Applying the Ad Coelum Rule Literally

For my Property class I'm currently reading a Ninth Circuit case from 1936 holding that land owners did not have the right to exclude air traffic from the airspace above (or, as the court put it, superjacent to) their property. The only reason anyone would think they did is the legal principle cuius est solum eius usque ad coelum et ad infernos. "Whoever owns the soil owns also to the heavens and to hell." Before the advent of air travel, people thought this applied literally, that property over a certain portion of the Earth's surface gave you the rights to everything above and below that surface. Since the 1940s, no one thinks that anymore; the principle still applies, but within reasonable bounds in both directions, more or less defined by what you can make use of. Airplanes can fly over your land, so long as they fly high enough so as not to do any damage to your property. The courts that rejected the ad coelum principle's application to air traffic gave a pretty plausible sketch of why it would be absurd to apply it literally. But they didn't go far enough, though.


Consider what ad coelum ownership would look like, given what we know about the universe. The "down to hell" part would need to be defined as the cone from the surface region down to the center of the Earth. The "up to heaven" part would, naturally, be defined as the extension of that cone. Forever. But "forever" is an awfully long way, billions and billions of light years out, and there's a lot of stuff there. Since, moreover, this is a cone we're talking about, it gets bigger the further out you go. Supposed you owned a square inch of land. (Another of my property readings mentioned that this actually happened once, as part of a promotional campaign by Quaker Oats.) The sides of your little plot of land are about one-250-millionth of the radius of earth. Proportionally, then, when we're one light year out from earth, your square would have sides nearly 25,000 miles long. That's, y'know, a lot bigger than the diameter of earth. A parsec out, we're talking 75,000 miles. The nearest star is Proxima Centauri, about 1.3 parsecs away, so that's almost exactly 100,000 mile long sides. Proxima Centauri has a radius of about 61,000 miles. So, if you were lucky enough to have your cone aligned correctly, it would include almost all of Proxima Centauri. The center of the galaxy is about 8330 parsecs away; the square would have sides about 6.85 astronomical units long at that distance. The supermassive black hole suspected to reside at the galactic center would have a radius of 0.08 AU. When your plot of land got out to the distance of the Andromeda Galaxy, it would take a photon something like 3 days and 16 hours to cross from one side of it to the other. Many galaxies in the Hubble Deep Field are around 13 billion light years away. At that distance, your property would have sides more than 50 light years across. Now, that's not enough to contain an entire galaxy, but, well, you started with a square inch of dirt. This is a powerful principle.

But that's just about how big your property gets when we get a long, long way away. There's also the problem that the earth spins. Relative to the stars, rather than to the sun, it takes the earth about 23 hours, 56 minutes to rotate 360 degrees. That's an angular velocity of 0.261 radians per hour. A radian, you'll recall, is equal to the radius of the circle, making the following calculation really easy: out by Proxima Centauri, your property would be moving at a little more than one light year per hour. (Obviously that's not possible, but only for an actual physical object; property is an idea, and an idea can move as fast as it wants to.) It would start to exceed the speed of light when it was 3.83 light-hours away. That's about four trillion meters, or about 2.5 billion miles. That's not very far; it's about 27.6 AUs. That's a little smaller than Neptune's orbit, so you haven't left the solar system before your property is outpacing photons. What you "owned" under this system, in other words, would be extremely unstable. Ownership of the entire universe, or at least that portion of it not corresponding to international waters, would rotate on a daily cycle. Actually, it's a bit more complicated even than that; if someone owned the 1-inch radius circle around the north pole, their patch of the universe wouldn't change at all. How quickly your extraterrestrial property changed would, therefore, depend a lot on the latitude of its location. Santa gets to keep his little column of space forever; someone in Ecuador, however, would see their property shift around at literally impossible speeds. (Actually, you wouldn't need to go far before the U.S.S. Enterprise wouldn't even be able to keep up going at, say, warp 9.)

This has been Taking Obsolete Legal Principles Way Too Literally For Random Fun.