240
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`NAVIGATIONAL ASTRONOMY
`
`Earth
`equator
`poles
`meridians
`prime meridian
`parallels
`latitude
`colatitude
`longitude
`
`Figure 1527b. The horizon system of coordinates, showing measurement of altitude, zenith distance, azimuth, and
`azimuth angle.
`Ecliptic
`Horizon
`Celestial Equator
`ecliptic
`horizon
`celestial equator
`ecliptic poles
`zenith; nadir
`celestial poles
`circles of latitude
`vertical circles
`hours circle; celestial meridians
`circle of latitude through Aries
`principal or prime vertical circle
`hour circle of Aries
`parallels of latitude
`parallels of altitude
`parallels of declination
`celestial altitude
`altitude
`declination
`celestial colatitude
`zenith distance
`polar distance
`celestial longitude
`azimuth; azimuth angle; amplitude
`SHA; RA; GHA; LHA; t
`Table 1527. The four systems of celestial coordinates and their analogous terms.
`As shown in Figure 1527b, altitude is angular distance
`tables for use in celestial navigation. All points having the
`same altitude lie along a parallel of altitude.
`above the horizon. It is measured along a vertical circle,
`from 0° at the horizon through 90° at the zenith. Altitude
`Zenith distance (z) is angular distance from the
`measured from the visible horizon may exceed 90° because
`zenith, or the arc of a vertical circle between the zenith and
`of the dip of the horizon, as shown in Figure 1526. Angular
`a point on the celestial sphere. It is measured along a
`distance below the horizon, called negative altitude, is pro-
`vertical circle from 0° through 180°. It is usually considered
`vided for by including certain negative altitudes in some
`the complement of altitude. For a body above the celestial
`
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`

`NAVIGATIONAL ASTRONOMY
`
`241
`
`horizon it is equal to 90° – h and for a body below the
`celestial horizon it is equal to 90° – (– h) or 90° + h.
`The horizontal direction of a point on the celestial
`sphere, or the bearing of the geographical position, is called
`azimuth or azimuth angle depending upon the method of
`measurement. In both methods it is an arc of the horizon (or
`parallel of altitude), or an angle at the zenith. It is azimuth
`(Zn) if measured clockwise through 360°, starting at the
`north point on the horizon, and azimuth angle (Z) if
`measured either clockwise or counterclockwise through
`180°, starting at the north point of the horizon in north
`latitude and the south point of the horizon in south latitude.
`The ecliptic system is based upon the ecliptic as the
`primary great circle, analogous to the equator. The points
`90° from the ecliptic are the north and south ecliptic poles.
`The series of great circles through these poles, analogous to
`meridians, are circles of latitude. The circles parallel to the
`plane of the ecliptic, analogous to parallels on the Earth, are
`parallels of
`latitude or circles of
`longitude. Angular
`distance north or south of the ecliptic, analogous to latitude,
`is celestial
`latitude. Celestial
`longitude is measured
`eastward along the ecliptic through 360°, starting at the
`vernal equinox. This system of coordinates is of interest
`chiefly to astronomers.
`The four systems of celestial coordinates are analogous
`to each other and to the terrestrial system, although each has
`distinctions such as differences in directions, units, and lim-
`its of measurement. Table 1527 indicates the analogous
`term or terms under each system.
`1528. Diagram on the Plane of the Celestial Meridian
`From an imaginary point outside the celestial sphere
`and over the celestial equator, at such a distance that the
`view would be orthographic, the great circle appearing as
`the outer limit would be a celestial meridian. Other celestial
`meridians would appear as ellipses. The celestial equator
`would appear as a diameter 90° from the poles, and parallels
`of declination as straight lines parallel to the equator. The
`view would be similar to an orthographic map of the Earth.
`A number of useful relationships can be demonstrated
`by drawing a diagram on the plane of the celestial meridian
`showing this orthographic view. Arcs of circles can be
`substituted for the ellipses without destroying the basic
`relationships. Refer to Figure 1528a. In the lower diagram
`the circle represents the celestial meridian, QQ' the celestial
`equator, Pn and Ps the north and south celestial poles,
`respectively. If a star has a declination of 30° N, an angle of
`30° can be measured from the celestial equator, as shown.
