I'm writing an orbital simulator program and I'm struggling to apply the two-body problem.
To simulate it properly I need values for the $x$, $y$, and $z$ coordinates for both bodies. Ideally, these would be in the form of:
x1(t) = ... y1(t) = ... z1(t) = ...
x2(t) = ... y2(t) = ... z2(t) = ...
Looking around online I'm seeing mixed messages about whether an analytical solution as a function of time is possible but no definitive answer. What are these equations or, if they don't exist, how can I simulate a 2-body orbit?
