Calc Storage - From The Toho Archives: Gorath (1962)
And, back to the more obscure elements of Toho filmography, specifically the last chapter of the 1960s space opera trilogy produced by the company: Gorath. Unlike the previous two films in the trilogy, the events of Gorath do not occur within the same continuity, so none of the previous feats or figures I calculated in those blog entries apply here.
Which is just as well, since humanity in this film is not facing extraterrestrial invaders as their 'antagonist', but something that even a bunch of megaton-calibre guns might find to be a wee bit of a pickle to hinder: namely, a rogue star.
But exactly how tough is this stellar sumbitch?
1# - Gorath
This half of the blog entry focuses on the physical properties of the rogue star in question, to get a sense of exactly how massively out of depth Earth would've been to attempt destroying the celestial body.
Basic parameters of Gorath are provided early in the film of the same name: being three-quarters the overall size of Earth, yet possessing a mass a whopping 6200 times greater than that of the Blue Marble's.
Gravitational Binding Energy
Firstly, I'll determine the minimum "durability" of the rogue star to, so to speak.
I will require the radius of Gorath for the upcoming formula, so I've decided to treat the 3/4 size statement as size = volume; the more dimensions taken into account, the more sense it makes to compare these two 'objects', given they both function as 3D shapes.
Earth's volume is 1.08321e+21 m^3.
1.08321e+21/4 = 2.708e+20
2.708e+20*3 = 8.124e+20 m^3
Treating Gorath as a uniform sphere:
Volume of a sphere =
(4/3)*pi*r^3 = 8.124e+20
pi*r^3 = 6.093e+20 (removing the fraction from the equation)
r^3 = 1.94e+20 (removing pi from the equation)
r = 5,789,421.64 metres = 5789.42 km (cubic root equation)
As mentioned above, Gorath is at least 6200 times more massive than Earth.
Earth's mass is 5.9726e+24 kg.
5.9726e+24*6200 = 3.703e+28 kg
The gravitational binding energy equation:
The gravitational constant (G) is 6.674e-11 N (m/kg)^2.
U = 3*6.674e-11*(3.703e+28)^2/(5*5,789,421.64)
U = 9.484e+39 joules or 2.27 tenatons (2,266,730 yottatons) of TNT equivalent.
One hell of a tough stellar nut to crack. What one has to also take into account is the fact that is actually a low-end estimate for Gorath's size and mass, as it constantly accumulates additional material by gravitationally absorbing 'local' cosmic matter as it travels through deep space: by the time of the film's climax, the star has also consumed Saturn's iconic rings and the Moon and thus further adding on weight and length.
So we've established the rogue star's GBE and thus its minimum capability to maintain structural integrity against aggressive energy output, but how about the level of destruction Gorath itself leaves in its wake with its nonexistant orbit?
We already have its mass accounted for, but what about velocity?
I initially thought I would have to make much more work out of this than necessary and use angular velocity statements in the film (without distinct units of measurement for the provided numbers) and rely on the angular and linear velocity correlation formula, but with immense luck, we're actually given a concise linear velocity figure, courtesy of relevant and accurate mathematical equations written up on a blackboard (for assurance that this km/second figure is indeed related to Gorath's travel speed, notice the '45 days' timeframe in the above link and compare with this statement).
Oh, the wonders of observant eyes and surprisingly insightful aesthetic props!
So, velocity is 1500 km/s or 1,500,000 m/s.
KE = (0.5)*3.708e+28*1,500,000*1,500,000 = 4.172e+40 joules or 9.97 tenatons (9,970,124 yottatons) of TNT equivalent.
Absolutely vicious stuff for Gorath, just sliding past the minimum threshold of small star-level destructive capability. And again, a reminder that this is only a functional low-end capacity for the rogue star at the time of its recorded measurements.
2# - Operation South Pole
So what is humanity's response to an incoming celestial ball of massively energetic death?
Moving the fuck out of its way.
Namely, by proverbially strapping thousands of nuclear-powered jet thrusters to Earth's chilly bottom and powering the planet out of its own orbit to avoid the linear path and collision with Gorath. Sounds like a piece of pie.
Indeed, the film is generous enough to even provide us with a seemingly sound energy output (presumably per second) for this mega-thrust: 6,600,000,000 megatons or 6.6 petatons of TNT equivalent.
That's all nice and dandy, but I then realised that "wait a minute, a 6.6 petatons/second output to move Earth clean out of its own orbit? That seems a little low!". And sure enough, it doesn't even match up to direct statements made in the film.
The primary protagonist, and one of the chief scientists of the Antarctic operation, estimates that Earth has to travel at least 400,000 km in 100 days to avoid irrepairable damage or total destruction from Gorath.
100 days = 8,640,000 seconds
400,000 km = 400,000,000 metres
400,000,000/8,640,000 = 46.3 m/s
(Cinematic visuals naturally disagree with this assessment vehemently, but I'll take a logically sound equation over film footage in this case)
KE = (0.5)*5.9726e+24*46.3*46.3 = 6.402e+27 joules or 1.53 exatons of TNT equivalent.
Now that's a bit more like it! A near 1000 fold increase in energy output makes for a hefty range of low-end to high-end values.
Gorath isn't the only scary motherfucker in this movie.
These results are by far the largest, and ultimately the largest you're going to see, figures in the entire Toho Studios calc compendium. It's what happens when everybody operates on such a cosmic magnitude. And to think, the film's events takes place in 1982 lmao).
Gravitational Binding Energy (Gorath): 2.27 tenatons of TNT equivalent.
Kinetic Energy (Gorath): 9.97 tenatons of TNT equivalent.
Kinetic Energy (Earth, Operation South Pole): 1.53 exatons of TNT equivalent.
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