Celestial navigation is finding your position using the stars, sun,
moon, and planets. Although easy in concept, in practice it is
complicated to determine your position on Earth; this page will
try to explain the principle, without the math.
## A FixAfix is defined as the intersection of two or more lines
of position. In piloting, a line of position or LOP
can be a compass bearing to a known point on land, such as a
lighthouse; when plotted on a chart, that bearing from the lighthouse
represents a line that your ship must be on. A crossing line of
position from another object produces a fix; additional lines of
position verify the fix by crossing on or near the intersection
point. A running fix uses a single line of position advanced
with the dead reckoning (DR) position to obtain crossing
bearings over time from a single navigation aid; similarly, LOPs
may be advanced or retarded with the DR to compensate for not having
been measured simultaneously. Due to the long time it takes to
complete a set of celestial observations, advancing and retarding
LOPs is a common feature of a celestial fix.
## The Celestial SphereTo the celestial navigator, the Earth is a perfect sphere. The stars are on thecelestial sphere-- remember globes you may
have seen with the Earth surrounded by
a clear sphere with the stars printed on it: that is the celestial
sphere. The stars are fixed upon the sphere in relation to each
other and thus are called fixed stars; 57 of them are
considered bright enough for use in celestial navigation. In fact
the fixed stars do move, but so slowly that only study of an almanac
would reveal it. Planets as a class move among the fixed
stars; the navigational planets are Mercury, Venus, Mars, Jupiter,
Saturn, the Moon, and the Sun. They confine themselves to a band
that extends 8° on either side of the ecliptic, the
apparent path that the sun follows through the sky. The ecliptic
is tilted relative to the Earth's equator due to the tilt of the
Earth's axis.
Positions on Earth are measured in
Positions on the celestial sphere have corresponding latitiude and
longitude; the
In the navigator's view of the Earth and celestial sphere, the
Earth is stationary and the celestial sphere rotates around it,
completing one rotation about every 24 hours. At this rate, the
celestial sphere rotates one degree every four minutes. Astronomers
measure celestial longitude ## The Basic ConceptImagine you are standing on the Earth, and one of the navigational stars is directly above you. If you know the time, you can use the Nautical Almanac to find the position of the star on the celestial sphere, and then the position of the spot directly beneath it on the Earth. That's your location. In this situation, if you measured the angle between the horizon and the star (using a sextant, which is merely a tool to accurately measure angles), it would be 90° (less the various corrections we will ignore for now). The line of position (LOP) for a star at an angular altitude of 90° is in fact a dot, called thegeographic position,
or GP.
Now, in your mind picture, step back until the angle of the star
above the horizon is 89°. The LOP in this case is a small
circle around the GP; someone standing anywhere on this circle
would get the same measurement of 89°.
This circular LOP is also called
a Over the years, mechanical navigational devices have been constructed to model just such a concept, where arcs representing the LOPs of stars at various altitudes were moved around a globe to derive a position; such devices ran into problems of complexity and scale. Similarly, attempts to plot the circles directly onto charts ran into problems both of scale, and of projection: the circles on the surface of a sphere would be distorted on a flat chart. What was needed was a way to accurately plot just a small segment of the circle of equal altitude: a small segment of a circle thousands of miles in diameter could accurately be represented by a straight line on a chart. ## Altitude InterceptThenavigational triangle
is a triangle formed on the surface of the Earth; its three points
are the Pole (either North or South, depending on your position),
the GP of the observed star, and your position. Knowing all three
points allows you to calculate the length of the leg from your
position to the GP, and the angle between the GP and the Pole,
which can be reduced to the GP's bearing. Now calculated by computer
or even calculator, the solving of this navigational triangle can
be done by publications called Sight Reduction Tables, which
give the solutions for whole degree positions of own ship and GP.
Interpolation could then be used to determine the exact solution.
There is a problem you may have noticed with the above procedure: it assumes own ship's position is known. Isn't that what we are trying to determine?
Very true: what is used in the calculations is the ships
The "fudged" DR is called the Now all that needs to be done is to compare the calculated value of the angle with what we actually observed. Say that the calculated angle was 60°, and the observed angle (after all the sextant corrections) was 59°. We know then that the LOP for the star will be a section of its arc, at right angles to the bearing through the AP (remember that the GP of the star is on that line of bearing, and the GP is the center of the circle that forms the LOP). We also know that there is one degree of difference between the calculated and the observed angles, which equates to 60 nautical miles. We need only plot a line at right angles to the bearing to the GP, 60 nautical miles from the AP, and we have our Line Of Position for that observation.
The question becomes, do we plot the LOP on the bearing towards
the GP of the star from the AP, or away from the GP? Remembering
our mental picture of the circular LOPs on the surface of the Earth
will help: if a star is measured at an altitude of 80° above
the horizon, it will be high in the sky and the LOP will be very
small (at 90° it would be a dot: we would be directly below
the star at its Geographic Position). At 60°, the same star
will be closer to the horizon, and the LOP would be much larger.
So, the smaller the angle above the horizon, the further away the
LOP will be from the star's GP. Applying this to our problem, if
the angle for the assumed position, our calculated angle, is 60°,
and the angle we actually measured, our observed angle,
is 59°, the actual LOP must be further from the GP than the
AP. The rule is commonly remembered by the saying, " We've done it: we've plotted a celestial Line Of Position; a line upon which our ship must have been at the time the observation was made. We need two LOPs for fix, of course, and three to five are more common: the same procedure is followed for each: decide upon an Assumed Position (it will be different for each star observed), perform the calculations and plot the LOP. Where they intersect would be the fix, although since the ship is moving between observations each LOP will need to be advanced or retarded with the DR before you can finally prick the chart.
All graphics on this page have been scanned from DMA Pub No. 9, |

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