Asteroid to Crack the Earth?

[Phawks]

I have an interesting question to ask; how large would an object have to be to crack the Earth apart? Understood, there are other factors involved, such as object velocity, object density, impact area, impact density, etc. A size of asteroid/comet is all I really need, or an impact energy estimate.

I'm asking this because I'm writing a novel in which such an impact takes place, and I would like for it to be as realistic and accurate as possible. Thanks, EP!

[Nemkoon]

An Asteroid twice the size of the planet?

[Red Skull]

Full power of the Death Star I superlaser was 2.4×1032 W. Canon suggests that two 30% power shots could crack a planet open. Full power turned Alderaan (an Earth-sized planet) into an asteroid field with one shot.

[Phawks]

Now that's 2.4x10^32, right? Two 30% shots...60%...1.44x10^32? That's a lot of energy.

[Sprung]

Now that's 2.4x10^32, right? Two 30% shots...60%...1.44x10^32? That's a lot of energy.

WHAT?

It would have to be gigantic. Some scientists posit that a planet nearly the size of Mars hit the young Earth at a slight angle, and excavated a large portion of the Earth, which then coalesced into what is now the Moon, and gave Earth it's increased spin. To crack the Earth into pieces would be an enormous feat.

[Phawks]

Actually, according to the Earth Impact Effects Program, an asteroid/comet roughly 150+ miles in diameter would have nearly enough energy for that. Considering the dimensions of Ceres, if it were to be knocked into an Earth-crossing orbit, it would be large enough to crack the planet.

[Red Skull]

Sprung, that comes out to 144,000,000,000,000,000,000,000,000,000,000 watts. Or (if I can figure this correctly), 1 billion cubed, times 144,000.

Force in Newtons * Velocity in m/s = Energy in watts

F*V=W

1.44x10^32=F*V

V is the speed of light, since that was the deathstar laser

so 1.44x10^32 = F*(299,792,458)

divide V over, and F = ~4.8 × 10^23 newtons

so to crack an earth-sized planet, it would take a force of 480,000,000,000,000,000,000,000 Newtons.

[Red Skull]

Actually, according to the Earth Impact Effects Program, an asteroid/comet roughly 150+ miles in diameter would have nearly enough energy for that. Considering the dimensions of Ceres, if it were to be knocked into an Earth-crossing orbit, it would be large enough to crack the planet.

Ceres is almost 600 miles in diameter, by the way.

[Phawks]

Oh, yeah, I originally put 150 into the calculator and wrote that sentence before checking on Ceres. Yeah. It's 590 miles, roughly.

Here's the calculator: http://impact.ese.ic.ac.uk/ImpactEffects/

[Red Skull]

Oh, yeah, I originally put 150 into the calculator and wrote that sentence before checking on Ceres. Yeah. It's 590 miles, roughly.

Here's the calculator: http://impact.ese.ic.ac.uk/ImpactEffects/

Yeah but for a planet-cracker, none of the crater calculations really matter.

I'm trying to figure out a Newtons-Joules conversion, but I'm having trouble figuring the "meters of work" for the joules conversion. Would it be the distance from the asteroid's starting location (IE the belt past Mars) or the distance from the entry into the atmosphere?

[Tassadar]

*Mistral to this thread please, calling Mistral to the Free for all section please*

[Phawks]

Well, the impactor wouldn't be actually applying work on the planet until impact, so I'm thinking the distance would end up being from the point of impact until the depth where the asteroid stops.

EDIT:

Bingo.
F = ma
F = 4.8e23 N
a = ([51] km/s)/([.01] s)
a = 5100 km/s2 or 5100000 m/s2
4.8e23 N = (5100000 m/s2)(m)
m = 9.41176471e16 kg

That's the minimum mass of the impactor. That could then be figured for density and dimensions, I believe. Thoughts?

[Red Skull]

Well, the impactor wouldn't be actually applying work on the planet until impact, so I'm thinking the distance would end up being from the point of impact until the depth where the asteroid stops.

Actually now that you mention that, it would most likely be an airburst, so that would be the distance from the explosion to the surface.

So Tunguska was a 5-10 KM airburst, generating 5-30 Megatons (21-130 Petajoules) of energy. So let's take the large numbers for dramatic effect.

480,000,000,000,000,000,000,000 Newtons applied over 10,000 meters = 4.8 × 10^19 Newton-meters or 4.8 × 10^19 joules (interchangable units in this case)

130 petajoules (tunguska) is 130 x 10^15 Joules

So a Planet-Cracker would be about 369.24 Tunguskas

[Phawks]

Depending on the composition of the impactor, it may either be too tough or too fast to airburst. At orbital speeds, it shouldn't take more than ten seconds to impact. That's enough time to airburst, possibly, but not much. Also, look at my previous post; I made an edit with new calculations that may help.

EDIT:

Not difficult. The Tunguska object wasn't very big, I believe. Wikipedia'ing the dimensions now.

[Red Skull]

Yeah, that's comparable to Ceres in terms of mass. Where'd you get the acceleration numbers though? That's a few hundred thousand times Earth's gravity.