Star shattering.

SS3 Goku punching King Kai's planet which has 10x gravity because of it's mass:

The first calculation is figuring out the mass of the planet using gravity and radius since those are the two things we know.

The next step is Volume, using the radius.

And the third is density using the mass and volume we calced.

I also have links to a few calculators/convertors I checked the answers on.

Rearanged gravity formula to calculate mass instead (had to do short hand got formula from wikipedia) http://en.wikipedia.org/wiki/Surface_gravity

g = m/r^2

m = r^2 x g

Volume formula

V = (4/3) × pi × r^3

Density Formula

P = M/V

*Very good overall calculator

http://web2.0calc.com/

cm/g to m/kg calculator

http://www.unitjuggler.com/convert-density-from-gpercm3-to-kgperm3.html

Density calculator

http://www.smartconversion.com/unit_calculation/Density_calculator.aspx

Volume calculator

http://www.basic-mathematics.com/volume-of-a-sphere-calculator.html

Heres the actual calcs

g = m/r^2

m = r^2 x g

m = 0.0000156961230576^2 x 10

m = 0.0000000024636827904 earth masses

Earths mass = 5.97219 × 10^24 kilograms

5.97219 × 10^24 X 0.0000000024636827904 = 14,713,581,723,998,976

m = 14,713,581,723,998,976 kg

This considers King akis planet as 100m radius and 10X gravity.

The small number is the size of king kais planets radius in relation to Earths.

volume of a sphere is V = (4/3) × pi × r^3

V = (4/3) × pi × 100m^3 = 4188790.2047863905m^3

This is using King kais planet as 100m radius.

Knowing the mass and Volume we can get density.

P = M/V

P = 14713581723998976kg / 4188790.2047863905m^3

P = 3.512608892.9415128417291527 X 10^9 kg/m^3

Density of a white dwarf star: "The average density of matter in a white dwarf must therefore be, very roughly, 1,000,000 times greater than the average density of the Sun, or approximately 10^6 g/cm3." Which translates to 10^9 kg/m^3. So in other words it is over 3.5 times as dense as a white dwarf star.

http://en.wikipedia.org/wiki/White_dwarf

If you don't believe this then I found soem other calcs.



It doesn't matter here the dimension of the planet, but the density, since we are talking about a PUNCH, not a Ki blast.

King Kai's planet is not more than 30 meters in diameter (pixels-scaling), but even if it is 40, 50 or 90 meters, the order of magnitude, physically talking, is still the same (i.e. 10).

Now, gravitational force of a planet is given by this formula:

F = (G*M*m)/r^2

G is the universal gravitational constant (6,67*10^-11 [m^3/(kg*s^2)];

M is the mass of the planet

m is the generic reference mass

r is the radius of the planet (or distance between the two masses' centers)

Since King Kai's gravitational force is 10 times the Earth gravitational force, we have Fk (gravitational force of King Kai's planet) 10 times bigger than Fe (Earth's gravity).

Fk/Fe = [(G*Mk*m)/rk^2]/[(G*Me*m)/re^2] = 10

G and m are in commons and go away, so we have:

(Mk/rk^2)/(Me/re^2) = 10

Mass is Volume (V)*Density (D), with Volume (of a generical planet) = (4/3)*π*r^3;

back to the formula:

((4/3)*π*rk^3*Dk)/rk^2 = Fk and ((4/3)*π*re^3*De)/re^2 = Fe, so:

Fk/Fe = (Dk*rk)/(De*re) = 10.

The only unknown term is Dk (density of King Kai's planet), while we know De and re of Earth and rk = 15 meters (assuming a diameter of King Kai's planet of 30 m, as previously said).

So, Dk = 1,17*10^10 kg/m^3, while density of Earth (De) is 5,5153*10^3 kg/m^3, so the density of King Kai's planet is around 2 millions of times higher than the desnity of Earth, and Goku punched a whole hole throughout this material.

The most dense material known is Osmium, which has a density of 22661 kg/m^3, and, because of that, it's also the material which is most resistant to compression (462 GPa).

King Kai's planet is still half a million times more dense than this, and thus even way more resistant to physical compression.

Even if King Kai's planet had the same gravitational force as Earth, the fact it has such a small diameter would still imply a huge density, and indeed, it would still have a density around 200000 times bigger than the density of Earth.

Dou you have some info about that planet destroyed by Gladiator?

Because it could be a planet 2 times bigger than Earth, but 100 times less dense, making this feat pale compared to Goku's striking punch.

Indeed, what really matters when talking about physical punches is the density, and AT, giving us a planet of a few meters of diameter and with a gravitational force 10 times bigger than the one on Earth, is indisputably giving us that previously said enormous level of density.

Imaging taking a cube of 1 meter of each side of the following materials:

- average Sun composition: it would weigh around 1,4 tons;

- average Earth composition: it would weigh around 5,5 tons;

- core of the Sun material: it would weigh 150 tons;

- King Kai's planet material: it would weigh around 10 millions tons;

- Neutron Star material: it would weigh around 280000 billions tons.

Punching the core of the Sun would obviously require inhuman physical strength, regardless of how much matter, in kg, you punch away; even worse would be just trying to physically scratch the surface of a Neutron Star.

Well, a not even bloodlusted Ssj3 Goku actually vaporizes, with one punch, a whole quantity of a material which, according to canon info about King Kai's planet, has thousands of times the density of the core of the Sun.