Subject

Knowledge required

Competence:

Plan and conduct a passage and determine position

Knowledge of basic nautical astronomy

Solar system
Composition and dimensions of the solar system; Ability to identify planets useful for navigation;
The earth’s elliptical orbit; The eccentricity of the earth’s orbit; The inclination of the earth’s axis to the plane of the orbit and the stability of the axis and how it causes seasons; The dates of the solstices and equinoxes; The concept of the earth’s axial rotation giving day and night; The varying length of daylight through the year; Daylight and darkness conditions in various latitudes at the solstices and equinoxes; The significance of the tropics of Cancer and Capricorn of the Arctic and Antarctic circles

Celestial sphere and equinoctial system of co-ordinates
Definition of the celestial sphere; The apparent annual motion of the sun and the concept of the ecliptic; Definition of celestial poles, celestial meridians, equinoctial and the obliquity of the ecliptic; The equinoctial as a fixed reference plane and the direction of the First Point of Aries as a reference direction; The equinoctial system of co-ordinates and definition of sidereal hour angle, declination and polar distance; Ability to extract information from the star diagrams in the Nautical Almanac.

Hour angle
The concept of the earth’s axial rotation causing change in the hour angle of bodies; Definition of Greenwich Hour Angle (GHA), Local Hour Angle (LHA) and longitude, and ability to explain their relationship; The rate of change of GHA of the sun and Aries; The tabulation of SHA, GHA and declination (and “d” and “v” corrections) in the Nautical Almanac for all celestial bodies; Ability to determine the geographical position of a body for any given GMT.

Daily motion and horizontal system of co-ordinates
Definition of rational horizon, zenith, and nadir; Definition of vertical circle and prime vertical circle; Definition of elevated pole and depressed pole; Ability to prove that the altitude of the elevated pole is equal to the observer’s altitude; Definition of the observer’s upper and lower celestial meridian; Ability to identify the apparent daily path of all bodies; Definition of true altitude, azimuth and true zenith distance; The relationship between azimuth, quadrantal bearings and 360° notation bearing; Ability to recognize rising and setting points and definition of amplitude; The meaning of the term circumpolar, and the conditions necessary for a body to be circumpolar; The condition necessary for a body to cross the prime vertical; The parts of the PZX triangle; Ability to draw figures on the plane of the rational horizon and of the observer’s celestial meridian, using the equidistant projection to illustrate navigational problems and principles

Ability to use celestial bodies to determine the ship’s position

Sextant and altitude corrections
Definition of sextant altitude; Ability to demonstrate how to use a sextant; Ability to correct a sextant into which has been introduced one or more of error of perpendicularity, side error or index error; Ability to find the index error of the sextant by the horizon; How to find the index error of the sextant by the sun and stars; Ability to use the sextant for taking vertical and horizontal angles; The purpose of altitude correction; Definition of visible, sensible and rational horizon; Definition of observed latitude and true altitude; Definition of dip, refraction, semi-diameter and parallax and explain their causes; Apply index error; Apply the corrections for the items listed in the above objectives and explain the factors determining their magnitude; Ability to illustrate the effect of terrestrial refraction on the dip and distance of the sea horizon; Correct an altitude using tables in the Nautical Almanac, including reference to critical tables, interpolation tables and low-altitude correction tables; Obtain the true zenith distance from the true altitude of the body.

Amplitudes
Ability to determine the observed altitude of the sun when the true altitude is zero; The effect of latitude on the accuracy of amplitude observations; Ability to calculate the LAT and LMT on the theoretical and visible rising and setting of the sun; Ability to extract the information from the tabulation of the rising and setting of the sun in the Nautical Almanac.

Time and equation of time
Definition of the apparent solar day and what is the relationship between LHA (sun) and LAT; Definition of the sidereal day and what is a fixed interval; The reasons for the sun’s irregular rate of change of SHA and the necessity to adopt the astronomical mean sun for timekeeping purposes; Definition of the equation of time (ET) and its components; Ability to determine the ET from the Almanac and its sign of application; Definition of GMT, LMT and longitude; Definition of zone times and standard times; How to alter the ship’s time during a passage with increasing or decreasing longitude; The use of time signals;

Nautical Almanac
The information contained in general in the Nautical Almanac and in detail in the daily pages; Ability to use the tables of corrections and incremental corrections in the Nautical Almanac; Ability to find the LHA of a body, given the date, GMT and longitude of the observer; The importance of the First Point of Aries; Ability to find the LHA of Aries, given the date, GMT and longitude of the observer; What is meant by the sidereal hour angle of a star and obtain it from the Nautical Almanac; Derive the LHA of a star from the LHA of Aries and the SHA of the star; Ability to use the information in the Nautical Almanac to obtain the LMT of the meridian passage of a body to the nearest minute and interpolates for the observer’s longitude when necessary.