`It could be measured either to the right or left, and would
`have been toward the south pole if the declination had been
`south. The parallel of declination is a line through this point
`and parallel to the celestial equator. The star is somewhere
`on this line (actually a circle viewed on edge).
`To locate the hour circle, draw the upper diagram so
`that Pn is directly above Pn of the lower figure (in line with
`
`the polar axis Pn-Ps), and the circle is of the same diameter
`as that of the lower figure. This is the plan view, looking
`down on the celestial sphere from the top. The circle is the
`celestial equator. Since the view is from above the north
`celestial pole, west is clockwise. The diameter QQ' is the
`celestial meridian shown as a circle in the lower diagram. If
`the right half is considered the upper branch, local hour
`angle is measured clockwise from this line to the hour
`circle, as shown. In this case the LHA is 80°. The
`intersection of the hour circle and celestial equator, point A,
`can be projected down to the lower diagram (point A') by a
`straight line parallel to the polar axis. The elliptical hour
`circle can be represented approximately by an arc of a circle
`through A', Pn, Ps. The center of this circle is somewhere
`along the celestial equator line QQ', extended if necessary.
`It is usually found by trial and error. The intersection of the
`hour circle and parallel of declination locates the star.
`Since the upper diagram serves only to locate point A' in
`the lower diagram, the two can be combined. That is, the LHA
`arc can be drawn in the lower diagram, as shown, and point A
`projected upward to A'. In practice, the upper diagram is not
`drawn, being shown here for illustrative purposes.
`In this example the star is on that half of the sphere
`toward the observer, or the western part. If LHA had been
`greater than 180°, the body would have been on the eastern
`or “back” side.
`From the east or west point over the celestial horizon,
`the orthographic view of the horizon system of coordinates
`would be similar to that of the celestial equator system from
`a point over the celestial equator, since the celestial meridian
`is also the principal vertical circle. The horizon would
`appear as a diameter, parallels of altitude as straight lines
`parallel to the horizon, the zenith and nadir as poles 90° from
`the horizon, and vertical circles as ellipses through the
`zenith and nadir, except for the principal vertical circle,
`which would appear as a circle, and the prime vertical,
`which would appear as a diameter perpendicular to the
`horizon.
`A celestial body can be located by altitude and azimuth
`in a manner similar to that used with the celestial equator
`system. If the altitude is 25°, this angle is measured from
`the horizon toward the zenith and the parallel of altitude is
`drawn as a straight line parallel to the horizon, as shown at
`hh' in the lower diagram of Figure 1528b. The plan view
`from above the zenith is shown in the upper diagram. If
`north is taken at the left, as shown, azimuths are measured
`clockwise from this point. In the figure the azimuth is 290°
`and the azimuth angle is N70°W. The vertical circle is
`located by measuring either arc. Point A thus located can be
`projected vertically downward to A' on the horizon of the
`lower diagram, and the vertical circle represented approxi-
`mately by the arc of a circle through A' and the zenith and
`nadir. The center of this circle is on NS, extended if
`necessary. The body is at the intersection of the parallel of
`altitude and the vertical circle. Since the upper diagram
`serves only to locate A' on the lower diagram, the two can
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`242
`
`NAVIGATIONAL ASTRONOMY
`
`Figure 1528a. Measurement of celestial equator system of
`coordinates.
`be combined, point A located on the lower diagram and
`projected upward to A', as shown. Since the body of the
`example has an azimuth greater than 180°, it is on the
`western or “front” side of the diagram.
`Since the celestial meridian appears the same in both
`the celestial equator and horizon systems, the two diagrams
`can be combined and, if properly oriented, a body can be
`located by one set of coordinates, and the coordinates of the
`other system can be determined by measurement.
