Would anyone be able to offer some advice on plotting the geocentric orbit of a planet (Venus) and getting a result in vector format?

Title says it all, looking for a vector path or a way to plot [Venus’s geocentric orbit.](https://en.m.wikipedia.org/wiki/File:Venus_geocentric_orbit_curve_simplified_Line_%28pentagram%29.svg) I’m coming to you because I’m an artist, not a scientist. I’ve been going nuts trying to find a good version but the ones on Wikipedia are imperfect which is giving me some problems (logo design) and obviously Shutterstock is pretty far off. And the terms vector and graph are really screwing with my search results. [I’ve found the equation for the path](https://eqnoftheday.com/2017/03/03/the-pentagram-of-venus/) but I’m genuinely not sure what to do with it, as far as I can tell I can’t do this in Illustrator (I’d love to be wrong but I don’t expect an answer to that here).

idk I’ll take any advice I can get. I’m prepared to figure out how to do this by hand but plotting and outputting a vector line would be ideal. Thanks in advance and sorry if this isn’t the right place to ask this.