Calculating Impact Energy

[Dominatus]

This is the beginning of my work... Stars are sometimes ejected from their parent galaxy by the Supermassive black hole they orbit. This kicks the star out into intergalactic space at hyper-velocities, achieving significant fractions of the speed of light. Taking this one step further, let's imagine a Pluto-sized body got kicked out of this star system as it was flung off into oblivion, and this dwarf planet eventually impacted a small terrestrial planet in a backwater system on the ourirts of a spiral arm of a completely insignificant galaxy.

Pluto has a mass of 1.3x10^22 Kg, and we will assign it a velocity of 1.6 million km/h

The impact with earth will have what energy value and what might our poor planet look like after this impact? Surely it would be sterilized at the very least, right?

[Ralathon]

It'd have a kinetic energy roughly equal to 1.3e33 joulles.

That's 6 times the gravitational binding energy of the earth and about half its orbital energy. In other words, there won't be an earth left after this hits us. It deposits enough energy into the earth to obliterate it 6 times over.

[Linear]

Running the figures, it's around 10 million times more KE than the asteroid that ended the dinosaurs.

Expect a bad Friday that week.

[peadar1987]

This is the beginning of my work... Stars are sometimes ejected from their parent galaxy by the Supermassive black hole they orbit. This kicks the star out into intergalactic space at hyper-velocities, achieving significant fractions of the speed of light. Taking this one step further, let's imagine a Pluto-sized body got kicked out of this star system as it was flung off into oblivion, and this dwarf planet eventually impacted a small terrestrial planet in a backwater system on the ourirts of a spiral arm of a completely insignificant galaxy.

Pluto has a mass of 1.3x10^22 Kg, and we will assign it a velocity of 1.6 million km/h

The impact with earth will have what energy value and what might our poor planet look like after this impact? Surely it would be sterilized at the very least, right?

The answer is actually pretty simple in this case. The planetoid will have a kinetic energy of 1.2E33 Joules. Earth's gravitational binding energy is about 2.24E32 Joules. The planet will be utterly obliterated, and the pieces flung off into space.

- - - Updated - - -

Such ninja, many late.

[Dominatus]

I had figured as much. Beat me to the calculations- hs makes it hard to find free time in class haha! Does this also take info account the differences in velocity between the object and earth though? While minuscule the earth still is whipping through space at- what- 8kph? Something like that. Anyways, couldn't that have an effect on the total energy output? And what's more, what might the escape velocity of the dwarf planet have been from it's parent star? How does that number affect the end result of the calculation? What's more, depending on how the body entered the solar system, Jupiter has a chance of flinging it off, I think, right? These are making it far more complicated of course, but I'm curious to see where things go from here.

[Ralathon]

I had figured as much. Beat me to the calculations- hs makes it hard to find free time in class haha! Does this also take info account the differences in velocity between the object and earth though?

While minuscule the earth still is whipping through space at- what- 8kph? Something like that. Anyways, couldn't that have an effect on the total energy output?

It'll have an effect. But it is utterly trivial. The outcome will be the same in either case.

And what's more, what might the escape velocity of the dwarf planet have been from it's parent star?

Depends on the relative velocity of the parent galaxy and the escape velocity of said galaxy.

How does that number affect the end result of the calculation?

Not at all. All that matters is how hard the thing hits earth, its history doesn't matter.

What's more, depending on how the body entered the solar system, Jupiter has a chance of flinging it off, I think, right? These are making it far more complicated of course, but I'm curious to see where things go from here.

Nope, it's moving way too fast for Jupiter to meaningfully adjust its orbit. Try it in KSP, turn on infinite fuel and fly past Jool at 400 km/s. It'll do zip all to your trajectory.

[Robotengineer]

This is the beginning of my work... Stars are sometimes ejected from their parent galaxy by the Supermassive black hole they orbit. This kicks the star out into intergalactic space at hyper-velocities, achieving significant fractions of the speed of light. Taking this one step further, let's imagine a Pluto-sized body got kicked out of this star system as it was flung off into oblivion, and this dwarf planet eventually impacted a small terrestrial planet in a backwater system on the ourirts of a spiral arm of a completely insignificant galaxy.

Pluto has a mass of 1.3x10^22 Kg, and we will assign it a velocity of 1.6 million km/h

The impact with earth will have what energy value and what might our poor planet look like after this impact? Surely it would be sterilized at the very least, right?

That is a very mean way to speak of our planet.

