Last week we were treated to the unusual story of a human-versus-meteorite collision.
According to the Daily Telegraph, the youth whose hand was in the path of the pea-sized meteor saw a “ball of light.” The article also made the claim that the impact with the ground left a “foot-wide crater.” Both of these assertions are highly unlikely, as we shall see by simply applying some basic physics to the situation.
We know that meteors approach Earth with speeds of up to several tens of thousands of meters per second. Without an atmosphere, and therefore any friction to slow them down, these grains of cosmic flotsam would impact the surface without any significant change in speed. Even a pea-sized fragment moving at 10 kilometers per second would have a significant amount of kinetic energy — about the same as a 100-pound boulder moving at 100 miles per hour. Now that might really hurt your hand, and put some cracks in the sidewalk.
In fact, though, we do have an atmosphere. Acknowledging this, what effect will this have on incoming space debris? Using some Newtonian mechanics, we can show that large enough rocks (on the order of 10 meters in diameter or more) will experience very little change in velocity due to air friction, and will impact Earth at velocities close to their original 11,000 m/s, with huge kinetic energies and the ability to form large impact craters. But, by the same mechanics, a pea-sized object will be slowed dramatically to a speed approaching its terminal velocity — maybe to a final speed of a couple of hundred meters per second at best.
How do we deduce this? The amount of atmospheric fluid drag acting on an object moving through the fluid at a given velocity is given by the following equation:
Fd = 1/2Dv2ACd
is the drag force,
is the density of the fluid,
is the velocity of the object,
is the cross sectional area of the object (
A = π r2
if the object is circular in shape) and
is the coefficient of drag. Assuming that the force of gravity acting on the meteor is small compared to the fluid drag we can apply Newton’s second Law approximately as
Fd = 1/2Dv2ACd = ma
is the mass of the meteor, and
is its acceleration. Now let’s compare fluid drag forces and the resulting accelerations for the respective space balls (or decelerations, if you prefer — after all, the forces are acting opposite to the direction of motion, causing the objects to slow down.) We’ll compare a meteor the size of a pea (1 centimeter in diameter or so) to one with a diameter a thousand times larger (10 meters).
depends on the square of the radius, our large rock has an area one million times that of the little rock, and assuming that the initial
are the same for both meteors, we get that the “big ‘un” experiences one million times as much drag force as the little guy, for the same initial velocity!
So does this mean that the big ‘un accelerates (slows down) at a rate a million times greater than the little fella!!? No, it does not. Remember: the acceleration depends not just on the force acting on the object, but also the mass of that object. The mass of the big guy is 1000 x 1000 x 1000 = one billion times the mass of the little one. (The mass of an object is equal to its density times its volume, and volume increases as the cube of the diameter. For example the volume of a spherical object = 4/3π r3)
The result? The acceleration of the pea will initially be around a thousand times greater than that of the large rock. The big ‘un won’t slow down significantly in the several seconds it takes to reach Earth’s surface, but the little guy will get down below the speed of a bullet in that same period of time.
Could a pebble-sized meteor moving at that speed be dangerous? It could. Will it have a velocity sufficient to induce enough compressional heating to produce a “flash of light”? Not likely. Could it create an impact crater a foot in diameter? No, it couldn’t. Busted!
Finally, for fun and comparison purposes, the video above shows a famous recorded meteorite flight culminating in an impact with the trunk of a parked car.
This space rock had a cannon-ball-sized mass of 12 kilograms when it hit the car, and while this would be approximately 1000 times the mass of our tiny pebble, it would still have been slowed to near terminal velocity before impact — just like the pebble.