`Refer to Figure 1528c,
`in which the black lines
`represent the celestial equator system, and the red lines the
`horizon system. By convention, the zenith is shown at the
`top and the north point of the horizon at the left. The west
`point on the horizon is at the center, and the east point
`directly behind it. In the figure the latitude is 37°N.
`Therefore, the zenith is 37° north of the celestial equator.
`Since the zenith is established at the top of the diagram, the
`equator can be found by measuring an arc of 37° toward the
`south, along the celestial meridian. If the declination is
`30°N and the LHA is 80°, the body can be located as shown
`
`Figure 1528b. Measurement of horizon system of
`coordinates.
`by the black lines, and described above.
`The altitude and azimuth can be determined by the re-
`verse process to that described above. Draw a line hh'
`through the body and parallel to the horizon, NS. The alti-
`tude, 25°, is found by measurement, as shown. Draw the arc
`of a circle through the body and the zenith and nadir. From
`A', the intersection of this arc with the horizon, draw a ver-
`tical line intersecting the circle at A. The azimuth, N70°W,
`is found by measurement, as shown. The prefix N is applied
`to agree with the latitude. The body is left (north) of ZNa,
`the prime vertical circle. The suffix W applies because the
`LHA, 80°, shows that the body is west of the meridian.
`If altitude and azimuth are given, the body is located by
`means of the red lines. The parallel of declination is then
`drawn parallel to QQ', the celestial equator, and the decli-
`nation determined by measurement. Point L' is located by
`drawing the arc of a circle through Pn, the star, and Ps.
`From L' a line is drawn perpendicular to QQ', locating L.
`The meridian angle is then found by measurement. The dec-
`lination is known to be north because the body is between
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`NAVIGATIONAL ASTRONOMY
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`243
`
`Figure 1528c. Diagram on the plane of the celestial meridian.
`
`the celestial equator and the north celestial pole. The merid-
`ian angle is west, to agree with the azimuth, and hence LHA
`is numerically the same.
`Since QQ' and PnPs are perpendicular, and ZNa and
`NS are also perpendicular, arc NPn is equal to arc ZQ. That
`the altitude of the elevated pole is equal
`to the
`is,
`declination of the zenith, which is equal to the latitude. This
`relationship is the basis of the method of determining
`latitude by an observation of Polaris.
`The diagram on the plane of the celestial meridian is
`useful
`in approximating a number of
`relationships.
`Consider Figure 1528d. The latitude of the observer (NPn
`or ZQ) is 45°N. The declination of the Sun (Q4) is 20°N.
`Neglecting the change in declination for one day, note the
`following: At sunrise, position 1, the Sun is on the horizon
`(NS), at the “back” of the diagram. Its altitude, h, is 0°. Its
`azimuth angle, Z, is the arc NA, N63°E. This is prefixed N
`to agree with the latitude and suffixed E to agree with the
`meridian angle of the Sun at sunrise. Hence, Zn = 063°. The
`amplitude, A, is the arc ZA, E27°N. The meridian angle, t,
`is the arc QL, 110°E. The suffix E is applied because the
`Sun is east of the meridian at rising. The LHA is 360° –
`110° = 250°.
`As the Sun moves upward along its parallel of
`declination, its altitude increases. It reaches position 2 at
`about 0600, when t = 90°E. At position 3 it is on the prime
`vertical, ZNa. Its azimuth angle, Z, is N90°E, and Zn =
`090°. The altitude is Nh' or Sh, 27°.
`Moving on up its parallel of declination, it arrives at
`position 4 on the celestial meridian about noon-when t and
`LHA are both 0°, by definition. On the celestial meridian a
`
`Figure 1528d. A diagram on the plane of the celestial
`meridian for lat. 45°N.
`body’s azimuth is 000° or 180°. In this case it is 180° because
`the body is south of the zenith. The maximum altitude occurs
`at meridian transit. In this case the arc S4 represents the
`maximum altitude, 65°. The zenith distance, z, is the arc Z4,
`25°. A body is not in the zenith at meridian transit unless its
`declination’s magnitude and name are the same as the
`latitude.