Ability to use celestial bodies to determine the ship’s position

Latitude by meridian altitude
Ability to apply the true zenith distance of a body when it is on the observer’s meridian to the declination of the body, to obtain the observer’s latitude; Apply these correctly when the declination and latitude have the same names or have different names; The relationship between the altitude of the elevated pole and the latitude of the observer; What is meant by a circumpolar star, and the terms upper and lower transit; Ability to find the value of the polar distance of the body, using declination; Ability to apply the polar distance to the true altitude of a body at a lower transit to find the altitude of the elevated pole and the latitude; Ability to calculate the direction of the position line and the latitude of the observer by meridian altitude.

Pole star observations
Ability to identify certain major stellar constellations and navigational stars describe their movement relative to Polaris and the movement of Polaris with change of latitude; Ability to identify Polaris; Ability to identify major constellations; Ability to describe the motion of the stars about Polaris; The relationship between the altitude of Polaris and the observer’s latitude;
Deduce from the above objective that the true altitude of Polaris can be used to find the latitude of the observer; Obtain the corrections, -1°, + a0, + a1, +a2, from Pole Star tables in the Nautical Almanac and apply them to the altitude of Polaris to find the latitude of the observer; Ability to find the true azimuth of Polaris from the tables and the direction of the position line.

Position fixing
Combine the equinoctial and horizon system of co-ordinates to determine the centre and radius of a position circle and its direction in the vicinity of a selected position; Apply the principles of a method of enabling the navigator to draw a small part of the position circle in his vicinity to at a practical problem; Ability to determine the direction of a position line through an observer and a position through which it passes; Ability to define and evaluate the co-latitude, polar distance and zenith distance and use them as the side of the PZX triangle; Ability to solve the PZX triangle to find the calculated zenith distance of the body when it is out of the meridian; Apply this calculated zenith distance to the true zenith distance of the body to find the intercept and the intercept terminal point through which to draw the position line (Marcq St. Hilaire method); Ability to determine the true azimuth of the body from tables and determine the direction of the position line; Ability to find the position of the observer at the time of the final observation, given two or more position lines with the courses and distances run between the observations

Determine position and the accuracy of resultant position fix by any means

Classify stars by apparent magnitude; Recognize stellar constellations as seen from earth; Kepler’s laws; Determine the hour angle and declination of the planets; Determine the time of visible rising and setting of the sun by use of the nautical Almanac; Determine the azimuth and hour angle of true rising and setting of the sun; Civil, nautical and astronomical twilights; The influence of latitude on the duration of twilight, including the conditions necessary for twilight all night, continuous daylight and continuous darkness; Ability to calculate the time of meridian altitude of the planets and stars; Altitude corrections for the planets and stars; The relation between time and longitude and between time and hour angle; Ability to calculate position lines by means of all the celestial bodies in any position; Ability to choose stars suitable for observation in the twilight period; Ability to identify stars by means of a star chart, a star finder and by calculations.

Subject

Knowledge required

Competence:

Plan and conduct a passage and determine position

Ability to determine the Ship’s position by Parallel, Plane and Mercator sailing

Sailings
Parallel sailing; Plane sailing; By Mercator sailing, ability to calculate course and distance between two positions; By Mercator sailing, ability to calculate the final position, given the initial position, course and distance; Why a navigation problem should be solved by using a Mercator sailing in preference to plane sailing because of the distance involved; How errors may occur in position fixing, and explains how to minimise the probability of errors; Demonstrate how erroneous position lines influence the positions.

Ability to determine the Ship’s position by Great Circle sailing

Great circle sailing
Ability to determine great circles tracks; Calculates initial course and distance of great circle track; Position of the vertex; Intermediate positions on the great circle and the course at these points; Ability to calculate the distance and time to sail 1 degree change of course;
Composite sailing; The use of gnomonic charts for plotting the great circle between two points;
Transfer the great circle to a Mercator chart; Find and apply the half convergency correction to a great-circle bearing to obtain the Mercator bearing to plot; The curve of constant bearing and calculates the direction of the position line in the vicinity of the D.R. position.