[kerbiloid]

http://impact.ese.ic.ac.uk/ImpactEffects/

[Newt]

Nope, it's moving way too fast for Jupiter to meaningfully adjust its orbit. Try it in KSP, turn on infinite fuel and fly past Jool at 400 km/s. It'll do zip all to your trajectory.

It depends how close it goes to Jupiter, and exactly how its path is taking it to Earth. Bear in mind, that the Earth is a tiny speck, and space is amazingly huge. If the course is off by a small bit, the object will fly past the Earth as a bright star like thing, leaving the Earth's orbit slightly perturbed but intact.

[Ralathon]

It depends how close it goes to Jupiter, and exactly how its path is taking it to Earth. Bear in mind, that the Earth is a tiny speck, and space is amazingly huge. If the course is off by a small bit, the object will fly past the Earth as a bright star like thing, leaving the Earth's orbit slightly perturbed but intact.

Fair enough, lets calculate this.

The maximum distance between Earth and Jupiter is about 6.2 AU. The projectile needs to be deflected by about 7000 km at worst. So its trajectory needs to be adjusted by 4.3e-4 degrees (7.54e-6 rad)

The angle between the 2 asymptotes in a hyperbolic trajectory is 2arccos(1/e) so our hyperbolic orbit would need an eccentricity 1e-11 off unity.

We can figure out the semimajor axis of our hyperbola using the reduced kinetic energy and the gravitational parameter of jupiter(the projectile's mass is negligible compared to mighty Jupiter).

a = -u/(0.5*v(inf)^2 = -1.25e6 meters. Using 4.5e5 m/s for v(inf) as per OP.

Now we have everything we need to figure out the periapsis.

r(periapsis) = -a(e-1) = 1.25e6*1e-11 = 1.25e-5 meters.

So for jupiter to adjust its orbit enough to miss earth it'd have to pass within 100 micrometers of Jupiters center. So yea, not happening. It's just going waaaay too fast.

[Dominatus]

That is a very mean way to speak of our planet.

I'm hardly the first to refer to the earth as such, and if you think about it it's true. We are in the boonies of the universe- an unimportant speck of dust around an ordinary yellow dwarf in a sparse stellar neighborhood in the outer arm of an average spiral galaxy that is itself in a sparsely populated region of the universe that is part of a local superstructure that is part of something even bigger etc. really the earth isn't that special and the only evidence of us after this event is an alien astronomer checking his instruments and wondering what could possibly have caused a star to hiccup like that, and how a particle could ever move so fast... Anyway I showed my physics teacher this and he got a laugh out of it, so thanks all!

[magnemoe]

Now try to hit Jupiter instead, it would have some fun effects, energy would be to small to destroy it however it will probably eject earth masses of its atmosphere and glow for months afterwards.

[Chiboko]

Being from another galaxy of unknown distance its relative velocity could be close enough to 'c' as makes no difference. So I'm gonna give it a slim chance of annihilating the surrounding chunk of galaxy.

[GoSlash27]

This raises a different question for me:

If the source galaxy is moving away from us at an appreciable fraction of C, how would the dwarf planet ever reach us?

Let me start over...

If the dwarf planet is ejected from another galaxy at 27 km/sec and the universe is expanding at 74km/sec, how would it ever reach us?

Curious,

-Slashy

*edit* correction

Edited February 6, 2015 by GoSlash27

[-Velocity-]

This raises a different question for me:

If the source galaxy is moving away from us at an appreciable fraction of C, how would the dwarf planet ever reach us?

Let me start over...

If the dwarf planet is ejected from another galaxy at 27 km/sec and the universe is expanding at 74km/sec, how would it ever reach us?

Curious,

-Slashy

*edit* correction

That is an incorrect unit for the expansion of the universe. The Hubble Constant is given as km/s/Mpc- that's kilometers per second per megaparsec. 1 Mpc is 3.26 million light-years. So if a galaxy is 100 million light years away, that's roughly 30 Mpc, and so it would be expanding away from us at 30 Mpc * Ho = 30 Mpc * 70 km/s/Mpc = 2100 km/s.

So whether an object ejected from another galaxy will reach us or not is a function of how fast it is ejected and how distant the galaxy ejecting it is.

[GoSlash27]

That is an incorrect unit for the expansion of the universe. The Hubble Constant is given as km/s/Mpc- that's kilometers per second per megaparsec. 1 Mpc is 3.26 million light-years. So if a galaxy is 100 million light years away, that's roughly 30 Mpc, and so it would be expanding away from us at 30 Mpc * Ho = 30 Mpc * 70 km/s/Mpc = 2100 km/s.

