How much energy need for a huge object to penetrate a planet?

All right, my big-thinking brain has come up with another problem that needs the help of resident math wizards. Inspired by a Superman comic (I think) where Supes, in a fit of rage, flies through a planet (just plowing a big ol’ corridor through it), I thought… wouldn’t it be cool if a sci-fi story dealt with a ship ramming a planet with enough speed so as to completely plow through the entire planetary diameter.

So, basically… assume the ship is an oval (or, at least, it projects energy fields in an ovaluar shape) 2 kilometers long by one kilometer wide by one kilometer tall, and weighs, say, 50 million tons. It starts off a light-minute away from the target planet. Assume that the ship (or, rather, its shields) are capable of withstanding the impact.

So… how fast, finally, would that sucker have to get going if it wants to plow through a planet the size of Earth? What sort of acceleration will that require? And, finally, how much energy would this impart on the shield around the ship?

Basically, I want to use this as a plot device in a story, and I want to use it as a technology base for starship capabilities.

Depends. Will the ship have the drives going on all the time or will it shut of the drives right before impact? Secondly, are we talking about a rock ball (such as the earth), a gas giant, or a snow ball (such as Pluto)? Thirdly, that’s a very big arsed ship you have there.

Well I don’t know how to figure the answer, but for starters, you’d need enough energy to pulverize (or vaporize?) and push aside about 10,000 cubic kilometers of rock (1km diameter of ship x 12,640km diameter of earth).

So if somebody knows either the heat of vaporization, density, and/or the energy to pulverize a given amount of granite(?), we can get started.

Of course, that ignores the fact that some of the path will likely be through water, some through iron and nickel, etc, instead of rock, and so on. But it’s an approximation.

The solution is to realize that the earth is vastly composed of empty volume, with bits of dust floating through it as protons.
More of a mist than a mountain.

The distances between atomic nuclei is huge compared with their meager
Thus, a gamma ray can penetrate quite deeply without hitting anything.
A massive nucleus, say of a heavy metal ion, can simply plow past the remaining stuff, leaving iron nuclei scattered like leaves on the freeway.

This all depends on how you wish to get rid of the intervening material. Say you wish to simply pass through the planet, then it’s probably better to convert said “ship” into highly energetic photons and send it on through and reassemble on the other side. That will be the easiest.

A one-time shot getting through the diameter of a planet is just a bit too far fetched for me to begin to figure out how do approach the problem. More reasonable would one that asked how to bore a hole the entire way through (digging it to China, if you will).

Anything that we consider a solid, like a 10 foot rock that is going fast enough to go clear through the planet will kill most everything above 2-3 cell creatures. The planet my explode from being rocked so hard on it’s axis or from it’s orbit. We know aprox, what BIG hits do that even get into the core, but to go all the way through and come out? Needs to be tougher that what we know of today because the heat developed will exceed anythings ability to not vaporize that we know of so far. :smiley:

The atomic level stuff does not do anything all that damaging so is no deal.

Snowballs and gas bags are some easier but for a story, we need the force field or shield. YMMV

Q, can an object traveling at .9999999999% the speed of light actually strike an object? (careful) :smiley:

Sure. That’s only a little bit slower than one hundredth the speed of light. To answer the question you intended, the answer is still yes. Morevoer, objects going a full 100% the speed of light strike other objects all the time, allowing you to have a sensory perception called “vision”.

SPOOFE: Two questions from another buddinf sci-fi writer.

What do you want to be the result of this penetration/impact? Do you want complete catastrophic devastation? Atmospheric interruption? Some unihabited neat looking planet? What exactly do you want for the aftereffects? In this case your desired aftereffects will dictate the nature of the impact.

As an example, if this vessel is moving at a good portion of c, perhaps it has a field around it which is frictionless, or nearly so to prevent damage from micrometeorites? Other examples abound. You get the gist.

Second question: Why not just overshoot the amount of energy needed. Writing a story where a ship is traveling at just the right speed to accidentally impact a planetary body for a specific result seems a bit of a stretch, no? Overshoot your mark by a good measure, then create a plausible variable to account for less overall destruction than would normally result from such an impact (micro black hole at center of planetoid absorbing impact, the frictionless ship thing, whatever).

