Spaceplan Guidance: Non-cardinal headings spiral towards poles

[nhnifong]

I recently tried using spaceplane guidance to fly a slow, unplanned airplane from one island on laythe to another, almost on the opposite side of the planet. The optimal path was a great circle arcing across the northern hemisphere. However, I had to adjust the heading hold every few minutes because it was moving relative to the great circle trajectory I was attempting to follow.

So it occurs to me that only 90 and 180 would go in straight lines. All the other headings terminate at the poles. 45 degrees for example will spiral northward around the planet.

What would have been more useful in this situation is a target or waypoint hold.