# How large would a chunk of ice have to be to do lasting harm if it were 'thrown' at Earth?

I'm working on a story involving life on Europa being upturned dramatically by contact from a probe sent from Earth. I know the chances of life, let alone intelligent life, are pretty slim on Europa, but I'm ignoring that for the sake of the story. The driving force of the story is that a probe that's come from Earth crashes/malfunctions after melting through the ice.The probe sinks to the bottom of a trench and sets off some sort of ecological disaster/collapse, that then has cascading effects on the civilizations living there. In retaliation, a fairly advanced society that has adapted to living in the ice (most of society is less advanced and lives on the sea floor), makes plans to retaliate against the Earth by breaking off a chunk of the crust and hurling it at Earth.

How big of a piece of ice would be needed to cause considerable damage to Earth? I'm thinking even if it burns up entirely on impact, if it adds enough water to our atmosphere it could really do some damage, but I'm not really sure what sort of size would make sense? I'm thinking it would need to be as little as possible while still big enough to ensure it does real harm to Earth. It would probably not be going very fast since they don't have engines attached or anything like that, and are purely working with controlling water pressure to push it the way they want (my idea is that they are basically creating their own plumes as initial propulsion out of orbit, and then just riding that momentum or possibly sling-shotting around other celestial bodies to compensate). I'm also just going to assume they have the capacity to calculate the trajectory correctly. So they are reasonably sure it will hit Earth.

I don't know much about physics, so I'm not sure how much Jupiter's gravity would have an impact, or whether they would be able to use that somehow to slingshot it around at their target and maybe increase it's speed that way, or if it would most likely just never be able to break free of Jupiter's orbit at all without a more powerful propulsion.

• "It would probably not be going very fast": Anything coming from outer space will come with at least 11.2 km/s (40,320 km/h, 25,054 mph). (Because mechanics is fully reversible; the minimum speed with which something can come to Earth from outer space is equal to the minimum speed needed to lauch it from Earth to reach outer space.) Jul 30 at 4:22
• Is that like terminal velocity? Like, once it comes to Earth, that's the min speed it would hit? Or does it have to be coming at that speed before it gets to Earth if it wants to make it? Jul 30 at 4:41
• That's the speed with which is will be approaching Earth, assuming is started with zero speed at infinity. ("Terminal velocity" is something else entirely.) For an example of what happens when a chunk of ice enters the atmosphere at cosmic speeds, see the Tunguska event. Jul 30 at 4:42
• @AlexP Good point, but wouldn't the minimum be Earth's escape velocity + Eruopa's + Jupiter's combined escape velocity at the orbit of Europa? And Brooke, what do you mean by "lasting harm" and "considerable damage?" Would the crater and odd genetic disorders resulting from the Tunguska Event be considered "lasting harm?" (No practical harm was done.) Or are we thinking Chicxulub crater kind of damage? (Think "dead dinosaurs.") Or something else? Can't judge the size of the chunk without knowing what you expect for damage (please be specific).
– JBH
Jul 30 at 6:07
• @JBH I think since they don't have the power to control where it hits on Earth, it would have to be more than the Tunguska Event. I don't think it's necessary to be extinction-level (though the one's responsible wouldn't be sad if it was). They are retaliating for an event that upended their whole society and caused massive ecological devastation. So they'd want something that would hurt humans regardless of where it hit the planet. I was thinking, since it's primarily ice, how big would it have to be to cause water levels to rise a la melting glaciers, but that might be too big? Jul 30 at 12:48

20 Kilometer Ice Cube

From Wikipedia, the asteroid that killed the dinosaurs is estimated at 10-15 km in diameter and hit the Earth at about 20km/s.

The mass and speed together give the amount of energy that was suddenly absorbed into the Atmosphere. Exactly what the projectile was made of does not matter.

D'Monlord says 20km/s is about the same escape velocity you need to escape from Jupiter's gravity well and the projectile will, regardless of what happens in between, hit Earth at least 11km/s. So let's split the difference and say it hits Earth at 20km/s.

Asteroids can be up to 5 times denser than ice. That means an ice asteroid of the same mass has $$\sqrt[3]5 \simeq 1.71$$ times the diameter.

So we get 10-15 km times 1.71 which is about 20km in diameter.

"how big would it have to be to cause water levels to rise a la melting glaciers"

According to Wikipedia Earth's ocean surface area is 361132000 km^2. To raise level by 1 meter you would need 361132 km^3 of water or ~392534 km^3 of ice which would be a cube with side of ~73 km.

Escape velocities were mentioned in comments. 11.186 km/s for Earth, 2.025 km/s for Europa herself, ~19.2 km/s for Jupiter from Europa's surface.

Ice cube with 73 km side would not melt in the atmosphere. Atmosphere is thin, at this speed and right angle it would penetrate the atmosphere in seconds and hit Earth harder than what killed the dinosaurs. Kinetic energy of this magnitude doesn't just dissipate in atmosphere.

But most of this energy has to be first supplied to this chunk of ice by Europeans. And if they can do that launching ice cube looks like a bad idea. Accelerating giant piece of ice to escape velocity using water is terribly difficult. It melts and breaks. I can't think of any plausible way of achieving it.

I would consider something else. E.g. Europeans are not carbon based but extremely proficient in building nano-machines. So they make a machine capable to replicate itself using any protein and send about a cup of it to Earth.

• I do have to point out that, contrary to what your intro suggests, melting glaciers do not raise water levels. Because of the very mechanics of buoyancy, a partially floating glacier displaces exactly the same amount of water than it does once it turns its full mass to water. Global warming makes water levels raise because of thermal expansion, not because of melted ice. It is a misconception that unfortunately hurts the credibility of many people that have the otherwise good intention of warning against the dangers of global warming. Melting glaciers is an ecological disaster on its own. Aug 1 at 6:29