# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**MOO MOB and Stationary observer**

**From:**Andrés Ruiz

**Date:**2018 Mar 22, 19:19 +0100

Coincidentally in a few weeks I have been consulted several times about the same topic, which came from members of NavList. Coincidences of time and space… J. I usually tell them it is better to start a new topic and talk about it in common, but.

It is about how to correct the change in position of the observed body, and also, in some cases about how to correct the change in position of the observer.

Let me explain it!

If **SOG** is the modulus of the observer’s
velocity vector and **Δt** is the difference
in time between the observations, one have:

Some recent publications use only the term fix, so using classic lexicon, these different cases are:

· Fix - 1, 2, 3

· Running Fix - 4

· Stationary observer – 1, 2

With the hypothesis that the speed in constant, SOG = cte, the mathematical basis is that in the differential equation of motion the partial derivatives en case 1, 2 & 3are cancelled.

Should the Nautical Almanac is used in order to obtain at the time of each sight the declination and the GHA of the observed body, the motion of the body is automatically corrected. But it is absolutely necessary to correct the effect of movement of theobserver.

What does “PUB. NO. 249 - SIGHT REDUCTION TABLES FOR AIR NAVIGATION” say?

Motion of
the observer (**MOO**). If it is desired
to get a fix from two or more observations, the resulting position lines must
be reduced to a common time, usually the time of one of them. This may be done
in two ways: the position lines of observations made earlier or later than this
time may be transferred on the plotting chart by the motion of the aircraft in
the time-interval concerned, or the corrected sextant altitudes (or intercepts)
may be adjusted to allow for the motion of the aircraft.

Motion of the
body (**MOB**). If the time of
observation differs from that used to obtain the tabular value of LHA, the entry
may still be used if a correction for the motion of the body (due to the
rotation of the Earth) in the time interval is applied to the altitude (or
intercept). Table 2, on page (i), provides for this correction. It enables
observations made at different times to be reduced and plotted as if they were
made simultaneously, and it thus facilitates precomputation from the Air
Almanac. Since the time used for reduction is normally the time at which the
fix is desired, it is convenient to combine the corrections for motion of the
body with those for the motion of the observer, as the time intervals are the
same.