I was contemplating this years ago, but I never got around to it till now.
Using nothing but this illustration
and basic math (point to point line, slope-intercept line, algebra, and trig) I figured how to calculate the 3D umbra cone. The only data I used is the Simon1994PlanetaryPositions built into Cesium itself, and Sun/Moon radius.
Pleasantly surprised to find that the cone to globe intercepts matched that found here
The 3D umbra cone is educational. It does not reach that far, and a combination of factors have to line up:
-The closer the Earth is to the Moon the better (deeper into the cone the Earth is.)
-The further the Moon is from the Sun the better (the more elongated the cone becomes.)
Going to test a couple more total eclipse dates, then finish up making a penumbra cone.
Just added 2021 Dec 04 total eclipse
It also matches up with http://eclipsetracks.org/#2021-12-04
I must say I’m very impressed by Cesium’s built-in astronomical data and shapes!
Here’s the eclipse list I’m using to find total eclipses
OK, this is the last total eclipse 3D umbra video before I add the penumbra cone. This one zips right down the middle of North America, and appears to be a good sized intersection.
As usual it matches up with http://eclipsetracks.org/#2024-04-08