`Continuing on, the Sun moves downward along the
`“front” or western side of the diagram. At position 3 it is again
`on the prime vertical. The altitude is the same as when
`previously on the prime vertical, and the azimuth angle is
`numerically the same, but now measured toward the west.
`The azimuth is 270°. The Sun reaches position 2 six hours
`after meridian transit and sets at position 1. At this point, the
`azimuth angle is numerically the same as at sunrise, but
`westerly, and Zn = 360° – 63° = 297°. The amplitude is
`W27°N.
`After sunset the Sun continues on downward, along its
`parallel of declination, until it reaches position 5, on the
`lower branch of the celestial meridian, about midnight. Its
`negative altitude, arc N5, is now greatest, 25°, and its azi-
`muth is 000°. At this point it starts back up along the “back”
`of the diagram, arriving at position 1 at the next sunrise, to
`start another cycle.
`Half the cycle is from the crossing of the 90° hour cir-
`cle (the PnPs line, position 2) to the upper branch of the
`celestial meridian (position 4) and back to the PnPs line
`(position 2). When the declination and latitude have the
`same name (both north or both south), more than half the
`parallel of declination (position 1 to 4 to 1) is above the ho-
`rizon, and the body is above the horizon more than half the
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`244
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`NAVIGATIONAL ASTRONOMY
`
`time, crossing the 90° hour circle above the horizon. It rises
`and sets on the same side of the prime vertical as the elevat-
`ed pole. If the declination is of the same name but
`numerically smaller than the latitude, the body crosses the
`prime vertical above the horizon. If the declination and lat-
`itude have the same name and are numerically equal, the
`body is in the zenith at upper transit. If the declination is of
`the same name but numerically greater than the latitude, the
`body crosses the upper branch of the celestial meridian be-
`tween the zenith and elevated pole and does not cross the
`prime vertical. If the declination is of the same name as the
`latitude and complementary to it (d + L = 90°), the body is
`on the horizon at lower transit and does not set. If the dec-
`lination is of the same name as the latitude and numerically
`greater than the colatitude, the body is above the horizon
`during its entire daily cycle and has maximum and mini-
`mum altitudes. This is shown by the black dotted line in
`Figure 1528d.
`If the declination is 0° at any latitude, the body is above
`the horizon half the time, following the celestial equator
`QQ', and rises and sets on the prime vertical. If the declina-
`tion is of contrary name (one north and the other south), the
`body is above the horizon less than half the time and crosses
`the 90° hour circle below the horizon. It rises and sets on the
`opposite side of the prime vertical from the elevated pole.
`If the declination is of contrary name and numerically
`smaller than the latitude, the body crosses the prime vertical
`below the horizon. If the declination is of contrary name
`
`and numerically equal to the latitude, the body is in the na-
`dir at lower transit. If the declination is of contrary name
`and complementary to the latitude, the body is on the hori-
`zon at upper transit. If the declination is of contrary name
`and numerically greater than the colatitude, the body does
`not rise.
`All of these relationships, and those that follow, can be
`derived by means of a diagram on the plane of the celestial
`meridian. They are modified slightly by atmospheric
`refraction, height of eye, semidiameter, parallax, changes in
`declination, and apparent speed of the body along its
`diurnal circle.
`It is customary to keep the same orientation in south
`latitude, as shown in Figure 1528e. In this illustration the
`latitude is 45°S, and the declination of the body is 15°N.
`Since Ps is the elevated pole, it is shown above the southern
`horizon, with both SPs and ZQ equal to the latitude, 45°.
`The body rises at position 1, on the opposite side of the
`prime vertical from the elevated pole. It moves upward
`along its parallel of declination to position 2, on the upper
`branch of the celestial meridian, bearing north; and then it
`moves downward along the “front” of the diagram to posi-
`tion 1, where it sets. It remains above the horizon for less
`than half the time because declination and latitude are of
`contrary name. The azimuth at rising is arc NA, the ampli-
`tude ZA, and the azimuth angle SA. The altitude circle at
`meridian transit is shown at hh'.
