Could you destroy the earth with a fast enough space ship?

Factual Questions
1

Ok here we go this is going to take awhile but bear with me on this because it points out a really good physics question…

A couple of years ago I read a science fiction book and it talked about a new “engine” that could put a ship to millions of multiples of c (the speed of light) these ships used a gravitational shield to accelerate almost instantly… Basically you could really really fast… Now the story went on to say something about they were impossible to buy or get unless you were sometype of government or business or something due to the fact that a single ship using one could aim itself at a planet and with so much force behind it would literally blow the planet up… Mind you f=m*a Force = Mass * Acceleration now at first I took this as sounding good but for whatever reason I started thinking about this again… now hear is the part that bugs me about this now…

what about the atmosphere?

at first I thought well it would just zip right through it super fast and hit the planet and not burn up like a meteorite would…

but then I though about this… if you throw an egg into water it will just sink/float in whatever won’t break… but if you where to throw it as hard as you could with enough peed it would instantly explode on contact and barely get into the water…

Now I think the same is with the atmosphere, which contains a “sorta” tangible substance which is mixed gasses… space is a void with no air no nothing… I know when Nasa re-enters the ships have special burn things to keep them from destroying themselves and burning up and once they get in a little more they slow down to reach terminal velocity or whatever and are fine…

Now here is the question would the ship just zip through the atmosphere and blow up the earth? or would it hit a substance that is miles and miles deep so fast it would explode against the atmosphere hailing down pieces of itself like meteors… or would it be vaporized hitting the atmosphere… or would it argh punch a whole in our atmosphere vaporizing and LET OUT ALL OUR AIR :slight_smile:

wow I love this…
I really think this is a good question…

2

You cannot go faster than light. That is why it is called science fiction.

If you really got enough energy to get it to 99.9999999 percent the speed of light, you’d probably wipe out the whole damn solar system. Your ship would become impossible massive and large too.

3

At millions of times the speed of light, it would be irelevant. Likely, a 2mm BB traveling at that speed would destroy the sun, much less Earth.

Inert warheads are incredibly effective for space combat or the like. I remember something about NASA doing some testing of the effects of hypervelocity impacts on satelites on a show I watched last night on TLC (“Space Junkyard” or something like that… Terribly over-dramatized and alarmist, but I managed to pick out some interesting tidbits before walking away in annoyance). A small projectile the size of a marble was fired at high velocity (Several miles a second) into a small test satalite. The impact was so severe, the satalite was completely obliterated. The only intact pieces were a couple of the heftier aluminum body-pannels (One with a massive cratered hole in it), and some fried circutry (Completely scorched by the massive heat generated on impact). The Challenger was almost lost to a 2mm fleck of paint traveling in opposite orbit (Combined total was somewhere around 35-40K miles/hour), which hit with about the force of a 50-caliber bullet, cratering one of the shuttle’s windows.

Now, the ship will not survive impact with the atmosphere by any means. One sci-fi work I read (Albedo; Also one of the best depictions of realistic space-combat I’ve seen) would describe the result as “aerosoling” the ship. It’s reduced to such tiny particulates that the nothing is left whole. However, it still has the same mass (Very important!). Effectively, it’s done the very same thing that a HEAT round does on impact with an armored vehicle. At such a high speed, it wouldn’t even have time to spray out any, so the entire mass of the ship would drive through the planet at the same speed, displacing the entire mass of the planet along its path in a period of time so quick it would be essentially instantaneous. Imagine a lightningbolt the thickness of that ship, and the whole length of the atmosphere; Even through just the atmosphere, the displacement would make a thunderclap deafening for quite a distance. Add in the entire distance through the earth, a good 7000 miles, and that’s millions of tons of mass instantly displaced. I’d say the effect of completely destroying the world it hit would be extremely likely; At best, it would be uninhabitable as the shockwave of the impact would probably stip away the entire atmosphere.

Then you’ve got the entry flash. At that speed, the heat generated from the impact would almost surely be great enough to incinerate a whole continent, if not the whole surface of the world, and the added heat will add to the destructive effect upon the world.

