I am studying the Apollo Guidance, specifically the derivation of guidance equation. While laying the baseline, a Target-referenced time (T) is chosen as time variable for guidance calculation of the trajectory evolving backward in time from landing target. T remains negative at all points before landing. In general sense, I understand back propagation however w.r.t. Guidance I dont understand this:

It is convenient to think of the reference trajectory as evolving backwards in time from the target point, with the time variable T reaching zero at the target point and negative prior to that point. Thus target-referenced time (T) is to be distinguished from clock-time (t). Because guidance gains would become unbounded, the target point is never reached. Instead, a guided phase is terminated at a negative time T and the succeeding phase is started. Both the terminus and the target point lie on the reference trajectory, but the target point lies beyond the portion that is actually flown.

Klumpp, A. R., “Apollo Lunar Descent Guidance,” Automatica, Vol. 10, No. 2, 1974, pp. 133–146.

What is meant by and how would guidance gains become unbounded?

What is meant in the last sentence specifically in " ... target point lies beyond the portion that is actually flown"?


1 Answer 1


Because some of the terms in the guidance equations divide by time-to-go and/or the square of time-to-go, relatively small input (sensor) errors can yield large effects, causing large steering oscillations at the end of the run. The early switchover to the next phase just avoids this effect.

"The part actually flown" means the part flown under that segment of the guidance program.


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