Hello Geoffrey. Yes, all the planets in the solar system revolve around the sun close to a disk-like plane with a little inclination and eccentricity. For Earth, the orbital inclination is about 7 degrees related to the Sun’s equator. The eccentricity of the orbit is 0.0167. And you’re right, the orbit does change over time and this can be recorded.
And as we observe and record everything from the Earth, we keep our Earth’s plane as the reference plane and call it the ecliptic. We observe other celestial objects relative to this ecliptic. So, for the orbital motion of the Earth relative to Sun, we can simply track the Sun’s position throughout the year. The coordinate system is called the ecliptic coordinate system. It can either be geocentric like the above case or heliocentric.
And as mentioned, there will be significant changes in the orbit over a longer time—but like in thousands of years. As it involves other planets in the solar system, it’s an n-body problem. The orbital change will be due to perturbation effects. From planets like Venus and Jupiter heavily affecting the eccentricity of the Earth. The precession of the Earth. The axial tilt. And other complex orbital perturbations along with any unexpected celestial activity that affects the solar system. We call the cyclical effect on Earth as the Milankovitch cycles. Hope this is what you are looking for.