`
`Figure 1528e. A diagram on the plane of the celestial
`meridian for lat. 45°S.
`
`Figure 1528f. Locating a point on an ellipse of a
`diagram on the plane of the celestial meridian.
`
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`

`NAVIGATIONAL ASTRONOMY
`
`245
`
`A diagram on the plane of the celestial meridian can be
`used to demonstrate the effect of a change in latitude. As the
`latitude increases, the celestial equator becomes more near-
`ly parallel to the horizon. The colatitude becomes smaller
`increasing the number of circumpolar bodies and those
`which neither rise nor set. It also increases the difference in
`the length of the days between summer and winter. At the
`poles celestial bodies circle the sky, parallel to the horizon.
`
`At the equator the 90° hour circle coincides with the hori-
`zon. Bodies rise and set vertically; and are above the
`horizon half the time. At rising and setting the amplitude is
`equal to the declination. At meridian transit the altitude is
`equal to the codeclination. As the latitude changes name,
`the same-contrary name relationship with declination re-
`verses. This accounts for the fact that one hemisphere has
`winter while the other is having summer.
`
`Measured from Measured along
`
`Measured to
`
`Units
`
`Coordinate Symbol
`
`latitude
`colatitude
`longitude
`declination
`
`L, lat.
`colat.
`λ, long.
`d, dec.
`
`polar distance
`
`p
`
`h
`
`equator
`poles
`prime meridian
`celestial equator
`
`meridian
`meridian
`parallel
`hour circle
`
`elevated pole
`
`hour circle
`
`horizon
`
`vertical circle
`
`S, N
`
`up
`
`NAVIGATIONAL COORDINATES
`Direc-
`Preci-
`tion
`sion
`0′.1
`N, S
`0′.1
`S, N
`0′.1
`E, W
`0′.1
`N, S
`0′.1
`0′.1
`0′.1
`0°.1
`0°.1
`0°.1
`0′.1
`
`parallel
`parallel
`local meridian
`parallel of
`declination
`parallel of
`declination
`parallel of
`altitude
`parallel of
`altitude
`vertical circle
`vertical circle
`body
`
`hour circle
`
`°, ′
`°, ′
`°, ′
`°, ′
`°, ′
`°, ′
`°, ′
`°
`°
`°
`°, ′
`
`down
`E
`E, W
`N, S
`
`W
`
`Maximum
`value
`90°
`90°
`180°
`90°
`180°
`90°*
`180°
`360°
`180° or 90°
`90°
`360°
`
`Labels
`
`N, S
`—
`E, W
`N, S
`—
`—
`—
`—
`N, S...E, W
`E, W...N, S
`—
`
`altitude
`zenith
`z
`distance
`Zn
`azimuth
`azimuth angle Z
`amplitude
`A
`Greenwich
`hour angle
`local hour
`angle
`meridian
`angle
`sidereal hour
`angle
`right
`ascension
`Greenwich
`mean time
`
`GHA
`
`LHA
`
`t
`
`SHA
`
`RA
`
`GMT
`
`vertical circle
`horizon
`horizon
`horizon
`parallel of
`declination
`parallel of
`declination
`parallel of
`declination
`parallel of
`declination
`parallel of
`declination
`parallel of
`declination
`
`local mean
`time
`
`LMT
`
`zone time
`
`ZT
`
`LAT
`
`parallel of
`declination
`parallel of
`declination
`
`parallel of
`declination
`
`zenith
`north
`north, south
`east, west
`Greenwich
`celestial
`meridian
`local celestial
`meridian
`local celestial
`meridian
`hour circle of
`vernal equinox
`hour circle of
`vernal equinox
`lower branch
`Greenwich
`celestial
`meridian
`lower branch
`local celestial
`meridian
`lower branch
`zone celestial
`meridian
`lower branch
`Greenwich
`Greenwich
`apparent time GAT
`celestial
`meridian
`lower branch
`parallel of
`local apparent
`local celestial
`declination
`time
`meridian
`Greenwich
`parallel of
`Greenwich
`celestial
`sidereal time GST
`declination
`meridian
`local sidereal
`parallel of
`local celestial
`LST
`time
`declination
`meridian
`*When measured from celestial horizon.
