It definitely extends to infinity. Why would it stop somewhere?

Why wouldn't it? If you think most people would consider a satellite passing overhead, an airplane flying high overhead, the Moon, the Sun, other objects in space etc. when directly overhead to be "in" a park, I think you'd be mistaken. And the results here bear that out, at least to the limited extent there were relevant questions.

Similarly a subway train passing underneath the park is not "in" the park, nor are vehicles that are at the antipode of the park on the polar opposite side of the Earth.

So you're saying that, for parks in there right location, for brief periods of time, parts of other plants, stars, and space are "part of the park"