Satellites and Polynomials

Contributions from Legendre

I wrote a couple blog posts today, one to start my day and one to wrap it up.

The first post was about the J2 effect, a small effect on the motion of a satellite that has a large cumulative effect over time. This effect is due to the fact that the earth is not exactly a sphere but rather an oblate spheroid; the diameter through the equator is a few miles longer than the diameter through the poles.

The J2 effect is named after the largest coefficient in a series for describing the gravitational potential of an axially symmetric planet. This series was discovered by Legendre and involves what we now call Legendre polynomials.

Legendre polynomials were the topic of this evening’s post, a brief introduction to these polynomials and how they are used in applications. If you’re familiar with orthogonal polynomials, you may still want to read the post for a geometric application you may not have seen before.

Enjoy.