`Figure 1528g. Navigational Coordinates.
`
`W
`
`E, W
`
`W
`
`E
`
`W
`
`W
`
`W
`
`W
`
`W
`
`W
`
`W
`
`hour circle
`
`hour circle
`
`hour circle
`
`hour circle
`
`hour circle mean
`Sun
`
`hour circle mean
`Sun
`hour circle mean
`Sun
`
`hour circle
`apparent Sun
`
`hour circle
`apparent Sun
`hour circle
`vernal equinox
`hour circle
`vernal equinox
`
`°, ′
`°, ′
`°, ′
`h, m, s
`
`h, m, s
`
`h, m, s
`
`h, m, s
`
`h, m, s
`
`h, m, s
`
`h, m, s
`h, m, s
`
`0′.1
`0′.1
`0′.1
`1s
`
`1s
`
`1s
`
`1s
`
`1s
`
`1s
`
`1s
`1s
`
`360°
`180°
`360°
`24h
`
`24h
`
`24h
`
`24h
`
`24h
`
`24h
`
`24h
`24h
`
`—
`E, W
`—
`—
`
`—
`
`—
`
`—
`
`—
`
`—
`
`—
`
`—
`
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`246
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`NAVIGATIONAL ASTRONOMY
`
`The error arising from showing the hour circles and
`vertical circles as arcs of circles instead of ellipses increases
`with increased declination or altitude. More accurate results
`can be obtained by measurement of azimuth on the parallel
`of altitude instead of the horizon, and of hour angle on the
`parallel of declination instead of the celestial equator. Refer
`to Figure 1528f. The vertical circle shown is for a body hav-
`ing an azimuth angle of S60°W. The arc of a circle is shown
`in black, and the ellipse in red. The black arc is obtained by
`measurement around the horizon, locating A' by means of
`A, as previously described. The intersection of this arc with
`the altitude circle at 60° places the body at M. If a semicir-
`cle is drawn with the altitude circle as a diameter, and the
`azimuth angle measured around this, to B, a perpendicular
`to the hour circle locates the body at M', on the ellipse. By
`this method the altitude circle, rather than the horizon, is, in
`effect, rotated through 90° for the measurement. This re-
`finement is seldom used because actual values are usually
`found mathematically, the diagram on the plane of the me-
`ridian being used primarily to indicate relationships.
`With experience, one can visualize the diagram on the
`plane of the celestial meridian without making an actual
`drawing. Devices with two sets of spherical coordinates, on
`either the orthographic or stereographic projection, pivoted
`at the center, have been produced commercially to provide
`a mechanical diagram on the plane of the celestial meridian.
`However, since the diagram’s principal use is to illustrate
`certain relationships, such a device is not a necessary part
`of the navigator’s equipment.
`Figure 1528g summarizes navigation coordinate
`systems.
`1529. The Navigational Triangle
`A triangle formed by arcs of great circles of a sphere is
`called a spherical triangle. A spherical triangle on the
`celestial sphere is called a celestial triangle. The spherical
`triangle of particular significance to navigators is called the
`navigational triangle, formed by arcs of a celestial
`meridian, an hour circle, and a vertical circle. Its vertices
`are the elevated pole, the zenith, and a point on the celestial
`sphere (usually a celestial body). The terrestrial counterpart
`is also called a navigational triangle, being formed by arcs
`of two meridians and the great circle connecting two places
`on the Earth, one on each meridian. The vertices are the two
`places and a pole. In great-circle sailing these places are the
`point of departure and the destination.
`In celestial
`navigation they are the assumed position (AP) of the
`observer and the geographical position (GP) of the body
`(the point having the body in its zenith). The GP of the Sun
`is sometimes called the subsolar point, that of the Moon
`the sublunar point, that of a satellite (either natural or
`artificial) the subsatellite point, and that of a star its
`substellar or subastral point. When used to solve a
`celestial observation, either the celestial or terrestrial
`triangle may be called the astronomical triangle.
