Physics: How much energy does it take to partially explode a planet?

I'm pretty sure somebody out there has done the maths on this, and if there's any place I can go to find links to this it'd be here :P.

Anyway. In a RPG campaign I'm currently running, the PCs discover a Mars-sized planet that has recently had a significant chunk of its mass blown apart.

The in-universe explanation (which the PCs might eventually discover) is that a scientific experiment went cataclysmically (is that a word? :P) wrong and produced a large amount of antimatter inside the planet's mantle with predictable (and spectacular) results.

The effect I'm looking for would be kinda like the hazard symbol for Explosives: A (badly-deformed, but still recognizably round) chunk of planet on the far side of the blast and nothing particularly recognizable on the front.

So, any takers? Is there a source where I can read up on the physics of exploding planets? :P

The gravitational binding energy of a spherical object of uniform density is given as:

U = 0.6*GM^2r^-1

where G is the gravitational constant, M is the object's mass, and r is the object's radius.

For Mars, we get an answer of about 4.9*10^30 joules. This is 2.3*10^13 times greater than the yield of the largest nuclear weapon in history, 9.8*10^6 times greater than the energy of the Chicxulub impact, or equivalent to the energy output of the Sun every three and a half hours. Alternatively, it would require the energy conversion of about 2.3*10^13 kilograms of antimatter with the local supply of matter.

The amount of energy required for your scenario would be less than this, but in the same ballpark, depending on how much you want to be blown off. Note however that an explosion adequate to remove a large portion of the planet beyond the gravitational dominance of the remaining portion would also cause the remaining portion to shatter and then fall back together, totally altering the geography and, in the case of a large enough planet, converting the surface into lava for a while afterwards. A planet also would not remain in a non-spherical form with a large portion missing; material from the edge of the 'crater' would fall into it, returning the planet to its round shape relatively quickly.

Moreover, if the planet were in the inner part of a star system, the debris would probably render all the other planets and moons in that part basically uninhabitable for some tens of millions of years.

Hmm, that may be a bit more energy than I had in mind, then.

For the record, the technology involved (a 'hyperspace catapult') was meant to shunt the object it was used on to another location at FTL speeds. Due to a fundamental flaw in the design, the target could, under certain circumstances, arrive as equal parts matter and antimatter.

The kind of mass needed for this kind of overkill effect would be a bit much to use in a test, though.

Back to the drawing board, time to tone down the kaboom a bit.

@Matt: This site might be both useful and entertaining to you. It simulates the effects of an asteroid impact, but you could use the effects to ballpark the effect of a similar sized explosion relatively easily.

For example, I entered a 1000 mile iron asteroid striking the earth at 100 miles per second. The result was the following:

The Earth is strongly disturbed by the impact, but loses little mass. 100.00 percent of the Earth is melted The impact does not make a noticeable change in the tilt of Earth's axis (< 5 hundreths of a degree). Depending on the direction and location of impact, the collision may cause a change in the length of the day of up to 291 milliseconds. The impact does not shift the Earth's orbit noticeably.

edited 29th May '13 6:36:21 PM by DeMarquis

That is awesome. Does it also list affects on planet life or just what effects it has on the planets?

Does it change anything if it was more implosion than explosion? Something like a mini black hole or some sort of temporary rift that just poofed a chunk of the planet away before collapsing? It's really going into ridiculously out there territory, but it's all I can offer.

edited 28th May '14 4:46:40 PM by Nadir

If it's an implosion, measuring the energy required is gonna be a lot more difficult, especially if it relies on a more exotic method like the black hole you mentioned. Measuring the energy output of a Portal Cut is pretty much pointless, but you can get a relative feel for the energy required to form a black hole by calculating its Swarzschild radius.

Forgive me for not realizing at first that this thread had been necro'd.

@Whymia: Sadly, only the effects on the planet itself.

@Nadir: I dont know of a black-hole collision simulator, but this article might help you.

