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

[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.