What will happen to Earth when hit by a Neutron Star at the Speed of Light?

[Zdenka]

Here's one for everyone to ponder.. Firstly, this question has always bugged me since I was born. It's not impossible to imagine an Alien civilization 1.5 billion years more advanced than us, using the method of 'Hurling Neutron Stars at 99% the speed of light, to destroy planets and their inhabitants. My question is:

If a Neutron Star 20 miles wide, traveling at .99c smashes into the Earth squarely, would the Earth

1. Shatter into a million pieces?

or..

2. Nothing would happen?. Like putting a pin through a large clay ball, the Neutron Star is too small to damage Earth. Since it's traveling so fast, it would just cause a very small tunnel through the Earth, but the soil (ie Earth) and water would seal it up quickly.

Please share me your thoughts on what'll happen.. or you might have some other scenarios.

 

[Janus]

At a diameter of 20 miles, a neutron star would mass about 10 times that of the Sun. At this mass, more damage would be done by its intense gravity than by the collision of the star itself. Earth would be in its Roche limit when it was still some 11,000,000 miles away.

At 6378 km (the radius of the Earth) its force of gravity would be 1.7 million g's

Large amounts of the Earth would be absorbed by the neutron star, adding to its mass, and the rest would be strewn by tidal forces.

 

[DaveC426913]

Earth would be in its Roche limit when it was still some 11,000,000 miles away.

True, although at .99c, the neutron star would cross that distance and be through Earth in less than a minute.

 

[Nabeshin]

Firstly, this question has always bugged me since I was born.

Really? You came out of the womb wondering what would happen if a neutron star collided with the Earth at close to the speed of light?

 

[DaveC426913]

Really? You came out of the womb wondering what would happen if a neutron star collided with the Earth at close to the speed of light?

No, he was born at 6 years old.

 

[Zdenka]

hahaha! I love the responses, humans! Especially from Janus... I've never thought of Earth getting torn apart even before the Neutron Star has reached it. Well then, I guess we're all doomed if an Alien race decides to take up on my offer, lol :)

Btw, I am not 6 yrs old! :)

 

[Zdenka]

True, although at .99c, the neutron star would cross that distance and be through Earth in less than a minute.

Upon second thoughts, I think you're right. Janus, you talk about Roche limit, but I remember reading about black holes (which produces as much gravity as Neutron stars), and that you'd need to be at the Event horizon to be affected by it's gravity.
[/quote]This is incorrect. A black hole's gravity reaches far beyond its event horizon. The event horizon just marks where the escape velocity equqls the speed of light.

The event horizon is only 20miles away from the core. What I'm trying to say is that I doubt that a Neutron Stars gravity would be able to cause damage to Earth at 11,000,000 miles away!

At the Roche limit, anything not nailed down will start to float away (including the atmosphere and oceans)

When the neutron star reaches the distance of the Moon's orbit, the tidal force across the Earth will equal 30 g. Even things nailed down will start to rip loose.

At the distance of geo-sync orbit the tidal forces across the Earth reach over 27,000 g.

At 2000 km, the tidal forces over a 1 meter distance is 34 g. (for a 5'8" person, this would be the equivalent of hanging from your heels with 58 times your weight hanging from your head.)

etc.

 

[Vanadium 50]

but I remember reading about black holes (which produces as much gravity as Neutron stars), and that you'd need to be at the Event horizon to be affected by it's gravity.

That's not correct. At large distances, a black hole has the same gravity as a star of equal mass.

 

[dorlomin]

The kenetic energy of the impact would be on the large side.

Edited to add, actualy thinking on it it would probibly be sufficient to ignite oxygen in nuclear combustion. The energy of the impact into the crust would travel round the world as a mega earthquake and perhaps have sufficient energy to melt much of it. As it entered the core there would be a tussle between the bow shock wave and gravity, what would win is beyond me but either the Earth would be sucked into the star or the pressure wave of the impact would tear it appart.

 

[Nabeshin]

The kenetic energy of the impact would be on the large side.

Hrm. For m=10 solar masses and v=.99c, I get the kinetic energy to be ~10^48J.