For that egg theory to be valid, consider that the water has much higher mass and surface tension than the air does. Then accelerate that egg to several times the speed of sound before firing it into the water, aimed at a target about 2 feet under the water (Compared to the earth’s diameter of about 7000 miles, the atmosphere only covers about 40 miles on either side, a tiny distance in relation to the overal target). The water wouldn’t make too much difference. And that’s a very forgiving example of a miniscule fraction of the relative energy-to-mass comparison here.

Or to sum up, yes, it would be destroyed on impact with the atmosphere. It just wouldn’t make any difference :slight_smile:

(Of course, this is all assuming that this drive nulifies the increased mass effects of approaching the speed of light, as I’d assume it would have to. Otherwise, you’d have an infinatly massive object impacting the planet, and the effect of having any object in it’s path would be completely unimportant; The ship would take a tiny bit of damage of its infinate mass, or, effectively, no damage at all; You’d even be able to turn around and hit a different planet if you felt like it)

4

In this thread, we established that the gravitational binding energy of the Earth is some 2×10[sup]32[/sup] Joules. If you wanted to destroy the Earth properly, and blow it into a zillion pieces (as opposed to, say, two), you’d need at least this much energy. So say you’ve got a 100-ton rocketship to do this with. Classically, you’d need to accelerate it to 224,000 times the speed of light to get this much energy. This, of course, is ridiculous. Relativistically, the necessary speed is 0.9999999999999999999992 times the speed of light, a much more reasonable number. Your ship would be indeed be massive, with a relativistic mass of 2.5 million megatons. But, it would not be all that large. If it started out as 40 meters long, it would shrink to about 1.6 nanometers in length. From the ship’s point of view, the atmosphere would be a few micrometers thick. I don’t think the atmosphere would cause much of a problem.

5

Not almost lost - it is quite common for the shuttle to come back w/ a cracked windshield and now orbits w/ one cargo bay door partially opened (vertical) as the shuttle travels sideways. The CBD acts as a shield to deflect any junk so as not to dammage the cooling system (which is the inside of the CBD’s. It used to orbit w/ both CBD’s fully opened.

2nd of all a ship travelng either .99999c relative to earth would be traveling 0c relative to the pilot and not hard to manuver at all. The mass relative to the pilot would also be whatever the ship’s rest mass was (execpt for spinning parts or other moving parts i.e. turbolifts)

now F=ma doesn’t really help up because we don’t know the rate of deceleration. perhaps energy PE=0.5mV^2 and momentum = mV(ship) = mV(earth) would be a better indication of the dammage that would be caused. With the energy equasion (and assuming the ship’s mass) you should be able to calculate the mega (giga? terra?) tonnage of the impact)

6

The original time I heard that (Not the TLC show, I’m sure they would have blown it out of proportion, but I can’t remember the original source) said it had cratered something like 90% of the way through the window. Wouldn’t have destroyed the shuttle, or even likely killed the crew (Would have taken a long time for it to depressurize, they could have suited up), but I doubt it could re-enter with a hole in it, and I don’t think they could have gotten another shuttle up in time. Could be entirely wrong on all that, though :slight_smile:

But you mentioned something I’ve been trying to work out… What would be the formula for determining the energy of a kinetic impact like that? It’d be pretty easy to get in a unite like joules, but I can’t seem to find how it would equate in the terms of kilo/mega/gigaton-yields.

7

As just suggested don’t overestimate the effect of the earth’s atmosphere. Certainly it protects us from a lot of junk but it is not as an effective shield as some think. Along with what Achernar just posted I heard a tidbit that said if you shrunk the earth down to the size of an apple the atmosphere would be thinner than the skin on an apple.

That’s just for a little perspective. Carry on…

8

If this happens, you’re going entirely too fast! Ease up on that accelerator, buddy. :wink:

Seriously, I don’t believe faster is always better. For maximum destruction, I think you’d want the ship and displaced tube of planet to come out at a little below escape velocity. Since the material is then essentially in an orbit intersecting the planet, it all comes back down, over the course of, I don’t know, days?

Oh, and you want to hit off-center a bit, so the spray lands over the whole planet.

As to the OP, all I can do is “me too” the earlier posts: the atmosphere is negligable once you’re punching through the planet.

