You've seen the footage of a rock falling past a skydiver. It looks like this particular object might be a rock accidentally packed in his parachute. So we've done the statistical analysis to figure out what the real chances are that a skydiver would eventually see a meteoroid.
The following is some hardcore estimating and order-of-magnitude geekery to determine how likely it is for a skydiver to see a meteorite during an average jump. Fans of xkcd and Randall Munroe's What if? know how the next part works. For everyone else, if you ever wondered what physicists do for fun, this is how I spent my Friday night.
The game is played by making assumptions for values based on orders-of-magnitude — what's the closest power of ten that describes the number (1 vs 10 vs 100) — then apply basic relationships to come up with a vague notion of how things interact. I strongly encourage you to play along at home — argue about my assumptions, come up with alternate methods, and please, please check my math!
How far away could you see a meteoroid?
Astronomers and optometrists measure the angular resolution of the human eye to measure how well we can distinguish objects of a particular size at a particular distance. Perfect 20/20 vision is defined as being able to identify a 1.75 mm gap from 6 meters away. Rounding to keep the numbers pretty, that works out to 0.01° angular resolution. For context, if you hold out your arm and spread your hand, your thumb is approximately 0.5°.
Let's work with a small-but-noticeable rock, something fist- to head-sized. That's closer to 10 cm diameter than it is to 1 cm or 1 m, so we'll roll with that as our meteorite-size.
Rearranging the angular resolution equations to use our two known inputs, that means that a skydiver with perfect vision could spot a 10 cm meteorite anywhere within a 500 meter radius (this is much shorter than their view-distance to the horizon!). Since meteorites have a much, much faster velocity than skydivers do, matching altitude doesn't matter since any meteorite would catch up and pass by any skydiver. Anyway, the skydiver can look not only in a 360° plane, but also up, down, and anywhere in-between.
How many people are skydiving?
So, how many people skydive? The United States Parachute Association lists 3.1 million jumps in 2012 with 0.006 deaths per thousand jumps. Assuming the mortality rate is the same internationally, working backwards from the global statistics of 49 skydiving deaths in 2012 means that world-wide, roughly 8 million jumps occur per year. For our orders-of-magnitude estimate, that's closer to 10 million jumps per year than 1 million. Combining free-fall and gliding under a canopy, the fall duration is on order of 10 minutes per jump.
So, that's 10 million jumps per year, at 10 minutes per jump, looking within a column with a cross-section area of πr2 ≈ 106 square meters. Run the equations out, that's the equivalent of saying skydivers survey 1013 square meters of the planet for ten minutes per year. The entire surface of the Earth is only 5 x 1014 square meters. For ten minutes, skydivers are surveying 1013/5 x 1014 = 2% of the Earth's surface. If skydivers were evenly distributed over the surface of the earth, skydivers survey the entire planet for ten minutes every 50 years.
How many meteoroids are falling?
...we really don't know.
Assuming our 10 cm meteorite is made of solid rock (3000 kilograms per cubic meter density), it is a hefty
10 1 kilogram.
A Canadian survey tracked meteorites that landed anywhere in a 1.3 million square kilometer detection area for fourteen years. Every year, about 5,000 meteorites greater than 1 kg fall on the Earth, each one taking less than a minute to pass from peak skydiving-altitude to hitting the ground.
Assuming the distribution is temporarily random (ignoring events like meteor showers), those 5 x 104 meteorites could fall on any of the 5 x 106 minutes in a year, or one falling every hundred minutes.
The survey only tracked frequencies for meteorites above 1 kilogram, not above 10 kilograms (our rock), so this is probably an over-estimate of flux but we'll use it for now.
So, what are the odds of a skydiver seeing a meteoroid?
In our idealized, simplified world: what are the chances that the meteorite will come down within the ten minutes and 2% of land-surface area where a skydiver is looking? If meteorites are randomly distributed across the planet, the chances that a meteorite will strike somewhere a skydiver is looking is 0.2%, or a near-certainty in 5 centuries of skydiving.
Hedging the Numbers
What happens if some of the starting assumptions are off?
- Skydivers might not notice something at the edge of their visual acuity. Running through the same math at a blindingly-obvious 1° angular resolution, twice the apparent size of the moon, drops visibility to rocks within a 5-meter radius, or 102 square meters. This drops the chances considerably, to 0.00002%.
- Skydivers aren't looking everywhere at all times. You could re-run this math limiting the field-of-view to a 120° cone instead of a full sphere of vision. This decreases the chances by an order of magnitude to 0.02%, ish, depending on which way the cone is oriented (up, down, to the side...).
- Skydivers aren't evenly geographically distributed over the entire planet. Over a third of jumps are over the United States, and I'm willing to guess none of them are over the North Pole. But, that doesn't really matter, since it means skydivers less likely (not at all likely) to spot a meteorite that happens to come down over the Arctic Ocean, but far more likely to see any that come down in skydiving hot-spots like California, Florida, New Zealand, several tropical islands, Spain, Italy, Nepal, or particular locations in Africa.
- Meteorite frequency rates by size are not well-constrained. Our ability to detect meteorites is increasing gloriously quickly, and I look forward to better estimates in the future. For now, every order of magnitude the flux rate is overestimated, drop the chances by the same amount: If 1 kilogram meteorites fall only 500 times a year, the chances of a skydiver seeing one is 0.02%.
- Jumps aren't actually 10 minutes. In the discussion, it's being argued that an average jump falls awkwardly in between 1 minute and 10 minutes. Luckily, the jump-time has a linear impact on the chances of seeing a meteoroid that happens to fall during that jump, so a 5-minute jump drops the percentage chance of seeing a meteoroid to 0.1%. (A 1-minute jump would drop by an order of magnitude compared to a 10-minute jump, to 0.02%).
But even with all these assumptions, when it comes to asking "What are the odds of a skydiver seeing a passing meteorite mid-jump?" the answer is, "Better than winning the lottery!"
We're starting to see all sorts of footage of these rare, amazing events. While the event that triggered this question probably isn't a meteoroid, it's also a reminder that "incredibly improbable" is actually really common when you start thinking about the billions of people on this planet going about their lives for year after year after year.