What if an Earth-mass object slammed into the sun at 50% the Speed of Light.

[daniel l.]

The title pretty much says it all.

What would happen?

[cubinator]

The Sun would probably radiate a bunch of light and matter for a while and irradiate the planets a lot more than usual, but when I tried it in Universe Sandbox one big thing I noticed was it got bumped about 450 m/s. That's enough to change the orbits of the planets slightly, so you'd have higher eccentricities and thus more extreme seasonal climate changes. It also turned blue, but I wouldn't really count on that that much.

[UmbralRaptor]

This feels a bit /r/theydidthemath/, but...

Lorentz factor at 0.5 c is γ = 1/sqrt(1-0.5^2) = 1.1547

Relativistic momentum is γmv = 1.1547 * (5.98e24 kg) * (149896229 m/s) = 1.03505e33 kg*m/s

Relativistic kinetic energy is (γ-1)mc^2 = (1.1547-1) * (5.98e24 kg) * (299792458 m/s)^2 = 8.314467e40 J

Using 4.184e9 Joules == 1 ton of TNT equivalent, this is ~2e13 exatons. That's probably not too meaningful, so let's consult the boom table.

Approximating the sun as an equal density sphere (very wrong, but I'm unsure of a good estimate of the density profile and this should give a decent lower estimate), the gravitational binding energy is 3 * (6.674e-11 m^3/kg/s^2) * (1.9891e30 kg)^2 / (5 * 6.9578e8 m) = 2.3e41 J.

Assuming a perfectly inelastic collision, I get a change in velocity of 521 m/s. An elastic collision would be, uh, silly. But if one could efficiently transfer kinetic energy, the sun could be accelerated to close to 300 km/s.

 

Overall, total energy release is comparable to a nova (not supernova), though it'll probably be way different in detail. Compression as the planet hits the sun will cause fusion, but beyond that I'm hesitant to say much. The sun will I think survive, but don't expect Earth to remain habitable.

[YNM]

Catastrophe ?

[PB666]

My guess that at 0.5 c that 150,000 km per second taking 4.5 seconds to reach the opposite side, the suns density is low. It would create a shock on the opposite side ejecting a large amount of plasma into solar orbit and possibly picked up by venus and earth. It might have a cooling effect on venus.

Why do you need to collide our sun when you have nice neutron stars you can watch merge. 

[daniel l.]

1 minute ago, PB666 said:

My guess that at 0.5 c that 150,000 km per second taking 4.5 seconds to reach the opposite side, the suns density is low. It would create a shock on the opposite side ejecting a large amount of plasma into solar orbit and possibly picked up by venus and earth. It might have a cooling effect on venus.

Why do you need to collide our sun when you have nice neutron stars you can watch merge. 

But those neutron stars are too far away. I want EVERYONE to be skeletonized.

[UmbralRaptor]

2 minutes ago, daniel l. said:

But those neutron stars are too far away. I want EVERYONE to be skeletonized.

Putting enough sulfur hexafluoride or the like into the air to initiate a runaway greenhouse would be far less hassle.

[daniel l.]

1 minute ago, UmbralRaptor said:

Putting enough sulfur hexafluoride or the like into the air to initiate a runaway greenhouse would be far less hassle.

I also want the sun to go FLASH. BANG. Then the solar system is stripped of all this silly air, and all is stripped of their silly fleshes to free their long-imprisoned skeletons. Just in time for Halloween.

Edited October 22, 2017 by daniel l.

[NSEP]

7 hours ago, daniel l. said:

 I want EVERYONE to be skeletonized.

Im with you.

It would vaporize i geuss? Thats all i know.

[YNM]

9 hours ago, daniel l. said:

I want EVERYONE to be skeletonized.

Get a plague. Astrophysical events more likely to just leave everyone freeze-dried.

[cubinator]

12 hours ago, daniel l. said:

I want EVERYONE to be skeletonized.

Ah, so that's the motive.

13 hours ago, UmbralRaptor said:

Assuming a perfectly inelastic collision, I get a change in velocity of 521 m/s. An elastic collision would be, uh, silly. But if one could efficiently transfer kinetic energy, the sun could be accelerated to close to 300 km/s.

I think you're about 10^3 times off there.

[Azimech]

Because I don't grasp the wonderful mathematics, I have to take a visual approach and it's pure speculation.

What I see in my mind, slowed down millions of times, is localized fusion in the compression wave, starting in the chromosphere. The planet is atomized before it hits the photosphere, the gigantic ongoing fusion explosion pushes the atoms from their original direction into the shape of a funnel until their kinetic energy has dropped to levels too low to induce localized fusion. The low pressure region in the wake of the planet produces a new pressure wave, probably enhanced by the Kadenacy effect, possibly creating some more localized fusion in the convection zone.

