Solar Eclipse Latitude / Longitude Calculations, Earth, Jupiter | Orbital Mechanics with Python 47

In this video we go over how to calculate the latitude and longitude coordinates of solar eclipses, using the examples of Earth with the 2017 great American eclipse and all total solar eclipses for the next 5 years, as well as Jupiter’s 2021 triple eclipse with Europa, Ganymede, and Callisto.

Link to root solvers videos:
   • Newton's Method for Root Solving | Numeric...   (math)
   • Newton's Root Solver Software | Numerical ...   (Python implementation)

Link to latitude / longitude calculations videos:
   • Latitude and Longitude Coordinates | Orbit...   (math)
   • Latitude / Longitude Coordinates Software ...   (Python implementation)

This video is building from the previous video and will go over more geometry since we are now assuming the eclipsed body to be a sphere instead of a point mass.

So in this new situation, we are going to add 2 new vectors to the analysis. One called r eclipse is going to be the vector from the center of the Earth to the intersection of the 3D cone on the surface. This is the vector that we ultimately want to calculate to then calculate latitude / longitude coordinates from it. The other called r intersect is the vector pointing from the Moon to that same point, and it is in the same direction as the sun vector but has an unknown magnitude which we’ll call sigma.

The first thing to notice here is that the vector pointing from the Moon to the Earth and these two new vectors form a closed triangle, so we can but their relationship in equation form.

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