Relativistic asteroid collision

[superpaul3000]

Just wondering here, how much energy (in Joules or Mtons) would an asteroid say 15 km wide have if it impacted the moon at 99.9% the speed of light?

btw, I'm trying to figure this calculation out in terms of SR where the mass of the asteroid would appear much greater than if it was traveling at classical speeds. Also what would we see from the Earth if this hit the moon? I know that a really large asteroid hitting the moon at high classical, but still possible, speeds could create a blast as bright as the sun. So at 99.9% of c the people on the wrong side of Earth would be toast right? Effects on the moon?

 

[Ich]

That should be about 10^34 J. Something like 200000 billions of the biggest H-bombs ever.
It would be bad.

 

[Frame Dragger]

That should be about 10^34 J. Something like 200000 billions of the biggest H-bombs ever.
It would be bad.

How do you calculate energy yield for an object defined by width and not mass, when the composition and therefore mass could vary greatly?

@superpaul: for the record... you realize that nothing as massive as an asteroid reaches those velocities relative to Earth?

That said, bottom line Ich is right about the result... if you just imagine an explosion of that magnitude on the surface of the moon... well...
...
...
...

The price of moon-rocks would PLUMMET!

 

[superpaul3000]

That should be about 10^34 J. Something like 200000 billions of the biggest H-bombs ever.
It would be bad.

Damn. That's like 20 billion times the event that killed the dinosaurs. Ok I guess that would fry any humans on the wrong side of Earth. In fact, that may even be enough to destroy the atmosphere. 3.86×10^26 J is the total energy output of the Sun each second. So this would be 100 million times brighter than the sun and a lot closer too. A supernova would be like 10^44 J So this is somewhere in between. You would be able to see this impact from other star systems lol. So does this mean the moon is just gone? And Earth is resurfaced?

 

[superpaul3000]

How do you calculate energy yield for an object defined by width and not mass, when the composition and therefore mass could vary greatly?

@superpaul: for the record... you realize that nothing as massive as an asteroid reaches those velocities relative to Earth?

Ok so let's just say it is a solid iron sphere with that diameter. I realize that naturally it wouldn't but it's fun to imagine...

 

[Frame Dragger]

Damn. That's like 20 billion times the event that killed the dinosaurs. Ok I guess that would fry any humans on the wrong side of Earth. In fact, that may even be enough to destroy the atmosphere. 3.86×10^26 J is the total energy output of the Sun each second. So this would be 100 million times brighter than the sun and a lot closer too. A supernova would be like 10^44 J So this is somewhere in between. You would be able to see this impact from other star systems lol. So does this mean the moon is just gone? And Earth is resurfaced?

If you want to get into the nitty gritty, I don't know what a mass of the kind you describe at those velocities would act like. I think it would massively blueshifted from our perspective, and starting to get perilously close to becoming an asteroid RAY redshifted in the "rear" of the trajectory!

In fact, I wonder if a better model for what you're thinking of (in terms of real physics) would be massive particles in Cosmic Rays, because there's just no thinking of an iron sphere at 99.99% c.

As for killing people, I think that the blast would probably blast the moon into many fragments... slowly falling in Earth's gravity well.

So, you have blast and radiation and probably the cherenkov radiation from hell along with all kind of seriously energetic particles. I'm fairly sure that the gamma radiation alone would be enough to do what a LGRB would at close quarters. An atmosphere choked with nitric oxide, constant bombardment from fragments of the moon, and the gravitational effects...

You know what, I'm going to quote Ich: "It would be bad."

 

[Ich]

How do you calculate energy yield for an object defined by width and not mass, when the composition and therefore mass could vary greatly?

A density of 3000 would not be too wrong. There are other problems; for example, somehow I needed four trys to get from exponents to that strange American billion zillion system, which means that I'm quite certainly off by some orders of magnitude. Just read: HUGE explosion.

 

[Frame Dragger]

A density of 3000 would not be too wrong. There are other problems; for example, somehow I needed four trys to get from exponents to that strange American billion zillion system, which means that I'm quite certainly off by some orders of magnitude. Just read: HUGE explosion.

Oh I get the idea, and what do you mean "strange American...". Why, we lead the world by being the ONLY major country to NOT adopt the metric system! Americans feel that precision is bad for the digestion.

 

[Ich]

Why, we lead the world by being the ONLY major country to NOT adopt the metric system!

You forgot majorer Liberia and majorest Myanmar. That makes three - well, at least in SI. Don't you have some special units for numbers of countries? Like 3 = 4 in American long count, tuesdays?
But that's not what I meant. You know that your trillions are my billions? Such things use up 80% of my brainpower, with the rest dedicated to browsing online dictionaries. Not much left for physics and correct numbers.

 

[Frame Dragger]

You forgot majorer Liberia and majorest Myanmar. That makes three - well, at least in SI. Don't you have some special units for numbers of countries? Like 3 = 4 in American long count, tuesdays?
But that's not what I meant. You know that your trillions are my billions? Such things use up 80% of my brainpower, with the rest dedicated to browsing online dictionaries. Not much left for physics and correct numbers.

*Opens a vein*

Edit: Fabulous... always good to be associated with Liberia and Myanmar... just... *fumes*