Looking at the fact the sun has the mass of 99.86% of the total solar system, I expect some waves to produce a short bulge, lots of ripples and solar flares and an increase in mass loss. The convection zone will probably absorb all of the kinetic energy and the end result would probably be not too dramatic.

 

[kerbiloid]

Earth mass = 6*10²⁴.
Sun mass = 2*10³⁰.

***
Earth velocity = 0.5 c = 1.5*10⁸ m/s.
Relativistic factor = 1 / sqrt(1-0.5²) = 1.15
So, relativistic effects are negligible, we can use Newton mechanics.

***

1 kg of hydrogen hitting the Earth at 0.5 c speed has:
Momentum = mv = 1 * 1.5*10⁸ = 1.5*10⁸ kg*m/s.
Kinetic energy = mv = 1 * (1.5*10⁸)² / 2 = 1.125*10¹⁶ J.

It gives the Earth its full momentum, causing delta-V = 1.5*10⁸ / 6*10²⁴ = 2.5*10^-17 m/s.
Corresponding kinetic energy = 6*10²⁴ *(2.5*10^-17)²/2 = 2*10^-9 J.
So, almost all hydrogen energy gets released as a heat.

***

Earth consists of the iron core (1/3 of mass) and mostly SiO₂ (2/3 of mass).
enthalpy of vaporization: Fe ~6 MJ/kg, Si ~10 MJ/kg, average ~9 MJ/kg.
Taking 15 MJ/kg because first it should be heated and melted.

So, total energy of the Earth vaporization ~= 6*10²⁴*15*10⁶ = 9*10³¹ J.

This is equal to collision with 9*10³¹ / 1.125*10¹⁶ = 8*10¹⁵ kg of solar hydrogen.

***

Sun radius = 7*10⁸ m.
Sun average density = 2*10³⁰ / (4 * pi * (7*10⁸)³ / 3) ~= 1400 kg/m³.
Sun is gaseous.

Earth radius = 6.4*10⁶ m.
Earth cross-section = pi * (6.4*10⁶)² ~= 1.3*10¹⁴ m².

So, 8*10¹⁵ kg of solar hydrogen is (in average) an Earth-wide column of solar matter,  8*10¹⁵ / (1400 * 1.3*10¹⁴) = 0.04 m long/high.

So, we can presume that the Earth will get vapourized by the solar hydrogen collision immediately on hitting the surface of Sun.

This means we can presume that the Earth won't be like a bullet piercing the Sun, but a gas cloud expanding into the Sun volume.

***

Now we can presume that the Earth will give to the Sun all its momentum and kinetic energy.

Total momentum of the Earth = 6*10²⁴ * 1.5*10⁸ = 9*10³² kg*m/s.

Delta-V of the Sun = 9*10³² / 2*10³⁰ ~= 450 m/s.

***

Kinetic energy of the Earth = = 6*10²⁴ * (1.5*10⁸)² / 2 = 6.75*10⁴⁰ J.

Kinetic energy of the Sun delta-V = 2*10³⁰ * 450² / 2 = 2*10³⁵ J.

So, almost full kinetic energy will be released as heat, cause local thermonuclear reactions and be radiated into space.

***

Released heat ~= 6.75*10⁴⁰ J.
Sun mass ~= 2*10³⁰ kg.
So, 6.75*10⁴⁰ / 2*10³⁰  ~= 3.3*10¹⁰ J/kg.

Taking hydrogen as a monoatomic gas with molar mass 0.001 kg/mol,
3.3*10¹⁰ = (3/2) * 8.31441 * T / 0.001

T = (3.3*10¹⁰ * 0.001) / ((3/2) * 8.31441) ~= 2.6*10⁶ K.

Sound speed for monoatomic gas = sqrt((5/3) * RT/M_r) = sqrt((5/3) * 8.31441 * 2.6*10⁶/0.001) = 190 km/s.
So, a shockwave will run throw the whole Sun in less than 700000/190 ~= 3700 s ~= 1 hour. I.e. in several minutes.
So, we can presume that the Sun will heat more or less uniformly.

***

Sun surface total area = 4 pi Rsun² = 4 * pi * (7*10⁸)² = 6.2*10¹⁸ m².

Sun luminosity will raise up to L = area * sigma * T⁴ = 6.2*10¹⁸ * 5.67*10^-8 * (2.6*10⁶)⁴ = 1.6*10³⁷ W.

Energy to radiate ~= 6.75*10⁴⁰ J.

