I guess the period of observation is the key variable here, since it lets you determine the normal and retrograde orbital periods that "solve" the equation. I

I guess the period of observation is the key variable here, since it lets you determine the normal and retrograde orbital periods that "solve" the equation. I don't think it's always a 10x difference, but I haven't thought too hard about the math. I think the difference depends on the relation between the observation period and calculated orbital period based on the observations. I can imagine a scenario where the difference would approach 0, the only difference being direction. For instance if your observation period is +/- 1% of an orbit, the major difference in orbit between the two predicted orbits would be direction, with only a minor difference in magnitude.