My apologies if this is too naive a question. I keep wondering what steered people away from assuming the new moon to be an eclipse and hence go on to figure the angular difference in the orbital planes. I'm trying to understand the hypothesis and the observations regarding the same.

The search on this question just results in the explanation of the angular differences in the orbital planes. I'm curious how through observations, the scientists concluded the new new moon is not the earth's shadow on the moon?

Through simple home-made experiments, are there ways to identify the relative positions of the earth, sun and moon? Like shadow experiments for e.g.