Cunning Linguist
Anbu Operative 🎭
- Joined
- Apr 7, 2014
- Messages
- 4,403
- Reaction score
- 806
Hello there. I'm The Hero NB Needs. Handsome, Brilliant, Warrior-poet. These are just some of the words that apply to me. Submitted below is some calculations that I have been working on for a while now. I apologize for the length, but it is worth the read. I hope you enjoy and maybe learn something.
Skip to the bottom if you just want to find out how much energy it took to lift the Moon off the surface of the Earth.
Pain talked about how the Sage created the Moon using Chibaku Tensei. For the sake of this discussion, I'm going to assume that the Naruto planet is like Earth and that the Naruto Moon is like our Moon.
It takes energy to lift something off of Earth. All objects on the surface of the Earth have a potential energy associated with them. When we lift something away from the surface, this potential energy changes. So we can calculate the energy required to lift an object off the surface of the earth by taking the difference between the two potential energies.
As the anime shows, Chibaku Tensei involves tearing earth out of the planet and smashing it into a ball the levitates off the ground. We're going to be examining the same situation.
I'm going to examine this in two simplified states: The first is the Moon, already created, sitting at the surface of the Earth. The center of the moon is at the radius of the Earth here.The second is the Moon in orbit around the Earth.
I'm going to be using "E" here as a replacement for x10x since it's easier to write. The mass of the Earth is 5.972E24 kg.The mass of the Moon is 7.348E22 kg. Since Chibaku Tensei takes the mass from the Earth to create the Moon, the pre-Moon mass of the Earth would be the sum of the two masses, meaning the initial mass was 6.045E24 kg. That means that the Sage took out about 1/10 of the planet's mass!
The distance between the Earth and the Moon (their centers) is 384,400 km or 3.844E8 m. So the Sage lifted a 7.348E22 kg object 384400000 meters off the surface of the planet.
Now that we've got those numbers sorted out, let's do some actual calculations. The gravitational potential energy of an object is described by the equation:
E = Ug = [-G(M1)(M2)]/r
Ug is the gravitational potential energy, G is the gravitational constant, 6.674E-11. M1 and M2 are the mass of the moon and Earth, respectively. r is the radius of the planet.
When an object is in orbit, it has a kinetic energy associated with it as well. The gravitational force provides the centripetal force on the orbiting object so:
F = ma = (M1v^2)/r' = Fg = [G(M1)(M2)]/r'^2
and Kinetic Energy is 1/2mv2 so
K = 1/2M1v^2 = [G(M1)(M2)]/2r'
so the total energy of the orbiting Moon would be E = Ug + K or
E = [-G(M1)(M2)]/r' + [G(M1)(M2)]/2r' = [-G(M1)(M2)]/2r'
Think of what just happened above as -1 + 1/2 = -1/2. So to define all the necessary values: F is force, m is mass, a is acceleration, v is velocity, and Fg (hey, our second modkage!) is the force of gravity. E is the total energy. r' is the distance of the moon from the center of earth (now in orbit). M2 is the mass of the Earth.
So to find out the energy needed to lift the moon, we simply find deltaE, which is the Final Energy - Initial Energy. In this case, the final energy was the orbiting moon and the initial energy was the moon on the surface of the planet. The orbiting moon had a kinetic and potential energy associated with it whereas the moon on the surface only has a potential energy associated with it. So now we calculate deltaE:
deltaE = Ef - Ei = [[-G(M1)(M2)]/2r'] - [[-G(M1)(M2)]/r]
or
deltaE = [-G(M1)(M2)](1/2r' -1/r)
G = Gravitational Constant = 6.673E-11 m3 kg-1 s-2
M1 = Mass of the Moon = 7.348E22 kg
M2 = Mass of the Earth = 5.972E24 kg
r = radius of the Earth = 6.371E6 m
r' = distance from center of Earth to center of Moon = 3.844E8 m
So the energy it takes to lift the Moon off the surface of the Earth is: 4.558E30 Joules.
To put that into perspective, one ton of TNT (a common comparison) has 4.184E9 Joules. The Sage used an energy equivalent to 1.089E21 TONS OF TNT. That's 1089000000000000000000 tons of TNT.
