JS and g8rguy: As we are talking about (or at least I was) speeds approaching c I was referring to relatavistic mass not invariant mass.
As theory states that mass of any object increases toward infinity as it approaches c.
Invariant mass refers to any objects at reast mass which is of course volume times density. At zero velocity relativistic and invariant mass are equal. For a photon I can think of only one place where it has an “at rest mass” which would be the specific band of an event horizon that affects that photon.
As I understand it loss of energy in a photon is what results in a “red shift” towards UV, ioncrease in energy has a “blue shift” effect. Enough red shift and the visible spectrum shifts down to radiant heat and I think at some point radio or micro waves shift into visible range.
(note on “loss of energy in photons” statement: I mean apparent loss relative to the observer. As in observer moving away from photon source at high velocity looking backwards.)
Well, it’s not “deep” so much as it’s “insanely armored and shielded against damage”. Of course, I don’t want the strength of this bunker to be so powerful as to be orders of magnitude more powerful than anything around… so I gotta find out how much energy is going to be imparted on the planet so I can decide if the story is viable or not.
zen101, non-physicists may use the term in other ways, but when a physicist says “mass”, he means “rest mass”, plain and simple. And you’ve got most of your examples of redshift backwards: A redshift would take visible light to infrared, not ultraviolet, and microwaves and radio waves are “redder” than infrared. On the “blue end”, past visible light, there’s ultraviolet, x-rays, and gamma rays.
SPOOFE, you are planning this as a suicide attack, right? It’s hard to say exactly what the effects on the planet would be, but I think it’s reasonable to suppose that whatever the collision does to the planet, it’ll do much worse to the ship.
And for your “bunker”, would it be reasonable to put your would-be survivors on a space station, rather than somewhere on (or in) the planet? I would think that that would greatly improve survivability.
Well, zen101, I was trying to support you, but then you write something that’s extremely misleading and now I understand why physicists get so nitpicky…
Sorry, this pretty much isn’t true. When moving at relativistic speeds its extremely important to use rest mass as your definition. “Effective mass” is something like what you call “relativistic mass” and in a certain reference frame may increase, but to be honest, that’s not a very good definition of mass. If the mass of any object really did increase toward infinity we would have a hard time defining a center of mass frame of reference (always useful when you’re dealing with relativistic massive particles). That’s why we use rest mass as what mass is… that is an intrinsic energy that cannot be converted away simply by changing position or velocity frames of reference. You are technically in the right ballpark as one would have to apply an infinite energy source in order to accelerate an object with a zero rest mass toward c assymptotically. One way of illustrating this to the general public is to say that the “mass” of the object increases. This is a very naive definition of mass, however. As I alluded to before, momentum and energy are really the quantities involved when in looking at lab-frame accelerations toward the speed of light.
Actually, what you want is the zero-momentum frame. In Newtonian physics, this is the same as the center of mass, so the terms are often used interchangeably, but they shouldn’t be, in relativity. And since the notion of “relativistic mass” comes from momentum in the first place, you’d actually be more correct to use “relativistic mass”, rather than rest mass, for “center of mass” calculations.
Of course, you’d be even better off dealing with momentum in the first place.
Not really, Chronos. I’m not trying to make this “hard” sci-fi. I’m trying to make it just yer basic space opera with some pretty friggin’ powerful technology. Think of warships that can shrug off teraton-level blasts like they were nothing.
So that’s why I need to find out how much energy this’ll need. A simple “F=MA” equation won’t do it… I also gotta take into account all the matter that needs to be moved out of the way to allow the ship to penetrate through the planet (as Joe_Cool said, above). If the number winds up too high, I’ll just set the story on/around a smaller planet, a moon, or a really big asteroid.
This whole excercise is to see, essentially, how strong these fictional starships would have to be in order to survive this maneuver.
Again, I’m trying to show how strong the bunker would have to be to survive. If it turns out to be too ridiculously powerful, I can always place it on a low-orbit station that has to fend off a bombardment of ejecta from the planet.
If this sucker has to go through the planet, and, no doubt come out the other side intact, guns blazing through a cloud of escaping plasma, I think the realism factor is . . . well, screwed.
By the time you compress an eight thousand mile cylinder of air, water, rock, magma, iron, and core material enough to get it out of your way, you will have built a plasma ball of huge proportions. You will also probably create a shock wave great enough to launch significant portions of the planet into space. The heat alone would vaporize huge amounts of the planet’s formerly solid materials.
Even an object as small as Superman would have to be traveling very near the speed of light to do something like piercing a planet the size of Earth. And still, I think the results would involve energy levels high enough to remelt the lithosphere, vaporizing significant amounts of it.
Have the captain crash land straight down, and then back out into the center of a fire storm created by his own impact. You get your titanic energies, your blazing circles of incandescence, your coruscating fountains of iridescent plasmas, the whole thing! And you don’t have to specify how deep, or how much energy, just enough to make it really cool. If you want your bunker to be the center of the story, make it the center of the impact! Then when the Ground Station commander launches his counter attack, the captain can stare dumbfounded as the “Bunker” rises out of the lava pool on its gravity repellor, with molten iron streaming off of it, on the way up.
Tris
" The worst policy is to attack cities. Attack cities only when there is no alternative." ~ Sun-tzu ~
I should point out that when actually boring through hard material and/or making a large hole it is better to go at a slow rotational speeds. If you go at high speeds (higher energy) you are likely to caues either your tool to break or fission of the material with which you are working.
I assume this would apply to this situation too. If you really want to bore through a planet, it’s better not to try going at it as quickly and as strongly as possible, lest you a) destroy your tool (ship) or b) fission the planet.
OK, suppose that we’ve got some ultra-righteous forcefield on the ships to enable this. Why can’t we put one of them forcefields on the planet, too? Or if we can’t make the fields that big, just put one over the point of impact. And if even that’s impractical (maybe they don’t know in advance where the impact is going to be, and can’t get a field generator out there in time), the bunker would at least have one. Since the bunker would have better protection (of whatever sort) than the ship, and the bunker isn’t right at the action, like the ship is, you can rest assured that anything the ship survives, the bunker survives.
Part of the plot involves the planetary shield to be sabotaged, and they’re trying to get it back up as the enemy ship is trying to ram the planet.
Just for clarification, there’s also another ship in orbit defending the planet, which is why the enemy ship doesn’t just pound on the planet’s surface from orbit. A ramming operation is the only tactic that’s quick enough and damaging enough to complete what the captain of the ramming ship wants to do.
Oh, another point: The ramming is supposed to be just barely within the capabilities of the ramming ship, which is why I need to know as accurately as possible how much energy will be required for such an operation.