`
`The navigational triangle is shown in Figure 1529a on
`a diagram on the plane of the celestial meridian. The Earth
`is at the center, O. The star is at M, dd' is its parallel of
`declination, and hh' is its altitude circle.
`
`Figure 1529a. The navigational triangle.
`In the figure, arc QZ of the celestial meridian is the
`latitude of the observer, and PnZ, one side of the triangle, is
`the colatitude. Arc AM of the vertical circle is the altitude
`of the body, and side ZM of the triangle is the zenith
`distance, or coaltitude. Arc LM of the hour circle is the
`declination of the body, and side PnM of the triangle is the
`polar distance, or codeclination.
`The angle at the elevated pole, ZPnM, having the hour
`circle and the celestial meridian as sides, is the meridian
`angle, t. The angle at the zenith, PnZM, having the vertical
`circle and that arc of the celestial meridian, which includes
`the elevated pole, as sides, is the azimuth angle. The angle
`at the celestial body, ZMPn, having the hour circle and the
`vertical circle as sides,
`is the parallactic angle (X)
`(sometimes called the position angle), which is not
`generally used by the navigator.
`A number of problems involving the navigational tri-
`angle are encountered by the navigator, either directly or
`indirectly. Of these, the most common are:
`1. Given latitude, declination, and meridian angle, to find
`altitudeandazimuthangle.Thisisusedinthereduction
`of a celestial observation to establish a line of position.
`2. Given latitude, altitude, and azimuth angle, to find
`declination and meridian angle. This is used to
`identify an unknown celestial body.
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`Figure 1529b. The navigational triangle in perspective.
`3. Given meridian angle, declination, and altitude, to
`distance. This involves the same parts of the
`find azimuth angle. This may be used to find
`triangle as in 1, above, but in the terrestrial triangle,
`azimuth when the altitude is known.
`and hence is defined differently.
`4. Given the latitude of two places on the Earth and
`the difference of longitude between them, to find
`Both celestial and terrestrial navigational triangles are
`the initial great-circle course and the great-circle
`shown in perspective in Figure 1529b.
`IDENTIFICATION OF STARS AND PLANETS
`1530a and Figure 1532a.
`Navigational calculators or computer programs can
`identify virtually any celestial body observed, given inputs
`of DR position, azimuth, and altitude. In fact, a complete
`round of sights can be taken and solved without knowing
`the names of a single observed body. Once the data is en-
`tered, the computer identifies the bodies, solves the sights,
`
`1530. Introduction
`A basic requirement of celestial navigation is the
`ability to identify the bodies observed. This is not diffi-
`cult because relatively few stars and planets are
`commonly used for navigation, and various aids are
`available to assist
`in their identification. See Figure
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`NAVIGATIONAL ASTRONOMY
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`Figure 1530a. Navigational stars and the planets.
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`
`and plots the results. In this way, the navigator can learn the
`stars by observation instead of by rote memorization.
`No problem is encountered in the identification of
`the Sun and Moon. However, the planets can be mistaken
`for stars. A person working continually with the night
`sky recognizes a planet by its changing position among
`the relatively fixed stars. The planets are identified by
`noting their positions relative to each other, the Sun, the
`Moon, and the stars. They remain within the narrow
`limits of the zodiac, but are in almost constant motion
`relative to the stars. The magnitude and color may be
`helpful. The information needed is found in the Nautical
`Almanac. The “Planet Notes” near the front of that
`volume are particularly useful. Planets can also be
`identified by planet diagram, star finder, sky diagram, or
`by computation.
`1531. Stars
`The Nautical Almanac lists full navigational informa-
`tion on 19 first magnitude stars and 38 second magnitude
`stars, plus Polaris. Abbreviated information is listed for 115
`more. Additional stars are listed in the Astronomical Alma-
`nac and in various star catalogs. About 6,000 stars of the
`sixth magnitude or brighter (on the entire celestial sphere)
`are visible to the unaided eye on a clear, dark night.
