Pies, in your post #30, your math you use will tell you the physical size of the Sun, the distance to the Sun from Earth, the Moon's physical size, and distance from Earth, but this may not be the correct solution though for the correct answers as modern astronomy uses. That is the whole point of your discussion as I see it. You are trying to show that the modern, heliocentric solar system astronomy does not know the true distances and sizes here for the Sun and Moon, same as the Flat Earth Society Moon and Sun wiki do. The umbra size is calculated and known before the total solar eclipse event takes place, e.g. the 2017 total solar eclipse as published by many, including the path covered over the Earth and time predictions when the umbra will cover a specific location on Earth so folks living in that area can see a total solar eclipse event. The umbra size will always be a smaller area on Earth than the diameter of the Moon or the surface area of the Earth. This involves much spherical trigonometry, differential calculus for the shape of the Earth, Moon's orbit, Earth's rotation velocity, Moon orbital velocity, etc. No matter though, the umbra size will be much smaller area and as measured from the mean distance of the Moon, 384401 km, the umbra size projected on Earth falls within 1 to 9 arcminute range or so. Your math suggest an umbra size on Earth closer to 32 arcminute angular size is what astronomy should observe, calculate and predict. This is something that is not documented or observed in astronomy. Just to demonstrate, the Earth as measured from the Moon using 384401 km mean distance, the Earth's angular size is about 108 arcminute across or close to 1.8-degrees. In astronomy, there are no giant Moon umbra(s) moving over the Earth during a total solar eclipse as your math shows.

This report may help,

https://www.space.com/17638-how-big-is-earth.html so the Earth diameter is 12756 km and observed from the Moon at 384401 km, angular size ~ 114 arcminute. The Moon's umbra on Earth during a total solar eclipse will be a much smaller angular size than 108 to 114 arcminute, but not 32 arcminute size. Smaller still using the correct solution.