Gravity field determination - Least squares revisited

Illustrated examples

This is the place where you will see the power of diagonalization in action (or SVD, for "Singular Value Decomposition"). We have prepared three illustration cases for you in the form of articles on the Stellar Space Studies website.

Focusing efforts in the right direction (eigenvectors) - Part 1. In this article, you will see the difference between a gravity field solution determined in the vector space of the spherical harmonics up to degree 50, and a gravity field solution determined in the vector space generated by the first 2601 eigenvectors of a normal matrix up to degree 80. The dimensions of the spaces are the same (2601), but the results are very different.
Focusing efforts in the right direction (eigenvectors) - Part 2. In this article, you will see the detailed pictures of the eigenvectors, compared to the canonical basis. You will understand exactly where the noise comes from, and why the previous results were so magical.
Focusing efforts in the right direction (eigenvectors) - Part 3: Gravity field and the Cullinan diamond. In this article, you will finally see the corrections, the paraboloid with its steep and flat axes, and the decisive impact of the truncation. This is the art of turning a raw diamond into a piece of jewellery.

And if you like the topic, you can find many more gravity field related articles on the Stellar Space Studies website. You can learn everything about gravity field, spherical harmonics, future missions, and so on...

Enjoy!

Thank you

This is already the end of this course. Thank you very much for joining us on this journey. We hope that you enjoyed it as much as we did, and that it will give you inspiration for your own research. Why not try to apply this to your own cases, and see what comes out of it? You might be pleasantly surprised at the results!

And if you liked this course, don't forget to:

Send us a hello at hello@stellarspacestudies.com. Your comments and suggestions are always appreciated.
Share it with your friends. If you know someone who loves maths or uses the least squares method, send them the link. This website is much more fun than a pure LaTeX document, so come back here to see us with your friends. Spread the word!

Mathematically yours,
The Stellar Space Studies team.

This work was done with and is dedicated to our good friend Abou.