So whether an object ejected from another galaxy will reach us or not is a function of how fast it is ejected and how distant the galaxy ejecting it is.

All true, but it doesn't answer the question

The nearest galaxy that I know of with a supermassive black hole is Andromeda, which is a little shy of a Mpc away. I don't see how anything ejected from it at that velocity could ever get here. Maybe something ejected from our own galactic center could do it, but I don't know how much velocity it'd lose on the way.

Best,

-Slashy

[Drunken Hobo]

It'd have a kinetic energy roughly equal to 1.3e33 joulles.

That's 6 times the gravitational binding energy of the earth and about half its orbital energy. In other words, there won't be an earth left after this hits us. It deposits enough energy into the earth to obliterate it 6 times over.

Work in the other direction, and it'd only take an object of around 6 x 10¹⁶ kg to obliterate the Pluto-sized body. So rather than hoping Jupiter's orbit perturbs it, let's just hope it smashes into Lysithea.

[-Velocity-]

All true, but it doesn't answer the question

Your question can't be answered because you didn't give enough information. Is "27 km/s" the object's initial velocity or final velocity- remember, you have to eject something at greater than escape velocity for it to escape, and if I remember correctly, the escape velocity of a Milky Way-like galaxy is a few hundred km/s. If that's the initial velocity the object is ejected at, then we'll need to know how massive the galaxy is.

The nearest galaxy that I know of with a supermassive black hole is Andromeda, which is a little shy of a Mpc away. I don't see how anything ejected from it at that velocity could ever get here. Maybe something ejected from our own galactic center could do it, but I don't know how much velocity it'd lose on the way.

Best,

-Slashy

I don't believe it would lose velocity from the universe's expansion, unless the expansion was accellerating. Yes, I know it actually is, but I don't think it would be a major effect at all between two relatively nearby galaxies. This would be an interesting point for me to research to make certain, because even if I'm correct in how the expansion of space works, I'd still probably learn something new. Unfortunately, I don't have the time right now, and I'm probably right anyway. If the expansion of the unvierse was capable of robbing objects of velocity, then galaxy clusters that were gravitationally bound would slowly come apart, would they not? Our orbit around the Sun would be slowly expanding.

I do know for a fact though that Hubble's "law" breaks down when the distances are "very short"- like the distance between the Milky Way and M31 (the Andromeda Galaxy). At distances of like 10 million light-years and less (depends on how clustered matter is) individual galaxy motion becomes more important that Hubble's Law. Only at longer distances does Hubble's law really become dependable.

A good case in point IS M31. It's moving towards our galaxy (at something like 200 km/s if I remember correct), and so its light is actually blue shifted, not red shifted. An object escaping M31 and moving towards the Milky Way will get here some time before M31 collides with us.

Edited February 6, 2015 by |Velocity|

[GoSlash27]

Your question can't be answered because you didn't give enough information. Is "27 km/s" the object's initial velocity or final velocity- remember, you have to eject something at greater than escape velocity for it to escape, and if I remember correctly, the escape velocity of a Milky Way-like galaxy is a few hundred km/s. If that's the initial velocity the object is ejected at, then we'll need to know how massive the galaxy is.

I don't know that myself, as the OP was the one who posed it. I took it as "initial" velocity.

It also appears that I misread the initial question...

Best,

-Slashy

[Dominatus]

This was purely hypothetical. I decided on ejection from another galaxy for the reason that the body would have slowed substantially prior to reaching earth in the outer arms of our galaxy. Of course, we could simply assume that the specified velocity is the final velocity and nothing is lost as it escapes our galactic center. Either way, earth is in for a world of hurt (despite the- pardon the pun- astronomically low probability of an impact event between planets of different systems, before taking into account the likelihood of a body achieving such a velocity.

[Techpriest93]

Alright, what would it look like if pluto skimmed earth like the mars sized protoplanet did back all those years ago?

Would we get a minmus?

(also, be great-full that earth decided to store 70% of its crust in a ball 384,000km away! If it hadn't, we might have ended up like Venus, where resurfacing events happen every half billion years or so, plate tectonics (an important part of the water cycle, just look up the subsurface water masses in plate graveyards deep in the mantel) probably wouldn't occur, and we wouldn't exist!)