# How fast would a one mile asteroid have to go for it to match the impact that killed the dinosaurs?

I was playing a silly asteroid game and had a question in my head: how fast would a mile long meteor have to go to match the impact of the Chicxulub impact? (The impact that killed the dinosaurs.)

• Our question is poorly phrased. A meteoroid is is defined as a space object larger than a grain of space dust and smaller than one meter in diameter; a larger object is defined as an asteroid. A meteor is defined as the trail of glowing gases left by the passage of a solid object like a meteoroid or asteroid though the atmosphere of Earth. Thus calling a solid object a meteor is inaccurate. Saying your asteroid is one mile long implies that it is rather cylindrical in shape and thus its volume is undefined by you, though James K assumed it was spherical. Commented Feb 18, 2023 at 8:27

This is a nice little Fermi problem, and can be answered if we don't take it too seriously. The Chicxulub impact was 20km/s and about 10 kilometers in diameter (with a density of about 3g/cm³). Mass is proportional to volume and so is proportional to the cube of the diameter.

Energy = ½mv² so energy is proportional to the cube of the diameter and to the square of the velocity.

One mile is about ⅙ of 10km so the mass decreases by a factor of 1/216, and so to keep the same energy the velocity must be increased by a factor of √216, which is 6√6 or about 15.

So the velocity of the one-mile impactor would have to be about 300 km/s to impact with the same energy. This is considerably higher than the maximum theoretical velocity that a solar orbiting asteroid could have with Earth (anything going that fast won't be orbiting the Sun).

There are lots of uncertainties here, which is why this is only a Fermi estimate.

• yes. However, it could be in an elliptical-type orbit around the sun (and I mean REALLY elliptical.) and the earth is at the periapsis of this orbit (where it will be going fastest) not only will this high velocity from the gravity assist type thing the elliptical orbit has, but the Earth's gravitational pull may also accelerate it. Still, like you said, we shouldn't take this too seriously. Especially not this theory. Commented Feb 16, 2023 at 20:52
• Even if you put this thing on a parabolic orbit, it will have a velocity relative to the sun of less than 45km/s at perihelion (that is escape velocity from the sun), if it is moving retrograde around the sun and colliding head on, that is 75km/s, adding 11km/s for the Earths gravity brings us to 86km/s. So that is the limit for any asteroid, The practical limit is less, more like 50km/s. Anything faster must be on a hyperbolic orbit. Commented Feb 16, 2023 at 21:20
• That's going on the list of one of my absolute biggest miscalculations. Commented Feb 16, 2023 at 21:23
• @Negdo The upper limit is about 7 times the density (pure osmium) but even in that case speed is still 100 km/s, so it doesn't actually change much. Commented Feb 17, 2023 at 8:12
• @ZizyArcher Of course, a pure osmium asteroid of that size would be positively terrifying for entirely different reasons, even if you ignore the question of how it exists in the first place. Commented Feb 17, 2023 at 17:22