Do flights affect tides?
Can artificial satellite positions affect tides? on Space Exploration.SE asks if artificial satellites can affect tides, because they are a lot closer than our natural satellite, even though they are much smaller in mass. The top answer to that question is basically "no."
A commenter estimates that Pluto might have a larger effect, but Pluto is such a distant object I didn't think most people could easily relate to that, so I tried running the numbers with something people might be more familiar with, closer to our surface: airplanes.
Let's start by considering a big plane in relatively common use. The Boeing 747 is well known as a popular aircraft type, and it seems that the version of it they're producing now is the Boeing 747-8. This page says it has a maximum takeoff weight of 4.48105 kg and a maximum landing weight of 3.12105 kg, with a service ceiling of 1.3104 m. I'll round that to a weight of 3.5105 kg mass and 1*104 m height above the surface of the ocean.
Now, the moon. 922
Wikipedia says the moon has a mass of around 71022 kg and a distance from the center of the earth on the order of 4106 km, which is 4109 m. Earth's radius, about 6.3103 km, is about a tenth of a percent of that distance and lost in the rounding/simplification of the Moon's orbit to be circular instead of its actual eccentricity.
This means that the moon's mass is (71022 kg / 3.5105 kg =) 21017 times that of the 747. The moon's distance from the surface of the ocean is (4109 m / 1104m =) 4105 times that of the 747.
Comments on this answer note that "the amplitude of tides is proportional not to the strength of the gravity force, which is proportional to r2, but to its gradient, which is proportional to r3...a factor of 103 in distance means a factor of 109 in tidal effect." Therefore, the effect that the distance has on the amplitude would be ((4105)3 =) 6.41016.
Thus the overall effect of the 747 on tides should be (6.41016 / 21017 =) about a third of the effect of the moon. It's a back-of-the-envelope order-of-magnitude calculation, but a much larger result than I expected.
Did I mess up somewhere in the math or facts above? (If not, I'm willing to cut & paste that content into an Answer, but for now it's just showing the work I've done in arriving at this question and attempting to solve it myself.)
Now, there are many flights in the sky at any given moment, all around the world, and to a certain extent any tidal effects of one flight would be cancelled out by the effects of one or more others. However, the flight map is not completely balanced or evenly distributed north-south or east-west.
Do flights affect tides? 319