How do rocky planet break up? Would they fragment into "a gazillion" rocky pieces pieces, or crack open like an egg?

Question

I remember seeing Star Wars, where Darth Vader shoots a superb laser (Death Star) to obliterate a populated planet, Alderaan (how inhumane).

The problem is, the planet cracked into a gazillion rocky pieces, like you would get if you dropped a marble ball from the top of the empire state building.

But, rocky planets (and perhaps other sufficiently large rocky bodies) have molten mantle. So I think, it should have cracked open like an egg, the crust shattering into a zillion pieces like an eggshell, with the viscous mantle liquid being sprayed across in space.

[Note that I am not referring to the firing of 'Jedha' (Rogue One) where a much reasonable planetary destruction was shown. I am referring to the original Star Wars, later dubbed The New Hope]

From Wikipedia's Terrestrial planet:

A terrestrial planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to the Sun, i.e. Mercury, Venus, Earth and Mars. Among astronomers who use the geophysical definition of a planet, two or three planetary-mass satellites – Earth's Moon, Io, and sometimes Europa – may also be considered terrestrial planets; and so may be the rocky protoplanet-asteroids Pallas and Vesta. The terms "terrestrial planet" and "telluric planet" are derived from Latin words for Earth (Terra and Tellus), as these planets are, in terms of structure, Earth-like.

Answer 1

Energy Intro

I think any good discussion of planetary destruction should start by talking about energy! Our SI base unit of energy is a Joule, which is defined as $\mathrm{J} = \mathrm{kg} \mathrm{m}^2 \mathrm{s}^{-2}$, or the force of one newton acting over one meter. Of course energy can also be stored thermally: $1 \mathrm{J } \approx 0.239006 \mathrm{ cal}$. A calorie here is the energy needed to raise the temperature of 1 gram of water by 1 degree Kelvin.

Minimum Planetary Destruction Energy

Just how much energy is needed to permanently destroy a planet? We can start with the idea of GBE (Gravitational Binding Energy), which is the minimum amount of energy required to cause a planet to cease being in a gravitationally bound state. One way to calculate this is to compute the energy needed to push successive shells of a sphere out to infinity. GBE is expressed by $$U=\frac{-3GM^2}{5R}$$ where $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is the planetary radius. This energy can be pretty huge for planets. Earth's GBE is about $2.49 \times 10^{32} \mathrm{J}$, while Mercury's GBE is about $1.8 \times 10^{30} \mathrm{J}$.

To practically destroy a planet, you need much more energy than the GBE. That is because the GBE doesn't take into account any cohesive properties of the planet. It doesn't account for thermal energy losses. It assumes all ejecta moves at the same rate: escape velocity.

Planetary Melting Energy

How much energy is needed to melt a rocky planet? We can start by looking at the geothermal gradient of Earth from wikipedia:

Rock melts at between 900 and 1600 Kelvin, so there is more than enough heat already in the Earth for it all to be molten if the heat was uniformly distributed and the material was not under pressure! We can estimate the energy just to melt the lithosphere, supposing average rock has a heat capacity of 2000 Joules per kilogram per °C. If the lithosphere is about 1 percent of the total mass of the Earth or $6\times 10^{22} \mathrm{kg}$ and the current average temp is about 700K, then to raise the temp to 1600K, we would need $1.08 \times 10^{29} \mathrm{J}$.

Suppose we had a cold-start rocky planet similar in shape and composition to Mercury, but at a uniform cold temp of 40K. Mercury has a mass of $3.285\times 10^{23} \mathrm{kg}$. So to bring its temp from 40K to 1600K, we would need $(1600-40)*2000*3.285\times 10^{23}= 1.025 \times 10^{30} \mathrm{J}$.

Answer

For an Earth like planet, the melting energy ($1.08 \times 10^{29} \mathrm{J}$) is much smaller than the GBE ($2.49 \times 10^{32} \mathrm{J}$). This means that even with a purely kinetic energy source, more than enough heat will be produced due to the friction and enthalpy that not much solid will be left after impact. In addition, the material around the impact will be ionized (turned into plasma), and material further away will be vaporized. As the Earth exploded, we could expect the ejecta to be in the form of droplets, gas, and plasma until they cooled as they expanded and passed through space.

