LESSON 21:
Celestial Applications
• Learning Objectives:
– Know the information that can be
obtained from the practice of celestial
navigation at sea.
– Know the correct procedures for
computing times of sunrise, sunset, and
twilight.
Determination of Latitude
• As we have already seen,
determining position using celestial
navigation is a lot of work.
• Under certain circumstances, it is
possible to determine latitude by
using methods which are much less
time consuming.
Determination of Latitude
• A latitude line (an LOP) can obtained by
observing a body at meridian passage.
• Two bodies are commonly used for this
type of latitude determination:
– Polaris, since it is always due north (and
therefore always at meridian passage)
– The sun, when it reaches its highest altitude
during the day (Local Apparent Noon)
Determination of Latitude
• By observing a body when it is at
meridian passage, the navigation
triangle is reduced to a line, greatly
simplifying our solution.
Determination of Latitude
Latitude by Polaris
• Polaris (the “pole star”) is so named
because it lies almost directly above the
north pole.
• Colatitude and coaltitude are the same.
• As a result, when in the northern
hemisphere, Polaris may be observed,
and the altitude of Polaris is equivalent
to the observer’s latitude.
Latitude by Polaris
Latitude by Polaris
• A cutaway, side view of the earth is
helpful in showing the relationships
involved...
Latitude by Polaris
• In reality, Polaris and the celestial Pn
are not exactly coincident; Polaris
wanders a bit with respect to the
north pole.
• To account for this, a correction table
is provided in the Nautical Almanac.
Latitude by Local Apparent
Noon (LAN)
• Observation of the sun at meridian
transit (“high noon”) is a very
convenient method for determining
latitude.
• The sun latitude line thus obtained is
considered one of the most accurate
LOPs available.
Latitude by Local Apparent
Noon (LAN)
• The sun’s declination changes from
N 23.5 o to S 23.5 o in the course of
each year.
• As a result, there are a number of
different relationships possible
between the elevated celestial pole,
position of the sun, and observer’s
zenith at LAN.
Latitude by LAN
Latitude by Local Apparent
Noon (LAN)
• Now we’ll work through an example
to illustrate the concept.
• Keep in mind that some corrections
must be applied to our calculations
to come up with an accurate latitude
by LAN. Here we are just addressing
the theory behind LAN.
Determination of Gyro Error
• Gyro error by Polaris
– used in Northern latitudes between the
equator and 65 oN.
– True azimuth of Polaris is extracted
from the Nautical Almanac, and
compared to the observed azimuth of
Polaris.
Determination of Gyro Error
• Sun Amplitude Sight
– sun is observed at sunset or sunrise.
– At this time, it is easy to measure the true
azimuth of the sun, since it’s right on the
horizon.
– True azimuth can be found without using a sight
reduction form, by using either an amplitude
table or the amplitude angle formula.
Gyro Error by Sun
Amplitude
Gyro Error by Sun
Amplitude
• The previous slide showed the sun at
the time of equinox; at other times of
the year, the sun’s declination will be
above or below the equator.
Gyro Error by Sun
Amplitude
• If we’re not at the equator, the
geometry is a bit more complicated,
but the idea is the same.
Determination of Gyro Error
• Azimuth of the Sun:
– Similar to the sun amplitude sight, but
can be done any time of the day. The
true azimuth of the sun is calculated
using a sight reduction form, and
compared to the measured value of true
azimuth.
– Calculations are more involved since a
complete sight reduction is required.
Determination of Times of
Sunrise and Sunset
• Important for the navigator.
• Determines the time of twilight, both
in the morning and evening, when a
celestial fix may be obtained.
• May also be important for other
operational reasons.
• Calculation requires use the Nautical
Almanac and the DR plot.
Determination of Times of
Sunrise and Sunset
• Good examples are in your text book.
We’ll work through one in class.
• Terms with which you should be
familiar:
– Civil twilight (sun 6o below the horizon).
– Nautical twilight (sun 12o below the
horizon).