has a diameter of 220,000 lightyears.
= 1.15746043 rad
= 66.31759759256 degrees
Once again using the angscaler, we get a distance of 16836 lightyears. The distance to the Andromeda Galaxy from Earth is 2,500,000 lightyears.
L = 2,500,000 - 16,836
= 2483164 LY
The timeframe is 9 seconds and 12 frames.
T = 41.6666667ms X 12
= 0.5s + 9s
= 9.5s
T = 2483164LY/9.5s
= 2.47284669e21/299792458
= 8248528690000 C
Finally, let's also go for a result using the other galaxies we see (once again using Andromeda for scale).
= 0.694165361 rad
= 39.7727454695738558 degrees
Using the angscaler one last time, we get a distance of 30410 lightyears to the galaxy.
L = 2,500,0000LY - 30,410LY
= 24969590LY
Let's get our timeframe one last time.
Timeframe is 3 seconds and 12 seconds
T = 3s + 0.5s
= 3.5s
T = 24969590LY/3.5s
= 6.74930044e22/299792458
= 225132429000000 C
Final Results
Ryuko & Ragyo fight across space (low end) = 630.322 C
Ryuko & Ragyo fight across space (mid end) = 8248528690000 C
Ryuko & Ragyo fight across space (high end) = 225132429000000 C
Ryuko and Ragyo fight across space, passing by different celestial bodies as they go. There was a lot of controversy over the past due to Kill La Kills wonky visuals, and that said visuals might not actually be a proper portrayal or not of what is happening. However, it should be noted to the contrary, that most of the wonky visuals in Kill La Kill have outright been directly noted to be canon. Gamagoori changing size is due to his emotions...
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Kill La Kill If's glossary directly makes reference to Bunny Boy, a character who only appears in Mako's zany moments, and whom Mako keeps inside her.
As such, I believe it's fair to say that if all of the other visuals are explicitly canon, so should this be too. However, even if the visuals are canon, it could still be troublesome finding a way to actually quantify it. Thankfully though, I've found a way. Take note of Ragyo's dialogue during this sequence.
Ragyo tells Ryuko to look at the shining Sun. The thing is though, the fight is taking place at night. When Ryuko blasts off into space it's night time, and when she falls back to Earth the Sun is only just beginning to rise. Even as Ryuko uses the Absolute Life Fiber Domination ability to save the world, the Sun is still not visible from Japan's side of the world, and only rises when Ryuko has fallen back down to Earth.
As such, Ragyo and Ryuko would have had to have moved a distance to allow the Sun to be visible during their fight. As such, we can confirm that they did indeed move during the fight. We'll go with a low end using the distance to the Sun, and a high end of the distance to one of the galaxies. The diameter of the Sun is 1391000km.
= 2*atan(1231/(1433/tan(70/2)))
= 0.773094324 rad
= 44.2950419308293064 degrees
Put that through the angscaler and we have a distance of 1708700km. The distance from the Earth to the Sun is 149,597,870km.
L = 149,597,870km - 1708700km
= 147889170km
Next for our timeframe.
T = 1s/24
= 41.6666667ms X 19
= 0.791666667s
Let's get our speed.
T = 149,597,870km/0.791666667s
= 1.8896573e11/299792458
= 630.321828 C
Now for our high end using a galaxy. I can't find reference for a galaxy with an Active Galactic Nucleus like we see, so I will just go with the Andromedra Galaxy for now, as it's the closest major galaxy to the Milky Way. The Andromeda Galaxy has a diameter of 220,000 lightyears.
= 2*atan(1976/(1433/tan(70/2)))
= 1.15746043 rad
= 66.31759759256 degrees
Once again using the angscaler, we get a distance of 16836 lightyears. The distance to the Andromeda Galaxy from Earth is 2,500,000 lightyears.
L = 2,500,000 - 16,836
= 2483164 LY
T = 41.6666667ms X 12
= 0.5s + 9s
= 9.5s
T = 2483164LY/9.5s
= 2.47284669e21/299792458
= 8248528690000 C
Finally, let's also go for a result using the other galaxies we see (once again using Andromeda for scale).
= 2*atan(1094/(1433/tan(70/2)))
= 0.694165361 rad
= 39.7727454695738558 degrees
Using the angscaler one last time, we get a distance of 30410 lightyears to the galaxy.
L = 2,500,0000LY - 30,410LY
= 24969590LY
Let's get our timeframe one last time.
T = 3s + 0.5s
= 3.5s
T = 24969590LY/3.5s
= 6.74930044e22/299792458
= 225132429000000 C
Final Results
Ryuko & Ragyo fight across space (low end) = 630.322 C
Ryuko & Ragyo fight across space (mid end) = 8248528690000 C
Ryuko & Ragyo fight across space (high end) = 225132429000000 C