Would there be a scientific way to determine how far Team Rocket would need to blast off to disappear into the sky? – Requested by @jc-75
Prepare for trouble, and make it double! If you are part of the pokémon fandom, you probably know Jessie, James, and Meowth’s motto by heart. Equally famous, however, is the fact that Team Rocket “blasts off” a lot. Nearly once every episode, Team Rocket is hurled into the sky, disappearing in a tiny sparkle.
Things look smaller the farther away they are: that much everyone knows. The relationship is not linear, however: something that is twice as far away does not necessarily appear twice as small. The numbers are actually related through angles and trigonometry: sines, cosines, and tangents.
Because of that, for this problem we want to use angular distances. Angular distance is a measurement of how much of your field of vision something covers. A full circle is 360 degrees. A full moon, for example, has an angular diameter of about 0.5 degrees: it covers half a degree in the sky.
Angles can be divided up into smaller units. There are 60 arcminutes in one degree, and 60 arcseconds in one arcminute. The human eye has an angular resolution of 1 arcminute (0.02 degrees). That is the smallest thing we can see in the sky: If something covers less than 1 arcminute, or eye can no longer detect it and it effectively disappears from view, like Team Rocket fading into the sky.
So: how far away does Team Rocket have to be to cover less than 1 arcminute in angular distance? I can’t find any official heights for Jessie and James, so I will estimate 6′0″ (1.8 meters) as an upper limit. After that, it’s just about drawing triangles.
Using 1 arcminute as the angular distance and 1.8 m as the height, you can easily solve for distance. Team Rocket effectively disappears at a distance of 6188 meters (3.84 miles).
Angular resolution is dependent on the size of the eyeball, so pokémon with large eyes like Claydol or Froakie would be able to see Team Rocket farther away than that. But for humans, that’s how far Team Rocket needs to blast off to disappear.