I don’t know… I would think that anything going fast enough to punch through the planet would split it open like a grape. Think about a block of ballistic gelatin hit by a high-speed rifle bullet. A shock wave would form in front of the object that would transmit a lot of energy into the Earth.

Another thing that can happen when you ram some volume of matter that hard is to transform it into some exotic state, such as what makes up neutron stars, that is going to stop the ship dead in the track.

Sam Stone: One reason ballistic gelatin deforms in the manner you describe is that it has a uniform density and the object impacting it is most typically designed to cause hydrostatic damage due to shape and/or deformation.

A solid tungsten rifle bullet at about .30 caliber fired at say 2,100fps (a decent bullet velocity for a rifle round) would damage the block, but not anywhere near the damage you get to the same block from a .45acp lead hollow point round travelling at just 800fps.

Now travelling at anywhere near c and massing the stipilated 50 million tons this ship will treat anything other than neutronium like a bullet hitting ballistic gelatin. The question is, what kind of bullet is it? If it’s a ship that isn’t streamlined for intra-atmospheric travel or lacking in “deflector screens” then I’m guessing it’s going to be more like the hollow point. If it’s a dart shaped ship with deflector screens or some freictionless surface then it’ll act more like a teflon coated FMJ round on that gelatin block. There are, of course, millions of variable anywhere in between but as this is in regards to a work of fiction it really depends on what the desired outcome for the author is.

Thanks JS…

DUH, I was so bussy doing 9’s that I forgot to go left. :smiley:

No, to my other question ----- the vision answer is cool and that I knew but I remember reading something about an large object like a big rock getting to very near C as being highly improbable. the force needed to acclerate it would destroy it unless it was applied very slowly and over a large amount of time.

Q, Do we know of any objects like that at this time or can they be even observed?

You can appraoch c assymptotically as long as you have the energy to do it. So what if it takes forever and a day to do it? it’s still doable!

Moreover, there are some objects with rest-mass (specifically nuclear particles) that travel nearly the speed of light and are passing through you at a rather respectable rate (on the same order of magnitude per year as the dosage of radiation you get in a medical xray). These particles are called cosmic rays.

Photons are objects? Doesn’t something have to have mass to be called an object?

maralinn: photons do have mass. This is why solar sails are a feasable concept and why those little lightbulb things with the black and white spinning flags actually work. It’s the impact of photons.

As long as the object gets a good night’s sleep, it should have all the energy it needs. However, the planet probably won’t go for it on the first date.

The idea is to cause mass destruction, pure and simple. I just want to make sure I give a very accurate description about the effects on the planet (for instance, I plan to have a very heavily armored/shielded bunker placed deep underground, and I want to show how the inhabitants fare… plus, I want to see if such a bunker would even be feasible with the level of fictional technology in the story).

Well, I want to figure out the minimum energy requirements, so that I can make it jibe with other incidents in the story. I don’t want to fall victim to Star Wars syndrome, where ships can withstand gigaton-level blasts but then have trouble dealing with 30-meter asteroids.

Primarily, I want to see if the planet-coring maneuver I described above will fall within the technological capabilities I’ve set up in my silly little fictional universe, or if it’ll be so insanely higher than everything else that I shouldn’t even bother (I don’t want the people in my stories to wind up wielding god-like power with their technology).

SPOOFE: You know you could cause a hell of a lot of devastation by just passing a small (sedan sized or so) car through the atmosphere at near c speeds. Violent tearing of the atmosphere away from the planet would be fun, or flouresceing it and cooking everyone lungs/gills (is this supposed to be Earth btw?).

One problem I see with a deep impact scenario and the old underground bunker is that with enough speed (remembering speed=mass) you are going to liquify the insides of the planet, ripples would likely crush any bunkers deep enough to escape the above ground shockwave.

zen, am I being whooshed here? Photons do NOT have mass. They do, however, carry energy and momentum. And I seem to recall that the toys you’re talking about (I had one at some point meself, in fact) are explained by something far less esoteric than radiation pressure.

g8rguy… it’s all in the way you look at things. In a certain reference frame, it’s okay to say that photons has “mass”. It’s technically not true, in the formal definition of mass (which is rest mass, which is indeed a big goose egg for our photons)… but we perhaps should let the nitpicking technicality slide as it is difficult for some people to understand how an object can have momentum without having mass.