I would like to be able calculate (or at least download some time-series data of) the position of the Earth on it's orbit at given date. For my purposes, it would be sufficient to account for the first and second Kepler's laws within the range of one Julian year (but any refinement would be welcome). So essentially, I would like to have a function $f(t) = (r, θ)$ where $t$ is date represented as the elapsed time since a selected referential event (I assume a perihelion would be the natural choice, but it could as well be a solstice, New year etc) and $(r, θ)$ are the polar coordinates of the Earth (preferably relative to the Sun as a focus). How would I do that? I thought this would be a standard problem, but I have failed to google it.
you obtain the position of the earth in its orbit on a given date and time by use of a resource called an ephemeris, which for example lets NASA plan space missions that require years to complete. Navigators who use celestial navigation do that job with an ephemeris; in the early days of exploration an ephemeris was a hard-bound book but now it can be a sophisticated computer program.