`Stars are designated by one or more of the following
`naming systems:
`• Common Name: Most names of stars, as now used,
`were given by the ancient Arabs and some by the
`Greeks or Romans. One of the stars of the Nautical
`Almanac, Nunki, was named by the Babylonians.
`Only a relatively few stars have names. Several of
`the stars on the daily pages of the almanacs had no
`name prior to 1953.
`• Bayer’s Name: Most bright stars, including those
`with names, have been given a designation
`consisting of a Greek letter
`followed by the
`possessive form of the name of the constellation,
`such as α Cygni (Deneb, the brightest star in the
`constellation Cygnus, the swan). Roman letters are
`used when there are not enough Greek letters.
`Usually,
`the letters are assigned in order of
`brightness within the constellation; however, this is
`not always the case. For example,
`the letter
`designations of the stars in Ursa Major or the Big
`Dipper are assigned in order from the outer rim of
`the bowl to the end of the handle. This system of star
`designation was suggested by John Bayer of
`Augsburg, Germany, in 1603. All of the 173 stars
`included in the list near the back of the Nautical
`Almanac are listed by Bayer’s name, and, when
`applicable, their common name.
`
`• Flamsteed’s Number: This system assigns numbers
`to stars in each constellation, from west to east in the
`order in which they cross the celestial meridian. An
`example is 95 Leonis, the 95th star in the constel-
`lation Leo. This system was suggested by John
`Flamsteed (1646-1719).
`• Catalog Number: Stars are sometimes designated
`by the name of a star catalog and the number of the
`star as given in the catalog, such as A. G.
`Washington 632. In these catalogs, stars are listed in
`order from west to east, without regard to constel-
`lation, starting with the hour circle of the vernal
`equinox. This system is used primarily for fainter
`stars having no other designation. Navigators
`seldom have occasion to use this system.
`1532. Star Charts
`It is useful to be able to identify stars by relative position. A
`starchart(Figure1532aandFigure1532b)ishelpfulinlocating
`theserelationshipsandotherswhichmaybeuseful.Thismethod
`islimitedtoperiodsofrelativelyclear,darkskieswithlittleorno
`overcast. Stars can also be identified by the Air Almanac sky di-
`agrams,astarfinder, Pub.No. 249,orbycomputationbyhand
`or calculator.
`Star charts are based upon the celestial equator sys-
`tem of coordinates, using declination and sidereal hour
`angle (or right ascension). The zenith of the observer is at
`the intersection of the parallel of declination equal to his
`latitude, and the hour circle coinciding with his celestial
`meridian. This hour circle has an SHA equal to 360° –
`LHA
`(or RA = LHA
`). The horizon is everywhere
`90° from the zenith. A star globe is similar to a terrestrial
`sphere, but with stars (and often constellations) shown in-
`stead of geographical positions. The Nautical Almanac
`includes instructions for using this device. On a star
`globe the celestial sphere is shown as it would appear to
`an observer outside the sphere. Constellations appear re-
`versed. Star charts may show a similar view, but more
`often they are based upon the view from inside the sphere,
`as seen from the Earth. On these charts, north is at the top,
`as with maps, but east is to the left and west to the right.
`The directions seem correct when the chart is held over-
`head, with the top toward the north, so the relationship is
`similar to the sky.
`The Nautical Almanac has four star charts. The two princi-
`pal ones are on the polar azimuthal equidistant projection, one
`centered on each celestial pole. Each chart extends from its pole
`to declination 10° (same name as pole). Below each polar chart
`is an auxiliary chart on the Mercator projection, from 30°N to
`30°S.Onanyofthesecharts,thezenithcanbelocatedasindicat-
`ed, to determine which stars are overhead. The horizon is 90°
`from the zenith. The charts can also be used to determine the lo-
`cation of a star relative to surrounding stars.
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`NAVIGATIONAL ASTRONOMY
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`Figure 1532a. Star chart from Nautical Almanac.
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`Figur