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.
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 • 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 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 • 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).