Wow.

 

[DaveC426913]

Hrm. For m=10 solar masses and v=.99c, I get the kinetic energy to be ~10^48J.

Wow.

The kinetic energy is the least of your problems. The material of the Earth will rend itself into its component atoms, which would then plate themselves onto the surface of the neutron star in a layer a few microns thick.

 

[DaveC426913]

Btw, I am not 6 yrs old! :)

No. You were born at 6 years old, which is why you were capable of being bugged about neutron stars "since you were born". Come to the meetings!

 

[Nabeshin]

The kinetic energy is the least of your problems. The material of the Earth will rend itself into its component atoms, which would then plate themselves onto the surface of the neutron star in a layer a few microns thick.

Indeed. Someone just mentioned kinetic energy so I figured I'd give a ballpark.

The plating of atoms is a pretty cool concept, too. And the neutron star would continue to mysteriously hurl through space at .99c unabated... only a few microns larger.

 

[Zdenka]

Such interesting responses, guys! thanks! I never thought of all the gravity involved would affect the Earth since the Neutron Star is traveling at the speed of light, and would arrive at Earth before the 'gravity effect' kicks in.

At most I thought the N.Star would just be like a heavier version of the Asteroid that killed off the dinosaur 64 million years ago..

So let's assume the gravity doesn't destroy the earth, so would then the Earth be split apart by the Neutron star or would it absorb the impact like an Asteroid.

 

[Zdenka]

No. You were born at 6 years old, which is why you were capable of being bugged about neutron stars "since you were born". Come to the meetings!

hahaha! I get ya... I was actually born 12 years overdue in the womb, which gave me plenty of time to wonder about Alien mysteries. ;-p

 

[Mr. Paradox]

Maybe the star would travel straight through the Earth taking it with it due to its large gravity.

 

[Zdenka]

My calculations show that the Neutron Star will simply leave a 20 mile diameter hole in the Earth, but our planet will remain intact, even though it's constantly spewing out volcanic lava due to the damage.

The 'super' gravity WON'T gobble up Earth because the Neutron Star is traveling way too fast (99% speed of light) to have enough time for the gravity effects.

 

[Waveform]

My calculations show that the Neutron Star will simply leave a 20 mile diameter hole in the Earth, but our planet will remain intact, even though it's constantly spewing out volcanic lava due to the damage.

The 'super' gravity WON'T gobble up Earth because the Neutron Star is traveling way too fast (99% speed of light) to have enough time for the gravity effects.

I tend to agree. Gravity reacts at 'C'. If the neutron star has a velocity of .99C then it is almost 'on top of us' before we run into gravitational problems.
If the Neutron Star entered at the equator the transit time would be something in the area of 1.21 X 10ˉ⁵ s through the earth.
At that speed, even the rotational velocity of the Earth I don't think would have much effect on the dimensions of the tunnel.

 

[Zdenka]

At that speed, even the rotational velocity of the Earth I don't think would have much effect on the dimensions of the tunnel.

Yep, the tunnel would be pretty much straight, and planes can fly through it. An asteroid of that magnitude would cause more catastrophe than a Neutron star, I would imagine.

 

[Chronos]

Earth would be ripped apart in such a collision. New asteroid belt is my bet.

 

[Zdenka]

Earth would be ripped apart in such a collision. New asteroid belt is my bet.

Do you have any proof for that? IMO, the Neutron star is way too small to do Earth any lasting damage. The 20 Mile tunnel will eventually seal itself up with soil and water.

 

[Chronos]

You must be kidding. a 10 solar mass anything hitting Earth at .99c will rip it to pieces. Fortunately, the probablity is small. What is needed to show the entire solar system might be at risk in such an event - math? Have you modeled such an event on your home computer? Try starting at one light year out and calculate the tidal trails. You will notice a perturbation in the orbits of every planet in the solar system.

 

[Zdenka]

Well, maybe you are right. But I'm just imagining the Earth like a large ball made of soil.. and the Neutron star is like a nail (in diameter) traveling extremely fast.. it might just make a tunnel. But then again, my calculations doesn't involve physics, so yea.