There is a guy who participated in the Star Wars vs Star Trek flame war. He had a Ph D in astrophysics or something and argued on the side of Star Wars. At one point he computed the amount of energy necessary to make Alderon go boom. I checked his work again E=MC^2 and it was more energy than if the entire mass of the Death Star was converted directly.

That sounds like rather a lot. Wasn't the death star supposed to be the size of a small moon? Or did the calculation not use minimum required energy but instead went for required energy when heating with a laser or something similarly inefficient?

Bit late, but regarding the OP: something like that is unfortunately physically impossible. Planets aren't round for the same reasons round rocks are, they're round because of their own gravity. If you blow a chunk out of a planet, it will immediately start flowing back into spherical shape like a drop of liquid. And you're not likely to get the halo of debris pieces either, because except for a very few that the explosion just so happen to throw into an actual orbit, the rest either fly away or fall back down. (because compared to the gravitational energies at that size, solid rock might as well be liquid) Iirc there was actually an xkcd what if that did the calculations for this, with the question being what'd happen to a planet sized bowling ball or something similar.

Well to be fair for a short time (anywhere from a few days to a few decades) you can create a Broken World effect of partially destroying the spherical nature of a planet. Granted the factors needed to accomplish this would pretty much wipe out most to all life on the planet but it is doable.

It's believed Earth was like that in the short time after the Great Impact that formed the Moon. Until the molten mantle and falling back debris ring returned it back to its spherical shape.

The only long lasting effect of this type of destruction is a ring system if it threw up sufficient amounts of material to orbit or if you really did it hardcore a new moon.

Well, i checked the xkcd what if(cause i'm to lazy to do the calculations), Randall gives an estimate of about half an hour for the collapse of the holes in a planet-sized bowling ball. Granted, that's not for rocky material, although while harder rock also has more mass. So i doubt anything much longer than a day would be very plausible as the time for a deformed planet to get back into roughly ball-shape.

^ Depends on the planet's composition. A hot ball of iron like ours would quickly regain shape through volcanic processes on top of gravity. A cold planet with no internal processes (think Mercury or some of the Jovian moons or Luna) would retain damage to its shape so long as the debris does not fall back into the crater/scar.

In short, you can blow away a quarter of the Moon and it can stay that way, blow away a quarter of the Earth and the Earth will "bleed" back into shape albeit with reduced density.

The bowling ball example is kinda bad because finger hole geometry is exceptionally rare in the natural world. Craters, scuffs, cracks, canyons, faults, and scarps are all quite common. Get a big enough crater and a planet is simply no longer spherical.

The whole point is that you can't get a big enough crater because gravity simply pulls the planet back into shape. depending on the size of the planet (i.e. it's gravity) you've got hard limits for how big features like mountains can be before they simply collapse under their own weight. Even on the moon, any crater large enough to noticeably distort the outline would quickly start filling up, sort of like a mudslide. It's the major reason why mountains on mars and the moon can be much higher and steeper than on earth for example. At the sort of scale where you'd notice a planet missing a slice, rocks simply aren't solid, not even cold ones.

The Death Star was apparently about 120 km in diameter which makes it less than one millionth the size of the Earth.

This might be the article, but I can't access it:

http://www.stardestroyer.net/Empire/Tech/Beam/DeathStar.html

This essay calculates the binding energy of Earth at about 2x10^32J

http://typnet.net/Essays/EarthBind.htm

One tonne of matter converts to about 9x10^19J http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

Given a radius of 60,000 metres the Death Star would be 9x10^14 cubic metres. (4/3xPIxR^3)

So then it depends on the density of the Death Star. Sure it is has a metal superstructure and armour but it is mostly air inside. Fudging at an average density of 1 then you get 8x10^34J

I did the calculation a few years ago so either I made a mistake then or now or the energy values from other people were wrong.

edited 7th Jul '14 8:08:52 AM by 66Scorpio

Thing is, what you're looking for isn't possible. Planets are round because gravitational forces won't allow any other shape. At that scale, the planet may as well be made of a liquid. If a huge chunk of the planet is blown out then the pressures involved will force the remaining matter back into a sphere.