You recent inquiry certainly has me thinking. I can think of two circumstances in which an unbounded runaway occurs, neither of them likely
The body is misidentified. The wrong body will yield an improper result in calculating Towards/Away and the azimuth. Continuously misidentifying the same body could result in the condition you suggest. This would be the garbage in / garbage out (GIGO) issue.
The system which is performing the updates has an algorithmic error. That is, an automated system like a star tracker may not be be reliable. Bug free software takes time and effort. If the system is buggy, then a runaway could occur. If its not automated, rather, its Johnny Sailor, then a similar condition applies. Johnny cannot make the same systemic error in each reduction. His process should follow standard practices and procedures. A simple one time arithmetic error will only cause a minor bobble. A repeated procedural error could be catastrophic.
We must further assume that the navigator ignores all other inputs. The compass is going to disagree after awhile, and perhaps other instrumentation will too. How will Johnny Sailor ignore the bearing to the body being in violent disagreement with his compass or pelorus. In the scenario suggested, this error keeps growing. This error is going to be more and more difficult to justify. "I expected the object to be 35° true, but last time it was 45°, and now its 55°. What the heck is going on??"
Further, we must not ignore the very item which permits the LoP to be approximated with a line. That is the azimuth to the body. That further restricts the length to a segment of the circumference.
Your reminder prompts an interesting observation, which I’d never considered before. If you’re not where you think you are, how accurate is a celestial heading check? In other words, if you’re using celestial to keep an inertial platform or similar aligned, what’s the chance of an unbounded runaway of position? E.g. error in position leads to error predicted azimuth leading to error in heading leading to bigger error in position leading to bigger error in predicted azimuth and heading found and so on and so forth. DaveP
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