A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2019 Dec 31, 17:08 -0800
Now let's talk about the "Motion Of the Observer" (MOO) adjustment. Every fix in the air is a
running fix because the aircraft moves a considerable distance between the first and last sight.
Assuming the normal eight minute spacing between the first and last shot, a slow
airplane, say 100 knots, will have traveled 14 NM while a 450 knot plane will have traveled 60
NM. In marine practice the navigator will advance the earlier LOPs to cross them with the last
shot when plotting a running fix. The MOO adjustment accomplishes the same thing.
Due to the slow speeds and the short period between the shots, this is not necessary for normal
As an example of how this works, consider a running fix on a ship. A sun shot taken at 1000Z
results in an observed altitude, Ho, of 35º 55'. After doing the normal sight reduction the
navigator ends up with an Hc of 35º 45' at the chosen “assumed position” (A.P) and an azimuth
(Zn) of 130º. This results in an intercept of 10 NM toward the body, 130º. To plot this LOP you
draw the azimuth line from the A.P and measure off the 10 NM intercept toward the sun and plot
the LOP perpendicular to the Zn.
Then, two hours later at 1200Z you take another altitude of the sun and to obtain a 1200Z
running fix you must advance the 1000Z sun line to cross the 1200Z line. There are three ways to
advance the LOP. First, you can pick any spot on the LOP and lay off a line in the direction of
travel of the vessel, measure off the distance traveled along that line, make a mark there and then
draw a line through that mark that is parallel to the existing LOP and label the advanced LOP
"1000-1200Z SUN." A second way is to advance each end of the LOP and then just draw a line
through these two points, this avoids having to measure the azimuth when laying down the
advanced line. The third way is to advance the original A.P and then from the ADVANCED A.P.
plot the LOP using the ORIGINAL intercept and Zn. Any of these methods will produce the
same advanced LOP.
Now let's consider a simple case. Suppose the vessel's course is the same as the Zn, in this case,
130º and the vessel's speed is 20 knots meaning it has traveled 40 NM in the two hour period. In
this simple case we can just extend the Zn line an additional 40 NM and then plot the advanced
LOP at that point. So, the LOP is now 50 NM from the original A.P., the original 10 NM
intercept plus the additional 40 NM that the vessel has traveled on the same course as the
azimuth. Since we have no interest in actually plotting the 1000Z LOP, as we are just
planning on having the 1200Z running fix, we can skip drawing the earlier LOP and just plot the
advanced LOP by adding the distance traveled to the length of the original intercept to get a total
intercept now of 50 NM and using that adjusted intercept to plot the advanced LOP using
the ORIGINAL A.P. This method also creates the exact same advanced LOP as the other three
methods. This last described procedure is how the MOO table is used.
Look now at the MOO table, page 4. Assume now we are in a 300 knot airplane and the first
sight is taken at 1152Z, eight minutes prior to the planned fix time. At the top of the column
marked "300" knots ground speed you find the number "20" showing that the plane will travel 20
NM (and so the altitude of the body should change by 20 minutes of arc) in a 4 minute period.
Also notice that the top row of values are marked for a relative Zn of 000º meaning the body is
directly ahead, as in our example. The plane will obviously travel 40NM in the normal 8 minute
period from the first to the last shot of a three star fix. The sign convention is the same as
that for the MOB table so simply draw a horizontal line across the center of the table and place a
big minus symbol for the top half and a big plus mark for the bottom of the table. If the body is in
front of you the sign is minus and the sign is plus if the body is behind you. With these markings
we can take out of the table a minus 20' value for our example and double it to have a total MOO
adjustment of minus 40' to apply to the Hc.
Let's do the math. Hc of 35º 45' minus 40' gives us an adjusted Hc of 35º 05'. Since the Ho was
35º 55' we now compute an intercept of 50 NM TOWARD and plot the LOP using the
ORIGINAL A.P. and Zn and this new adjusted intercept. You can see that this method produces
the same advanced LOP as the previous methods.
In the more normal case the course will not be the same as the Zn so the change in altitude will
be less since the maximum change occurs when the body is straight ahead or directly behind the
aircraft. The change in altitude due to MOO is computed by the cosine of the
difference between the Zn and the course ( "track" in the air), the relative Zn multiplied by the
maximum change possible, the zero degree relative Zn case. So, in our example, if the track of
the plane (course) were 070º then the relative Zn would be 60º (130̊-70̊=60̊) and we would
look in the table for that relative Zn in the 300 knot column and take out a value of 10' which we
would expect since the cosine of 60º is .5 so the MOO should be one half of the maximum
possible for a 300 knot ground speed.