For a theoretical, small, cold, rocky planet near a Pluto like orbit, the melting energy ($1.025 \times 10^{30} \mathrm{J}$) is the same order of magnitude to the GBE ($1.8 \times 10^{30} \mathrm{J})$. Hence, while heat will be sufficient for matter phase transitions near the impact, we could expect large chunks of solid ejecta away from the impact area. This is a partial "shattered marble" scenario.

Out of any source of planetary destruction, I think a kinetic impactor has the smallest thermal component. A nuclear bomb blast big enough to destroy a planet would likely liquify even our theoretical cold Mercury, since much of the energy of a nuclear bomb blast is thermal. Credit Atomic Archive:

Gamma ray bursts ($10^{50} \mathrm{J}$) have enough energy to destroy a planet, but would transfer energy thermally since they are electro-magnetic. Direct, close exposure would vaporize (ionize?) a planet. Sufficiently close supernovas ($10^{48} \mathrm{J}$), hypernovas ($10^{46} \mathrm{J}$), and AGN (Active Galactic Nucleus) bursts ($10^{55} \mathrm{J}$) also have enough energy, but would also certainly vaporize (ionize?) a planet. (Energy estimates credit to wikipedia)

Finally, the Death Star's laser would also primarily transfer energy to the planet thermally, rather than kinetically. So, we would expect more of a melting and vaporizing effect than a kinetic explosion!

Example:

But a planet could never really be destroyed, right?

Maybe not! The "de facto working model for lunar origin" according to Lock et. al 2018, is that "the proto-Earth suffered a collision with another protoplanet near the end of accretion that ejected material into a circumterrestrial disk, out of which the Moon formed." Further, they suspect that the protoplanet might have been the size of Mars and have struck at "near the mutual escape velocity." This wouldn't impart more energy than Earth's GBE, so Earth would not have un-bound. But it certainly would have rendered what was left of Earth fully molten, with a disk that was a "multiphase mixture of liquid and vapor."

In the same paper, Lock et. al offer a variation on the standard giant impact hypothesis, that instead of a liquid/gas disk being formed, the collision fully vaporized both bodies and resulted in a synestia, which is a rapidly rotating vaporized tauroid (donut shaped object). As the synestia lost heat, the authors theorize that the gas condensed into liquid, eventually allowing the Earth and Moon to form. Here is a graphic from their paper:

While the various lunar forming hypotheses don't permanently destroy the Earth, it seems very unlikely any life would survive. The various hypotheses may vary on how much liquid matter would remain after such a high energy collision, but they agree that the ejecta certainly wouldn't be solid!

Answer 2

Well... a few issues here.

Firstly, the mantle of the Earth isn't molten. It is solid. It is hot enough for there to be slowly moving currents of solid rock. On the other hand, the outer core is liquid, and very liquid. It is about as viscous as water.

Now, superlasers aren't real, but planetary collisions are real, and did occur in the early evolution of the solar system. However neither the "shattering" nor the "cracking" metaphor would describe the consequence of such collisions. Instead the impact would have sufficient energy to completely melt, (and probably vaporise) the planet. In any case, the forces resulting from such an impact would be so great that solid rock would behave like a liquid or gas.

Answer 3

Its worth noting that not all plants have a liquid core and not all planets are rocky. You can't expect a gas giant like Jupiter to shatter like glass.

To shatter a rocky planet like earth into a gazillion number of pieces needs very high amount of energy which is unlikely to happen. Talking about super-lasers, There are only naturally occurring events than can be as energetic to even vaporize earth can be from events like Gamma ray bursts from Supernovae happening near Earth. And destroying the whole earth by a collision is very unlikely

And like you say, when a rocky planet with molten core inside, bursts or cracks up due to a collision ,say Earth, the molten core will not be liquid anymore due to the absence of the pressure to keep them in liquid state (most of the core will vaporize), rocky mantle and crust will then form a ring around the sun which one day may become planet by the same way our moon is said to have formed.