Celestial Applications

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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.

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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.

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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)

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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.

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Determination of Latitude
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Latitude by Polaris

• Polaris (the pole star) is so named because it
  lies almost directly above the north pole.
• Colatitude and coaltitude are one and the same.
• As a result, when in the northern hemisphere,
  Polaris may be observed, and the altitude of
  Polaris is equivalent to the observers latitude.

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Latitude by Polaris
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Latitude by Polaris

• A cutaway, side view of the earth is helpful in
  showing the relationships involved...

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Latitude by Polaris

• In reality, of course, 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.

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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.

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Latitude by Local Apparent Noon (LAN)

• The suns 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
  observers zenith at LAN.

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Latitude by LAN
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Latitude by Local Apparent Noon (LAN)

• Now well work through an example to illustrate
  the concept.
• Keep in mind that, in reality, 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.

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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.

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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 its 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.

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Gyro Error by Sun Amplitude
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Gyro Error by Sun Amplitude

• The previous slide showed the sun at the time of
  equinox at other times of the year, the suns
  declination will be above or below the equator.

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Gyro Error by Sun Amplitude

• Obviously, if were not at the equator, the
  geometry is a bit more complicated, but the idea
  is the same.

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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.

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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.

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Determination of Times of Sunrise and Sunset

• Good examples are in your text book. Well work
  through one in class.
• Terms with which you should be familiar
• Civil twilight (sun6o below the horizon).
• Nautical twilight (sun 12o below the horizon).