9

from http://www.matter-antimatter.com/energy.htm

1.0 Megatons of TNT = 4.18 x 10^15 Joules

at the above equasion should be KE not PE
Anyone out there willing to chug the numbers and find out how explosive a ship traveling near c

10

ok http://www.matter-antimatter.com/energy.htm might not be the best ref. sorce but the conversion seems to hold on several web sites.

11

ok I’ll take a tired stad at it

c = 3.00e8 m/s = speed of ship = v
m = mass of ship = 10,000kg (very small ship)

KE=1/2mv^2 which we will divide by 4.18 x 10^15 to get megatonnage

megatonnage = 0.5 mv^2 /(4. x 10^15)
= 0.000000000000000125 mv^2

so at c the ship will have the energy = 1,125,000 megatons TNT or about 1 terraton

a 100,000 kg ship traveling at 10c (yeah but it’s sci-fi) would have the erergy of 112,500,000 or 100 terratons of TNT

Thats if I did my math and units correctly.

12

I am making a bit of an assumption here but IF this ship could travel at a multiples of the speed of light and IF it came into contact with the atmosphere. Isn’t there something about the conservation of energy that would come into play here ? Can someone please confirm / dispute ?

Thanks

13

Hmm… Would be very hard to get the speed juuuust right, though. :slight_smile: But at that point, I don’t think it would matter. The impact flash would have incinerated a huge chunk of the surface, most of the atmosphere has been stripped away from the shockwave, and the overpresurization effect has likely destroyed much of the surface structures, including hardened/sealed ones. I can’t see much surviving that… But then, I can’t really see anything ever getting that much speed. A 100-ton kinetic-kill missile traveling at a few (Or maybe even a few dozen) kilometers per second might be reasonable, but not a million times C. But being science fiction and all…

Thanks k2dave, finally can find out how destructive some of this stuff could be… :slight_smile:

14

Remember, folks, kinetic energy is not KE = 1/2 m*v[sup]2[/sup]. That’s a good approximation for low speeds, and will work just fine for almost any physics problem you’ll see, but when you’re close to the speed of light, you have to use the relativistic formula, KE = ([sym]g[/sym]-1)c[sup]2[/sup], where [sym]g[/sym] = (1 - (v/c)[sup]2[/sup])[sup]-1[/sup]. If you want to totally obliterate the Earth, then Achernar’s got the number (assuming that all of the projectile’s energy gets deposited into the Earth). Note that “really close to c” doesn’t tell you much of anything: .999 c is vastly different from .9999 c. If you’d settle for some lesser amount of destruction, then you need to decide how much energy you’d need, and re-do the calculation.

15

The dominant assumption seems to be that a significant portion of our death-star’s kinetic energy will be broadly transferred to the body of the Earth, including the atmosphere.

I’ll stand for the minority opinion. Set’s say we have a shuttle-sized vehicle that has accelerated so close to velocity C that it has an inertial mass somewhat equivalent to that of a quantity of neutron-matter filling the same volume. That’s a lot of energy on the hoof. (I think the following description is fairly independent of how much mass/energy we’re talking about.)

So what happens? It passes through the effective depth of the atmosphere in something like one-four-thousandth (1/4000) of a second. Note that sound waves make little forward progress during such a span of time. Every single particle of the ship is incredibly massive: mere percussive impact with floating molecules will mean essentially nothing to the sip–they’ll be shoved aside. Those molecules won’t have time to lazily bounce off other molecules and form a classical sound wave; instead you’ll have, for a fair part of a second, a sort of “pipe”–a cylinder-- made of super-dense, hyper-compressed air with a true vacuum in the middle. The substance of the pipe will be mega-hot, an ionized plasma; it will explode outward at (when it stabilizes) the speed of sound, losing heat in all directions as it spreads; there will be an incinerating flash of heat and blinding light within the circle of the surface horizon (the region with a view of any part of the pipe, including the top); massive electron discharges (mostly along the path of the ship); microwave stuff, x-rays, sonic-boom-like aerial aftershocks; God knows what else. But but but-- no chain reaction, no fusion, no hard radiation. The real sci-fi disaster effects will be pretty much limited to the area mentioned above.