Now, as you can see, I've made certain assumptions about the situation. However, these calculations should give you an idea as to how powerful the Sage must have been. Hope you enjoyed the read.
Skip to the bottom if you just want to find out how much energy it took to lift the Moon off the surface of the Earth.
Pain talked about how the Sage created the Moon using Chibaku Tensei. For the sake of this discussion, I'm going to assume that the Naruto planet is like Earth and that the Naruto Moon is like our Moon.
It takes energy to lift something off of Earth. All objects on the surface of the Earth have a potential energy associated with them. When we lift something away from the surface, this potential energy changes. So we can calculate the energy required to lift an object off the surface of the earth by taking the difference between the two potential energies.
As the anime shows, Chibaku Tensei involves tearing earth out of the planet and smashing it into a ball the levitates off the ground. We're going to be examining the same situation.
I'm going to examine this in two simplified states: The first is the Moon, already created, sitting at the surface of the Earth. The center of the moon is at the radius of the Earth here.The second is the Moon in orbit around the Earth.
I'm going to be using "E" here as a replacement for x10x since it's easier to write. The mass of the Earth is 5.972E24 kg.The mass of the Moon is 7.348E22 kg. Since Chibaku Tensei takes the mass from the Earth to create the Moon, the pre-Moon mass of the Earth would be the sum of the two masses, meaning the initial mass was 6.045E24 kg. That means that the Sage took out about 1/10 of the planet's mass!
The distance between the Earth and the Moon (their centers) is 384,400 km or 3.844E8 m. So the Sage lifted a 7.348E22 kg object 384400000 meters off the surface of the planet.
Now that we've got those numbers sorted out, let's do some actual calculations. The gravitational potential energy of an object is described by the equation:
E = Ug = [-G(M1)(M2)]/r
Ug is the gravitational potential energy, G is the gravitational constant, 6.674E-11. M1 and M2 are the mass of the moon and Earth, respectively. r is the radius of the planet.
When an object is in orbit, it has a kinetic energy associated with it as well. The gravitational force provides the centripetal force on the orbiting object so:
F = ma = (M1v^2)/r' = Fg = [G(M1)(M2)]/r'^2
and Kinetic Energy is 1/2mv2 so
K = 1/2M1v^2 = [G(M1)(M2)]/2r'
so the total energy of the orbiting Moon would be E = Ug + K or
E = [-G(M1)(M2)]/r' + [G(M1)(M2)]/2r' = [-G(M1)(M2)]/2r'
Think of what just happened above as -1 + 1/2 = -1/2. So to define all the necessary values: F is force, m is mass, a is acceleration, v is velocity, and Fg (hey, our second modkage!) is the force of gravity. E is the total energy. r' is the distance of the moon from the center of earth (now in orbit). M2 is the mass of the Earth.
So to find out the energy needed to lift the moon, we simply find deltaE, which is the Final Energy - Initial Energy. In this case, the final energy was the orbiting moon and the initial energy was the moon on the surface of the planet. The orbiting moon had a kinetic and potential energy associated with it whereas the moon on the surface only has a potential energy associated with it. So now we calculate deltaE:
deltaE = Ef - Ei = [[-G(M1)(M2)]/2r'] - [[-G(M1)(M2)]/r]
or
deltaE = [-G(M1)(M2)](1/2r' -1/r)
G = Gravitational Constant = 6.673E-11 m3 kg-1 s-2
M1 = Mass of the Moon = 7.348E22 kg
M2 = Mass of the Earth = 5.972E24 kg
r = radius of the Earth = 6.371E6 m
r' = distance from center of Earth to center of Moon = 3.844E8 m
So the energy it takes to lift the Moon off the surface of the Earth is: 4.558E30 Joules.
To put that into perspective, one ton of TNT (a common comparison) has 4.184E9 Joules. The Sage used an energy equivalent to 1.089E21 TONS OF TNT. That's 1089000000000000000000 tons of TNT.
Now, as you can see, I've made certain assumptions about the situation. However, these calculations should give you an idea as to how powerful the Sage must have been. Hope you enjoyed the read.
