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