I'd like to be able to project the position of a system body (at an arbitrary point in the future), given its orbital parameters and current location.
Would that be a straightforward formula you could share?
It's not really straightforward due to it being an eccentric orbit, plus planets move at different speeds at different points of that eccentric orbit, and planets can potentially orbit a star that orbits a second star, that orbits a third star.
It's a few hundred lines of code, including some parts you wouldn't need, such as moons and environmental changes, but I would need to figure out which parts. Essentially, I calculate the movement as degrees of arc, based on body speed and time elapsed, then calculate the distance of the planet at that point of the arc, primarily using trigonometry, although some conversions are needed for the way C# handles it. If you orbit something that orbits something else, etc. you need to calculate everything in order.