The probably of something like this could happen if an Advanced Alien race decides to destroy Earth that way.. it'll be easy and quick, because we can NOT detect something heading towards us at almost the speed of light.

 

[.:Endeavour:.]

You can find the amount of energy that the Neutron Star is impacting the Earth using the KE formula:
KE = mv²
m is the mass of the Neutron Star which is 1.35 solar masses (2.685042*10³⁰)
v = 299,792,458 m/s (speed of light)

KE = (2.685042*10³⁰)(299,792,458 m/s)²
KE = 2.4132*10⁴⁷Joules or 2.4132*10²³ YottaJoules

With that energy hitting the Earth, directly I presume, the Earth is going to be surely destroyed.

 

[Vanadium 50]

Endeavour, you should be commended for posting your equations. They are wrong - you missed a 1/2 in your definition of KE, you used the non-relativistic expression for KE for an object moving near the speed of light, and not all the KE is transferred in a collision. But you should get credit for posting your thoughts in a clear way.

Zdenka, you keep talking about "your calculations", but then say "my calculations don't include physics". Then what the heck are you calculating? It sounds like you aren't calculating so much as guessing.

Janus provided a cogent argument that tidal forces would rip the Earth apart. This seems to have been generally ignored.

 

[Vanadium 50]

Oh, and your putative aliens need the entire power output of a galaxy for a century to get this neutron star up to speed.

 

[.:Endeavour:.]

Endeavour, you should be commended for posting your equations. They are wrong - you missed a 1/2 in your definition of KE, you used the non-relativistic expression for KE for an object moving near the speed of light, and not all the KE is transferred in a collision. But you should get credit for posting your thoughts in a clear way.

Zdenka, you keep talking about "your calculations", but then say "my calculations don't include physics". Then what the heck are you calculating? It sounds like you aren't calculating so much as guessing.

Janus provided a cogent argument that tidal forces would rip the Earth apart. This seems to have been generally ignored.

Thank you for that correction. The next step now is to divide it by 0.5 to get the final answer. But if the star did, it will destroy the Earth or make it inhabitable after a collision like that which unlikely to happen which will need something to accelerated to the speed of light.

 

[Vanadium 50]

The next step now is to divide it by 0.5 to get the final answer.

No, that's wrong too.

(1) You have to multiply mv² by 1/2 to get KE, not divide.

(2) You have to use the relativistic equation for KE if something is moving at 99% of the speed of light.

(3) You have to solve the collision problem to see how much energy is transferred; you can't just assume all of the kinetic energy of one object is transferred to the other.

 

[RiseAgainst]

Oh, and your putative aliens need the entire power output of a galaxy for a century to get this neutron star up to speed.

How did you calculate that?

 

[.:Endeavour:.]

Kinetic energy isn't going to be transferred from one place to the next on impact. But still at that velocity and that massive it is going to be destructive. Ok this is what I got for the KE again: 1.2066*10⁴⁷. Either way that's a huge amount of energy. Can you please post the collision formula to get a more approximate result.

 

[Nabeshin]

Just saying I already did the correct kinetic derivation in post 10. Didn't show the formula, but the ballpark is right and it's pointless to use so many sig figs anyways.

 

[jambaugh]

I think "ripped apart" would be too mild a term. I would think the temperatures reached would spray what matter didn't get plated on the front of the neutron star outward at cosmic ray energies. I suspect such a collision would sterilize life in this arm of the galaxy as the high energy particles which were once our planet radiated outward.

 

[flatmaster]

Even if the projectile does nothing but punch a big hole, All planets and the Earth are thrown into chaos from an object on the order of a solar mass flying through. Best case senerio, we're thrown into a highly eleptic orbit, with the Earth's rotation axis pointing who know which way. "Seasons" and "days" and "years" are no longer enough to parameterize Earth's orbit. Worst case, se achieve the sun's escape velocity and dye a cold and lonely death.

 

[Zdenka]

Thanks for all your honest answers, guys! At first I thought an impact from a Neutron star would be like a heavy Asteroid but now I'm not so sure!

