On a clear night how far away can a plane's flight path be (in terms of distance over land)?

I often wake up late at night to see 4+ planes flying in the sky..but surely it's impossible that there are so many planes flying over my small town all the time. I have come to believe that the planes must actually be flying on a path some distance away but because the sky is clear and because they are flying so high it looks like they are right above me. So if a commercial jet is flying at 23,000ft and is at a 45 degree angle from me .. how far away (over land) is it actually away? Is it flying on a path 100km away along the coast? Or is it actually not that far away?On a clear night how far away can a plane's flight path be (in terms of distance over land)?
At 23,000 feet, the line-of-sight distance between an aircraft and an observer on the ground (assuming flat terrain) is about 186 statute miles, and the aircraft is visible from an area of around 108,000 square miles. At this distance, though, the aircraft may not be visible to the naked eye, as even a large aircraft would visually be right at the limit of human vision (about 42 seconds of arc for a 200-foot aircraft). The distance over land would be practically the same (very slightly shorter).





If you are looking up at an aircraft at a 45-degree angle, its distance from you over land is roughly equal to its altitude (actually just a little bit less), so if it's at 23,000 feet, it's 4.4 miles away. The curvature of the Earth is not significant at this distance.





(I did all these calculations rather quickly but hopefully I haven't messed anything up.)On a clear night how far away can a plane's flight path be (in terms of distance over land)?
Plans fly on routes that contain departure sequences(SID), en-route sequences, and an arrival sequence(STAR). They are probably flying on one of these routes. There can be up to 15,000 planes in the sky at one time, so when you think about it, its not unlikely a few will be over you!





When I'm flying over the middle of nothing I wonder what people in small towns are thinking.. I guess I know now!





Hope I helped!


-Lonestar