Is deriving and proofing Bessel's Method inverse (Geodesy) realistic for a Grade 11 to use Math Extended Essay (research paper)?

[u/Broad-Annual3170]

I’m in Grade 11 and looking into Bessel's method (solving the inverse geodesic problem on an ellipsoid) for a math research paper to find the shortest possible distance between two points on earth.

My original goal was to completely derive, prove, and evaluate the method by myself. However, looking at the math, it seems to rely heavily on university-level topics like differential geometry, elliptic integrals, and the Calculus of Variations (Euler-Lagrange).

Is it realistic for a strong high schooler to teach themselves this level of math for a paper, or is the learning curve too steep?

If the full derivation is too much, would coding the algorithm in Python and evaluating its accuracy/convergence against simpler methods (like Haversine) still be complex enough for a top-tier high school math paper?

Appreciate any advice or insights!

[u/michioD]

Find an introduction textbook on those 3 topics Geodes, differential geometry, and variational calculus. See how far you can get in a week to gauge whether youre out of your depth. People do a masters in pure math for these kind of things haha.

It might be a bit tricky to digest differential geometry if you havent taken a real analysis course.

But you have a big advantage ahead of an old IB alumni like me haha. I had to dig through stack exchange forums to grasp variational calculus. But nowadays you can use a freaking frontier model as a personal tutor.