Roughly estimated duration of emission = 6.75*10⁴⁰ / 1.6*10³⁷ ~= 4200 s.

So, we can take that most of the released energy will be emitted in about an hour after the collision.

This means we can presume that any planet orbiting the Sun will quickly get its portion of light energy and warm up.

***

Total released energy ~6.75*10⁴⁰ J.

Planet radius = Rplanet.
Planet orbit radius = Rorbit.

Gravitational energy = (3/5) G Mplanet²/Rplanet ~= 2.26*10³² * Mplanet, earth^,2/Rplanet, earth, J
Vaporisation energy (for rocky planets) ~= 15*10⁶ * Mplanet ~= 9*10³¹ * Mplanet, earth, J.

Portion of the released energy received by the planet = pi * Rplanet² / (4 * pi * Rorbit²) = Rplanet² / (4 * Rorbit²) ~= 4.5*10^-10 (Rplanet, earth / Rorbit, earth)².

Total energy received by the planet = Total released energy * Portion of the released energy received by the planet = 6.75*10⁴⁰ * Portion of the released energy received by the planet, J.

Specific energy of the planet warming _{(don't know how to say)} = Total energy received by the planet / Planet mass, J/kg.

Heat energy per area = Total released energy /  (4 * pi * Rorbit²) = 2.4*10¹⁷ /  (Rorbit, AU²), J/m².

Temporarily established surface temperature = (Heat energy per area / (Duration * sigma))^0.25, K

***

value	Mer	Venus	Earth	Mars	Jup	Sat	Ura	Nep	Plu
Mass, Mearth	0.055	0.815	1	0.11	318	95	14.5	17.2	0.002
Rplanet, Rearth	0.38	0.95	1	0.53	11	9.1	4	3.9	0.19
Rorbit, AU	0.387	0.723	1	1.524	5.2	9.6	19.2	30	39.5
Gravitational energy, J	1.8*1030	1.6*1032	2.3*1032	5*1030	2*1036	2.2*1035	1.2*1034	1.7*1034	5*1027
Vaporisation energy	5*1030	7.3*1031	9*1031	1*1031					2*1029
Portion of the released energy received by the planet	4.4*10-10	7.8*10-10	4.5*10-10	2.34*10-12	2*10-9	4*10-10	2*10-11	7.6*10-12	1*10-14
Total energy received by the planet	3*1031	5.3*1031	3*1031	1.6*1029	1.35*1032	2.7*1031	1.35*1030	5.1*1029	7*1026
Specific energy, kJ/kg	90 000	10 000	5 000	240	70	47	16	5	58
Heat energy per area, J/m2	1.6*1018	4.6*1017	2.4*1017	1*1017	8.9*1015	2.6*1015	6.5*1014	2.7*1014	1.5*1014

(Btw, notice an interesting thing:
smaller rocky planets like Mars, Mercury have vaporisation energy greater than the gravitational energy,
while bigger rocky planets like Earth and Venus have gravitational energy greater than vaporisation energy.

Probably, this should be used in a planet classification. Major rocky planets which stay in place even being vaporised, while minor rocky planets dissipate once being vaporised.
Threshold is a little bigger than Mars).

 

Presuming that the emission duration is ~5000 s
Temporarily established surface temperature = (Heat energy per area / (Duration * sigma))^0.25 ~= 7.7 * (Heat energy per area)^0.25, K

value	Mer	Venus	Earth	Mars	Jup	Sat	Ura	Nep	Plu
Temporarily established surface temperature, thousand K	274	200	170	137	75	55	39	31	27

(Can't remove empty lines from the table).

***

Mercury.

Fully evaporates and dissipates.
>Search planet: Mercury.
>Planet not found.

It expands as an iron + silicon + oxygen gaseous cloud.
Total heat energy of the cloud ~= 2*10³¹ J.
Mass = 3.3*10²³ kg.
Molar mass ~0.04 kg/mol.

Cloud temperature ~= 2*10³¹ / ((3/2) * 3.3*10²³ * 8.31441 / 0.04) ~= 2*10⁵ K.

Thermal speed = sqrt(3RT/M_r).

Thermal speed of iron atoms = sqrt(3 * 8.31441 * 2*10⁵ / 0.056) ~= 9 400 m/s.
Thermal speed of oxygen and silicon atoms = sqrt(3 * 8.31441 * 2*10⁵ / 0.017) ~= 17 100 m/s.

Orbital speed at the Mercury orbit ~= 30 * sqrt(1/0.387) = 48 km/s.
Escape speed ~= sqrt(2) * 48 = 68 km/s.
Difference = 68 - 48 = 20 km/s.

So, most part of the Mercury iron will stay on the latter Mercury orbit as a hot iron gas and dust cloud.
It will be heated by the Sun, partially shadowing other planets from the Sun, but re-emitting received energy in infrared and visible spectre.

Most part of silicon and oxygen will dissipate across the Solar System as a sandy dust and oxygen.

The cloud gets unstable due to the Venus gravity and to the heated Sun continuing radiation.
Probably, slowly disspates around the Solar system, mostly condensing on in the Venus and on the Earth.

***

Venus.

Evaporates by half, but stays a dense self-gravitating cloud of gas and rocks around a melted iron ball. and later condensates back into a hot rocky planet without any atmosphere or hydrosphere.
Very probably, changes it orbit due to jet side effect of vaporisation.

Orbit gets unstable.

***

Mars.
Being heated, fully loses all atmo- and cryosphere.
Becomes a useless piece of rock.

***

Jupiter.
Gets heated, loses some amount of hydrogen evaporated from the surface.
The hot hydrogen, the heated Jupiter heat emission and the direct heating of its icy moons makes them to melt and crash.
A hot cloud of water and hydrogen covers the Jupiter system. Later condenses into secondary (tertiary?) system of icy moons and rings.

***

Other giants.
Puny cosplay of the Jupiter drama.

***

Pluto.
Still not a planet.
Though, rather than Mercury, it at least is a celestial body.

***

Earth (the one which orbits, not that one which has collided).
Totally metled, partially vaporized, though still self-graviting.
Will condense back into a rocky planet, but there will be very few amounts of fluids.

***

Sun.
Gets several hundred m/s delta-V, which slightly change planetary orbits.

Though, "slightly" is for the inner planets.
Beyond ~500 AU this can make orbits a little chaotic, as several hundred m/s is comparable to those orbital speeds.
So, this can throw out many comets and transneptune objects, and throw close to the Sun others.
"Very Too Late Heavy Bombardment" is in order.

Edited October 23, 2017 by kerbiloid

[p1t1o]

The higher the kinetic energy of an impact is, with respect to the bonding energies of the materials involved, the more "spherical" the energy release is. That is, the more the impact resembles an "explosion" rather than a "penetration".

This is an extreme case, so I would expect the impact to generate a large fireball close (within a distance of 1 earth-mass, earth-diameter,  column of sun-material) to the surface of the sun, resembling a titanic nuclear explosion.

Whether or not the magnitude of this explosion is sufficient to disrupt the sun in any significant manner is up to the folks crunching the numbers above.

Given that the total kinetic energy of the Earth in this case is very large compared to the Suns total luminosity in Watts, I'd say disruption was likely.

Answering the question of "What form that disruption takes, and the consequences", probably requires some time on a supercomputer.

[kerbiloid]

26 minutes ago, p1t1o said:

resembling a titanic nuclear explosion.

No fission materials, to cold for fusion.
Just local fusion flashes.

27 minutes ago, p1t1o said:

Whether or not the magnitude of this explosion is sufficient to disrupt the sun in any significant manner is up to the folks crunching the numbers above.

No.
According to my calcs, average temperature of the Sun will reach ~ 2.6*10⁶ K.
Thermal speed = sqrt(3 * 8.31441 * 2.6*10⁶ / 0.001) ~= 250 km/s.

Orbital speed on the Sun surface ~= sqrt(1.5*10¹¹/7*10⁸) * 30 ~= 440 km/s.

So, with this speed Sun surface cannot "jump" even at a half of the Sun radius.

[p1t1o]

20 minutes ago, kerbiloid said:

No fission materials, to cold for fusion.
Just local fusion flashes.

I said "resembles". It will resemble a large amount of energy being dumped in a small space.

20 minutes ago, kerbiloid said:

No.

Im not sure if the "average temperature of the sun" is relevant, this event will be highly localised in the initial energy exchange. 

Also, not for nothing but disrupting the sun even somewhat less than a half-radii is still a massive stellar event and the sun, and possibly the rest of the system, may never be the same.

 

Edited October 23, 2017 by p1t1o

[kerbiloid]

3 minutes ago, p1t1o said:

Im not sure if the "average temperature of the sun" is relevant, this event will be highly localised in the initial energy exchange. 

The small space where it is localized, is moving into the Sun at 0.5 c speed, quickly decelerating.

Gulp... Pshhh. Bang! Pew-pew-pew...

Edited October 23, 2017 by kerbiloid

[p1t1o]

11 minutes ago, kerbiloid said:

The small space where it is localized, is moving into the Sun at 0.5 c speed, quickly decelerating.

Gulp... Pshhh. Bang! Pew-pew-pew...

Yes, very quickly decelerating. Deceleration proportional to the square of the velocity.

I think its more of a fffffff-SHEEEEEW!!

Edited October 23, 2017 by p1t1o

[Cassel]

Depends on angle I guess. At some angles part of sun could be ripped off and create small and very hot object orbiting sun?

[kerbiloid]

29 minutes ago, p1t1o said:

Deceleration proportional to the square of the velocity.

The Earth here doesn't decelerate like a solid body.
Its front half is a cloud expanding into the Sun with initial speed 0.5 c. Its rear part is still moving with 0.5 c.
So, the pressure of this cloud is much greater than any pressure which a gas from inside can create. Like a volcano eruption inside.

And 0.5 c means  4..5 s to reach the center of the Sun. So, all this collision will last for a second, and even with 1000 km/s the gas atom can move only for <0.01 of the Sun size.
While the energy will be distributed_(?) across the Sun matter wiih X-ray radiation, so the Sun will warm up before its atoms could significantly move.

16 minutes ago, Cassel said:

Depends on angle I guess. At some angles part of sun could be ripped off and create small and very hot object orbiting sun?

Yes, I was calculating a central collision.
But this is almost only possible case for such huge explosion, because almost any trajectory here leads to something like that..
Only if the Earth had scratched the Sun with its very surface that could happen.

Edited October 23, 2017 by kerbiloid

[p1t1o]

27 minutes ago, kerbiloid said:

The Earth here doesn't decelerate like a solid body.
Its front half is a cloud expanding into the Sun with initial speed 0.5 c. Its rear part is still moving with 0.5 c.
So, the pressure of this cloud is much greater than any pressure which a gas from inside can create. Like a volcano eruption inside.

And 0.5 c means  4..5 s to reach the center of the Sun. So, all this collision will last for a second, and even with 1000 km/s the gas atom can move only for <0.01 of the Sun size.
While the energy will be distributed_(?) across the Sun matter wiih X-ray radiation, so the Sun will warm up before its atoms could significantly move.

Of course it wont decelerate like a solid body, the state of matter stops being a factor many orders of magnitude of speed less than this. But it will decelerate. 

I think we are operating on two opposing sets of assumptions that, though possibly both relevant in their own context, cannot be used together - or, one of us is completely, totally wrong.

For example, the sun is not transparent, even to X-rays. There will be a fireball, similar to a nuke, of expanding "shells" (really a smooth, continuous process of course) of radiatively heated gas.

The way you describe it sounds like the sun would just quietly absorb the impact and get slightly brighter.

No, Im strongly of the opinion that this event will cause a localised explosion. The effects of that on the sun itself needs supercomputer time.

 

[tomf]

The shockwave compression is going to pretty extreme, I would expect a significant amount of fusion to be taking place in the compression zone. Does anyone have an idea of how much energy that would release relative to the kinetic energy of the impact?

[kerbiloid]

43 minutes ago, p1t1o said:

For example, the sun is not transparent, even to X-rays. There will be a fireball, similar to a nuke, of expanding "shells"

It isn't transparent, but such amount of energy will spread much faster by re-emission of X-rays than by atomic movement.
Like in the famous Rapatronic film.

Spoiler

Here you can see that the plasma cloud still keeps the shape of the nuke and even metal ropes which kept the test tower vertical (those sharp pins below the bomb),
The bomb was even less transparent to X-rays than hydrogen.
Atoms just had not enough time to move. So, they had not enough time to collide with each other and redistribute their kinetic energy. But they had enough time to re-emit the excessive energy.

43 minutes ago, p1t1o said:

The way you describe it sounds like the sun would just quietly absorb the impact and get slightly brighter.

Not slightly (its emission maximum will temporarily get into far X-ray), but kinda so.

Edited October 23, 2017 by kerbiloid

[p1t1o]

26 minutes ago, kerbiloid said:

It isn't transparent, but such amount of energy will spread much faster by re-emission of X-rays than by atomic movement.

This is exactly how a nuclear fireball propagates and is well studied, and still would represent a shock-front...from the explosion that is occurring.

It is going to be nowhere near fast enough for your hypothesis, very much slower than c.

 

31 minutes ago, tomf said:

The shockwave compression is going to pretty extreme, I would expect a significant amount of fusion to be taking place in the compression zone. Does anyone have an idea of how much energy that would release relative to the kinetic energy of the impact?

This is where the supercomputers come in. Or at least very advanced physics. Its safe to say there would be some, but whether or not it will be insignificant in terms of the energies already in play, is a non-trivial question..

Edited October 23, 2017 by p1t1o