Orbits are mathematically predictable ... in both directions. Using a bit of calculus, astronomers can pretty much determine the configuration of any orbit for any time period. I've got a cheapy astronomy program on my machine at home that generates night skies for any date and time over the past several thousand years and into the future several thousand years.
You know, I've got one of those too, and it didn't even occur to me. I tend to think of those as star mappers or, as you described yours -- it "generates night skies." Of course, it would have to calculate Earth's position to do that.
Duh!