# How much of the solar system would be damaged if the earth was destroyed by lightspeed ship collision?

If a large spaceship travelling at near-lightspeed hit the earth and destroyed it, how far into the system would the devastation travel? Would colonies on Mars and Venus (and perhaps ships in orbit there) also be destroyed by the shockwave? Would the moons of Jupiter and Saturn be affected?

I know the shockwave/energy produced by the collision, plasma and radiation would be a problem, but I'm not sure how to calculate how far they would travel, or how lethal they would be.

Addition: The ship would be a passenger vessel, roughly the size of a cruiseship, so I would imagine made of steel, or perhaps a harder alloy.

• What do you mean by "shockwave"? (And we absolutely need to know how large the colliding body is, and what it is made of, or at least its average density. Size matters quite a lot.) – AlexP Nov 14 '20 at 14:10
• Ah, a tiny colliding body. Why would you think that the collision will "destroy" Earth? Earth is big. The collision will likely melt (part of) the crust, and eject some material into space, of which a small fraction may even escape Earth's gravity. But Earth will continue to exist, just about as big as it was before the collision. (The major problem with "destroying" Earth is that to do that you must somehow ensure that energy couples with every little piece of Earth; this is not a trivial exercise.) – AlexP Nov 14 '20 at 14:18
• I honestly didn't realise that the energy involved wouldn't be enough to destroy the planet. I'm clearly going to have to take this in a new direction, or upscale the size and density of the colliding body by a significant factor. Thank you for your reply. – Redpanes Nov 14 '20 at 14:24
• Near lightspeed? It depends utterly on your definition of "near". As you get very close to lightspeed, relativistic effects accumulate. But 90%, 99.9%, even 99.999999% is not enough. (that last one might wipe a country, but the planet itself will barely notice) – user79911 Nov 14 '20 at 14:45
• Obligatory XKCD. what-if.xkcd.com/20 – Futoque Nov 14 '20 at 14:51

Space is big.

Really big. You just won't believe how vastly, hugely, mind-boggling big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space. Listen; when you're thinking big, think bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real 'wow, that's big', time. It's just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we're trying to get across here.

(Douglas Adams, The Hitchhiker's Guide to the Galaxy)

## Don't Panic!

If you increased the ship size to that of Luna, our beloved moon, and changed the incoming travel vector such that, in the fullness of time, the debris from the impact would exactly collide with Mars — it would cause (at best) a delightful but completely harmless meteor shower.

If (and it's a big if) you hit the planet with enough kinetic energy to shatter the planet...

1. The planet is in orbit around the sun and most of the mass would continue in that orbit.

2. The planet is rotating, so the exploding mass is spinning away like a top.

3. Space has three dimensions and the location of a planet is actually an infinitesimally small point within the massive and voluminous sphere that encloses the solar system. If you actually could cause the planetary mass to eject away such that the planetary orbit didn't matter, the vast, vast, vast, vast, vast majority of mass wouldn't go anywhere near another planet. (That same number of vasts could be said of the amount that wouldn't go anywhere near the Sun....)

So, from the perspective of the blown apart mass being a threat to any other planet in the solar system the answer is no, zilch, nada, niet, ei mitään.

But there would be a small effect

The eventually distribution of planetary mass means that the gravity well represented by Earth is gone. That will effect the other planets to a small degree. They'll slightly change position, but I suspect not by much. Someone with more experience in Celestial Mechanics is needed to say how much. But I doubt it would be catastrophic in any sense of the word.

### If it's very close to $$c$$ - Mars and Venus will also have a very bad day

This basically comes down to "how many 9's?". At 0.99c you'll expose mantle and kill all life but Earth will remain a planet. But if we add a few more 9's it's a different story.

So I'm assuming 0.9999999999999999999999951c - which is the fastest speed we've ever observed a particle travel.

The physics behind this have been calculated by someone smarter than me. Basically it's 10,000 times stronger than gravitational binding energy, and turns the entire planet into an expanding cloud of plasma.

The sun will flicker and flair, but survive, but everything on the moon, Mars and Venus will be vaporised by the expanding plasma.

• "Everything on the moon, Mars and Venus will be vaporised by the expanding plasma": are you sure? Citation needed. (Yes, I've read the XKCD What If. Randall Munroe clearly states that he didn't even attempt to calculate the effects.) – AlexP Nov 14 '20 at 17:47
• @AlexP He stated that even his simulation tools broke down under these conditions. I'm deferring to his judgement on what will happen due to his experience in this area. Needless to say it's a lot of energy a 1au sized plasma ball seems within the realm of plausible. – Ash Nov 14 '20 at 17:57
• Just for curiosity, have you even bothered to calculate the density of a sphere with a radius of 1 AU filled up with the mass of Earth and nothing more? You know, in order to get an idea about whether "everything on Mars and Venus will be vaporised by the expanding plasma" is reasonable or not. – AlexP Nov 14 '20 at 18:43
• First, this is for a 100 meter diamond hitting the Earth at that speed. Since it's 10,000x the binding energy it's way beyond what this question asks. – Loren Pechtel Nov 15 '20 at 0:47
• Second, you're talking about 2e36 joules of energy. The closest approach to Venus is 3.8e7 km. The surface area of sphere 3.8e7 km across is 1.81e16 km^2. The cross section of Venus is 1.15e8 km^2, thus it catches 6.34e-9 of the energy for a total of 1.27e28 joules. While I'm not finding the binding energy of Venus note that we are at less than 1 part in 10,000 of Earth's binding energy and Venus isn't that much smaller than Earth. Venus is not destroyed. Note that we are at less than 20x the energy of the Caloris Basin impact event on Mercury. – Loren Pechtel Nov 15 '20 at 0:59