So what happens when it plows into the ground? Pretty much the same thing for the first “few” miles–another pipe, this time of silicate materials. But increasing density does begin to slow the ship a bit, and declining velocity leads to declining relativistic mass. It’s all in the numbers; the ship could well punch right through (all in less than a second). So Earth vaporizes? Not hardly. Super-heat is pumped into it along the thinnest of threads; relative to the total heat content of the entire bulk of the planet, I think it would be insignificant. The ground shockwave would be on the order of that produced by underground H-bomb testing: locally noticeable and probably enough to set off tectonic slippages and conventional earthquakes. But not world-fatal.

The point is: our hypothetical ship packs a powerful but very CONCENTRATED punch. A Manhattan-sized asteroid falling on us at 7 mps is a much, much greater danger to the biosphere.

16

Scott Dickerson very interesting. Your assumption really depends on the ship actually punching through the earth and exiting out the other side - which is possble given the circumstances but as I calculated above the energy that a ship would have would be on the order of hundreds of terratons of TNT. I’m sure the numbers would be simular using Chronos’ equasions but they don’t work at speeds greaater then c even though are more correct - again I use the excuse of this is sci-fi.

THe biggest nuke we got is on the order of 100 megatons (IIRC) and can no way destroy this planet but we are talking about the energy 1,000,000x of that - this could be enough to blow apart the planet? It all depends on how much of the 100 terratons of energy is transfered to the planet, how much gets neatly blown off the planet and how much stays with the ship.

Could such an impact significantly effect the orbit also?

I would say that the ship travelig multiples of c could cause all types of changes in matter as nuclei are forced together and ripped apart. I don’t know if this would lead to a net gain or loss of energy.

17

How big can your space ship be? If you can propel an earth size planet and call it a space craft, then I think amout 10 mph would be enough to do it.

But if you can double the speed, you can reduce the mass to 1/4 and still hit with the same impact. Velocity is squared in these force equations, which is why the “multiple light speed” thing might let you detroy earth with a Yugo. But you don’t need it if you have enough mass.

18

To get the energy you quoted, the ship would only have to be going about three quarters of the speed of light. There’s two sides to looking at things relativistically: On the one hand, speeds greater than c are no longer accessible. On the other hand, though, speeds greater than c are no longer necessary, either. Name any energy you want, and any mass, and I can tell you the speed of that mass, and it’ll be less than c. If you get a 100 ton ship going at 0.9999999999999999999992 c, it’s enough to blow the planet to smithereens. Given that, what happens when you go into a science fiction world, and take a speed of several times c? Anything the author darn well wants, because our physics sure isn’t going to tell you.

19

I agree with you to a point, but I think you’re underestimating the overal impact here. I’m pretty sure it would be MUCH more noticable than an underground nuclear detonation. With such destruction, the additional effects of a nuclear detonation such as radiation become completely irrelavant, the damage is already done.

I worked out a much more realistic missile, than the planet-busting ship above. A 220-ton solid kinetic-kill missile, deployed far out in the system and accelerating untill it reaches a speed of around 5800 kilometers per hour (Done from a story I’m working on, though somewhat rough-guessed as I havn’t worked out the missile’s endurance yet… I took a low estimate). On impact, it would have kinetic energy equal to the energy released by a roughly 900 megaton nuclear detonation.

With that power, it would likely not penetrate too far into the earth. It would certainly leave a huge crater! By comparison, the Berringer meterorite, which caused an almost mile wide crater, impacted with the equivelent force of (By the same formula) 135 megatons, going from the rough estimates (Though the only cite I could find for -yield- indicated only 20 megatons). This site has a good diagram of the shockwave effect that happened on impact with the ground; For these more powerfull examples in this thread, the effect would be even greater, as the shockwave would be generated with much more impact energy, and continue further before disipating. Also notable is the fact that the crater is about ten times wider than it is deep.

On top of that, you’ve got the heat flash, microwave flash, and overpressure wave to deal with. It’d be somewhat like hydrostatic shock on a person, but over a much, much larger scale. While it’s certainly not a world-ending attack, it would certainly be -noticed- over a good portion of the world. I would estimate the global effect to be somewhere close to the eruption of Mt. St. Helens, though it could easily be more or less.

I certainly wouldn’t want to be nearby, in any case :slight_smile: