Property ownership is one of those seminal things that most people see as finally being able to state as well as to know that they are now the king and queen of their own castle, no matter how grand or how modest that castle may be. Unfortunately, what a given owner owns in regards to that land is dependent upon Federal law, State law, local law, and the court of law. Back before modern times, it was common to believe that one owned their land “to the heavens and to hell.” However, nowadays, with the prevalence of underground utilities, as well as mineral and water rights, one's ownership of the land underneath their property typically comes with caveats, and it is those property restrictions that limit how much land underneath the property is actually owned by the owner of the land above ground. In regards to air rights, in the age of airplanes, the general rule is that the owner of property owns, depending upon the height of their building, and air traffic around such a building, 80 - 500 feet above the property, as their own private airspace, but as with most everything, it depends upon the circumstances so involved. That is to say, a helicopter or a drone for that matter, do not have the uninhibited right to specifically hover above your property for purposes of an invasion of your privacy or surveillance, even if they are above the airspace so defined, whereas airplanes and similar that are passing through are permitted to do so.
When it comes to the land below the property, the legal ownership documents so created upon the purchase of the home, usually specify what is or is not owned beneath the property, with any and all exceptions to mineral rights or similar, being so noted. Of course, when it comes to governments and their needs, in most instances within land ownership, their right of eminent domain trumps the owner's right to be the master of what is allowed to occur underneath that land. On the other hand, while most owners intuitively understand that the air directly above their property is not something tangible that they really can own, as well as acknowledging the typical restrictions as to how high one can build their property per the local zoning laws; so too, they understand that aircraft of all sorts have an imminent need to utilize airspace to travel to and fro. However, now that drones have come down significantly in price, so that, even the next door neighbor can own one, and further that drones can be outfitted with recording devices; there obviously is a potential issue with any neighbor that flies a drone over private property and records such, especially when that has been done, deliberately. While certain States have passed legislation, outlining the rights of property owners and providing such with redress for grievances of this sort, even without new laws being written, each owner is entitled to privacy on their own property, and the flying of a drone, that is taking pictures or video of another person's property could easily be seen by a court of law as an invasion of the privacy of the owner of that property.
The old days of owning “to the heavens and to hell,” are long gone, if they ever really existed, and it is up to individual property owners in conjunction with their legislators to see that those that own property are properly protected in this era in which search, seizure, and privacy are all seemingly ceding more and more ground to governmental and institutional agents of all sorts.