Set the size, make-up, speed and angle of an incoming space rock and see how much energy it carries, whether the air stops it or it reaches the ground, and how big a crater it would leave. The physics behind every number is explained below the calculator.
–
–
Each step along the bars is a thousand times more energy. Results are estimates from simplified physics and can be out by a factor of two or more.
Four well-studied events span a huge range of energy. Load any of them into the calculator to see how the model compares with what really happened.
On 15 February 2013 a stony asteroid of roughly 12,000 tonnes entered at about 19 km/s on a shallow path over Russia and broke apart about 30 km up. The flash outshone the Sun, and the shock wave arrived over a minute later, breaking windows across the region. About 1,500 people needed medical help, almost all from flying glass. Many small meteorites, and one piece of over 600 kg from a lake, were recovered.
On 30 June 1908 an object exploded above the forest of central Siberia and flattened around 80 million trees over some 2,150 km². It left no crater and no confirmed meteorite, which fits a stony body that burst in the air. Estimates of its energy vary widely; about 10 megatons is often quoted.
An iron asteroid struck what is now Arizona and blasted a bowl about 1.2 km across and about 170 m deep, one of the best-preserved young craters on Earth. Being iron, it was strong enough to survive the air largely intact, although much of it broke up and slowed on the way down. Pieces of it are known as the Canyon Diablo meteorite.
A body more than 10 km across struck the Yucatán coast of Mexico. Its buried crater is about 180 km wide. The impact threw out debris and gases that changed the climate worldwide, and it is linked to the mass extinction that ended the age of the non-bird dinosaurs. At this size the atmosphere barely slows the impactor at all.
Almost all of an impactor's power comes from its speed. Its kinetic energy is half its mass times its speed squared. For a sphere of diameter L and density ρ, the mass is ρ × π/6 × L³, so:
E = ½ m v² = (π/12) ρ L³ v²
Because size is cubed, doubling the diameter gives eight times the energy. Because speed is squared, doubling the speed gives four times. At 20 km/s, every kilogram carries about 200 million joules, roughly fifty times the energy of a kilogram of TNT.
Energies this large are easier to picture in tonnes of TNT. One tonne of TNT is defined as 4.184 × 10⁹ joules; a kiloton (kt) is a thousand tonnes and a megaton (Mt) a million.
Earth's gravity accelerates anything that falls from far away to at least about 11.2 km/s, the escape speed, before it reaches the air. The fastest possible arrival is a head-on meeting between Earth, moving round the Sun at about 30 km/s, and an object falling inwards at the Sun's own escape speed at our distance, about 42 km/s. Together they make about 72 km/s.
As the body plunges in, air piles up in front of it. The pressure on its front face is roughly the air density times its speed squared, ρairv². The air thins by a factor of about 2.7 for every 8 km of height, so this pressure climbs steeply as the body descends.
When the pressure exceeds the body's strength it breaks apart. The fragments spread sideways like a flattening pancake, which suddenly increases the area meeting the air. Drag then rises so fast that most of the energy is dumped into the air within a few kilometres of height: an airburst. The hot air and shock wave spread outwards, but no crater forms.
This calculator uses a widely used simplified pancake model. It estimates the body's strength from its density, finds the height where the air pressure first exceeds that strength, follows the spreading cloud of fragments, and calls it an airburst if the cloud reaches seven times its starting width before hitting the ground. Weak, small or fast bodies burst high; strong irons and very large bodies reach the surface.
An impactor that reaches the ground at several kilometres per second is stopped almost instantly. A shock wave runs into the rock and back into the impactor, which melts or vaporises. The shocked rock flows outwards and upwards, opening a bowl-shaped transient crater in seconds to minutes.
The transient crater does not last. In small craters, loose rubble slides back down the walls and the bowl widens by about a quarter: a simple crater like Meteor Crater. Above about 3 km across on Earth the walls collapse in great terraces and the floor rebounds into a central peak or ring, making a wider, relatively shallow complex crater.
Nobody can test a kilometre-wide impact, so scientists combine laboratory shots, explosion craters and computer models using dimensionless numbers called pi groups. The key one compares the pull of gravity with the impactor's momentum:
π₂ = g L / v²
For craters larger than a few metres, gravity, not rock strength, is what finally stops the excavation. Experiments show the crater's size, measured against the impactor, falls as a power of π₂. Written out for Earth, the transient crater diameter in metres is approximately:
Dtc ≈ 1.161 × (ρi/ρt)1/3 × L0.78 × v0.44 × g−0.22 × (sin θ)1/3
Here ρi and ρt are the densities of the impactor and target, v is the speed at the ground and θ the angle. The power of L is less than 1 because a bigger crater must lift its rock higher against gravity, so craters grow more slowly than impactors. A crater is typically about 10 to 30 times wider than the body that made it. For deep water the calculator uses a slightly larger constant (1.365) and shows only the short-lived cavity in the sea.
The final crater is about 1.25 times the transient one for simple craters. For complex craters the calculator uses D = 1.17 × Dtc1.13 ÷ 3.20.13 (in kilometres), where 3.2 km is the size at which craters on Earth switch from simple to complex.
Only the downward part of the motion digs, so shallow impacts make smaller craters: the factor (sin θ)1/3 shrinks a crater at 15° to about two-thirds of its size at 90°. A shallow path is also longer, so the air has more time to slow and break the body; that is why Chelyabinsk, arriving at under 20°, burst so high. Only at very low angles, roughly below 10 to 15°, do craters become noticeably oval.
Real asteroids are irregular, may be loose rubble piles, spin, and lose mass by melting as they fall. Real targets have layers, water and soft sediment. The model treats each body as a single sphere with an average strength, so it gives the right size of answer rather than a precise one. For the four yardsticks it lands within about a factor of two of the measured craters and burst heights; for Chicxulub it comes out somewhat smaller than the real crater.
Earth sweeps up many tonnes of dust and small meteoroids every day, almost all of it burning up harmlessly as meteors. Chelyabinsk-sized objects arrive perhaps once or twice a century, mostly over oceans or empty land. Tunguska-sized events are rarer still, and a Chicxulub-sized impact happens on average only once in a hundred million years or so.
Telescope surveys have now found the great majority of near-Earth asteroids larger than 1 km, and none of them is on course to hit Earth in the foreseeable future. In 2022 the DART spacecraft showed that a small asteroid's orbit can be changed by crashing into it, a first real test of planetary defence.