Kewl. I have one in mind. Just give me a few minutes to pack my bags and rent a shuttle.
Anyway, I found this...
"Calculations:
Notations to be used:
r = distance from core of planet
R = Radius of planet
p = density of planet
G = Newton's gravitational constant = 6.67 x 10^-11
M = mass of core
m = mass of planet = p times V
U = gravitational potential energy
E = energy (total)
pi = 3.14159...etc
V = volume, for a sphere = (4/3)pi R^3
I will calculate the gravitational potential energy between a "shell" of the planet and the core, then integrate from r=0 to r=R. A shell can be imagined by visualizing the planet as composed of many layers of infinetely thin shells with thickness dr. There would be shells at every distance r from 0 to R.
A shell would have mass dm = p times dV. dV is the volume of the shell, which would be the surface area of the shell times the thickness. So dV =
(4*pi*r^2)*dr. Thus, dm = p * (4*pi*r^2)*dr
First, the gravitational potential energy is:
U(r) = -GMm / r
So, the potential energy of a shell of mass dm at distance r would be
dU(r) = -GM dm / r
The mass M is the mass of the core: ie. the mass of everything from radius 0 to radius r where the shell is. From the shell theorem, we can regard this mass as acting as a point mass at the centre of the planet. Mass is p times V so M = p*(4/3)*pi*r^3.
So then plugging in the above values for M and dm, we get:
dU(r) = -(16/3)G*(p^2)*(pi^2)*(r^4)*dr
Everything on the right is a constant except for the (r^4)dr part, whose integral is (1/5)*r^5. Now integrating the above expression from r=0 to r=R, we will get:
E = U (total) = -(16/3)*G*(p^2)*(pi^2)*(R^5)
So then, to free all these particles and explode the planet, we need to make the total energy be at least 0. So if we gave the planet the amount of energy E as above then it would explode. Any extra energy more than E would give the particles kinetic energy and determines how fast the pieces fly about.
For the Earth, R = 6.38x10^6 metres.
And density, under our assumptions = mass / volume = 5497 kg/m^3
Putting these numbers in, we get the energy to "explode" the Earth to be 2 x 10^32 J. So then the magnitude of energy to explode the Earth is somewhere in the range of 10^32 J."
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Shinier than a speeding bullet.
It's so strange that you would start this topic, as I just changed my you_tube video page to "gravitational topic/physics" yesterday.
I hope you aren't cyber staking a person (I've had that happen and it's a very strange feeling, it doesn't make you think of the person/group or think well of them, I think I had proven it happened in another msg board, as she kept the same user name, but mocked my thread in another forum (w/o mentioning my user name, but less then 5 hours after she posted on here, she started a mock thread in another msg board about the same topic but with a negative slant, but she kept the same user name in both msg boards))..., it's easy to do b/c it's been done to me many times before, for example, in this situation, in some posts or threads, I leave comments on the you_tube links, so once you see the link, and look at the comment sections, it's easy to see my user name (CC) and look at the main page.
But, I don't know, if you are doing that to someone (or myself) and they figure it out, it's usually not a good thing. It's like you are following a person and trying to copy or mimick them b/c you haven't developed your own interests or you want to test that person's interest and see how others respond to it. It's as if you aren't your own person yet, and SEEMS like you're taking a possessive route with someone you don't know, following a person is taking a possessive route, it demonstrates the idea that the other's person's liberty isn't important and you are latching onto that person (either by gender, race, ethnicity, or interests...)w/o their permission, so it's stalkerish, either online or in person.
not really, i'll look it up...i never read anything about someone or some group wanting to blow up the entire planet (wwIII, but that wouldn't destroy the entire planent)...