Lunar eclipse part 1

I saw part of last week's lunar eclipse but my photographs didn't work. This new camera doesn't work well in low light levels. There's a great composite image showing the stages of the eclipse at https://apod.nasa.gov/apod/ap190122.html However, the nagging question remained about why it doesn't happen every month. The shadow that the Earth casts into space is there all the time so why doesn't the Moon end up in it every month? I know that the answer is that the Moon's orbit is at an angle to the shadow but then why does it clip it some months but not others? I decided to start by calculating the length of the shadow cone that the Earth casts behind it. I used the method of similar triangles to get a length of 1.4 million km. This is the dark central shadow or umbra. The diagram has been simplified by ignoring the outer paler shadow or penumbra. The Moon is 0.4 million km from the Earth so definitely in range. Next up will be to put the Moon's orbit onto the diagram and then find out about precession.