 

[Vanadium 50]

How did you calculate that?

(Kinetic energy of neutron star) / (Power output of a typical galaxy) = time

 

[Chronos]

An interjection, if I may. A neutron star traveling at .99c is a fantasy, so imagining its potential destructiive power is also fantasy.

 

[Chronos]

We need not worry much about such an event. No star is currently traveling at any threatening velocity towards our solar systen

 

[DaveC426913]

An interjection, if I may. A neutron star traveling at .99c is a fantasy, so imagining its potential destructiive power is also fantasy.

I beg to differ. It's highly contrived, granted. But it is simply the very far end of a probability curve; there is no reason why it can't happen.

A giant asteroid wiping out the Earth is less fantasy only in degree, not in principle.


Besides, why dismiss unlikely events? Two forums over, they're talking about The Big Bounce. Is that not worth discussing either?

 

[Chronos]

Well Dave, anything is possible, but few are as improbable as a neutron star traveling at .99c in this, or any other galaxy. No known force in the universe could impart the amount of energy necessary to accelerate such an object to near light speed. An asteroid on an Earth collision orbit - not at all improbable over the next million years.

 

[jambaugh]

Be careful of "possible in principle"...
It is "possible in principle" for all the atoms of radioactive isotopes in the Earth to decay within the next hour. It isn't likely but it is "possible". There's a level of improbability which you must treat as impossibility. 1 in a billion is one thing one in a google is another.

That having been said the question is meaningful in an operational sense because we can infer what happens from theory and scale calculations. Start with say a 1.5 solar mass neutron star moving at speed V punching through the Earth.
... working the numbers...

Assuming it punches through like a pellet gun through a foam ball the mass of that part of the Earth it intersects will be 3.2E19 kg.

Assume all of this "sticks" the energy of falling into the Neutron star will be 7.6E25 J or equate to total conversion of 8.4E18 kg using Newtonian gravity and neglecting nuclear energy effects. Note this is about 25% of the effected mass.

Accounting for speed you can treat the impact as if the Earth hit the Neutron star so figure the kinetic energy (relativistic or not) of the 3.2E19 kg that gets hit. Let \beta = v/c then the energy (in units of converted mass) released will be:

E = 3.2\times 10^{19}\left( \sqrt{1+\beta^2} - 0.75\right)
That's the KE minus rest mass plus 25% conversion factor due to gravity of neutron star.

E=3.2\times 10^{19}\left(0.25 + \frac{1}{2}\beta^2 - \frac{1}{8}\beta^4 + \frac{1}{16}\beta^6 \cdots\right)
where I am using the power series expansion of (1+\beta^2)^{\frac{1}{2}}-1 to get the relativistic corrections to Newtonian kinetic energy.

Assume most of the energy is released into the Earths core and a speed of about 0.5 c. The energy released will then be about equivalent to 36.8% of the intersected mass being converted or about 1E19 kg or 1E36 Joules. I leave it as an exercise to figure the heat of vaporization for the entire Earth and see if anything is left after the impact.

You might start with heat of vaporization of of iron and silicon of about 350kJ/mole.

To put that in perspective 1 foe = 1x10^46 Joules is the typical energy of a supernova so my earlier post was too extreme. If I have time I'll work out the speed necessary to get 1 foe of energy. For now I got to run.

 

[DaveC426913]

Well Dave, anything is possible, but few are as improbable as a neutron star traveling at .99c in this, or any other galaxy.

Yes but this was a thought experiment by the OP. He didn't say he was getting ready to add a layer of tinfoil...

 

[DaveC426913]

Well Dave, anything is possible, but few are as improbable as a neutron star traveling at .99c in this, or any other galaxy. No known force in the universe could impart the amount of energy necessary to accelerate such an object to near light speed.

Never say never.

http://www.sciencecodex.com/nasas_fermi_telescope_sees_most_extreme_gammaray_blast_yet

"...gas bullets must have moved at 99.9999 percent the speed of light..."

While it may not actually be a neutron star, I'll bet the mass of erupted gas is comparable.