Self Assessment 4
§ 14 – 17
ALTITUDES AND THE ASTRO—NAVIGATIONAL TRIANGLE
63. Explain how to take a sextant altitude of
a. the Sun
b. a star or planet.
In measuring the sextant altitude of either (a) The Sun or (b) a star or planet as described below the observer should adopt a comfortable stance, feet and legs firmly braced with the upper part of the body free to move, in a sheltered place protected from spray, preferably on the centreline of the yacht.
To observe the Sun ,set the shades and focus the telescope as required, aim the sextant at the horizon directly beneath the Sun and move the Index Bar slowly backwards and forwards until the Sun is located when the index Bar should then be moved forwards smoothly until the Sun is near the horizon, clamped, and exact contact between Sun and horizon made with the micrometer or tangent screw. Note the exact time, the sextant reading and the reading of the vessel’s log (distance meter).
To observe a Star or Planet no shades are required but the telescope should be focused as required and the body observed exactly as described for the Sun in (a) above except that contact is made by the horizon cutting the centre of the observed body. If difficulty is experienced in locating the required body, the sextant may be inverted with the Index Bar set at zero and the telescope pointed straight at the star or planet while the Index Bar is moved slowly away until the horizon appears near the body. The sextant is then held normally while final contact is made between body and horizon with the micrometer drum or tangent screw.
64. Draw a diagram indicating the three horizons and explain it.
65. Define each of the four altitudes, explaining the relationship of each altitude to each horizon.
The adjacent figure represents a plane through an observer A. a celestial body X and the centre of the Earth. C.
The three horizons are: –
Visible Horizon AVH1 – circle bounding observer’s view.
Sensible Horizon SAH2 – the horizontal plane through the observer’s eye.
Celestial Horizon RCH3 – the horizontal plane through centre of Earth parallel to Sensible Horizon.
The four altitudes for an observer whose height of eye is at A and who observes the celestial body X are:
The Sextant Altitude – angle XAV uncorrected for Index Error of Sextant }*
The Observed Altitude – angle XAV after correction for Index Error of sextant }*
The Apparent Altitude – angle XAS — altitude of body above the Sensible Horizon
The True Altitude – angle XCR — altitude of body above Celestial Horizon.
* altitude above visible horizon
66. What is a so—called ‘circumpolar body‘?
67. Under what circumstances will a body be visible at its lower transit?
A Circumpolar body is one whose transits across an observer’s meridian are both visible above the horizon (i.e., both lower transit and upper transit).
The lower transit of a body is visible when the Latitude of the observer is greater than the Polar Distance of the body.
68. Why is the celestial triangle PZX so important in nautical astronomy?
69. Name and define each of the three sides of the PZX triangle, and the two angles ZPX and PZX.
The PZX triangle is important because it relates the celestial position of a body at any given instant of time using the equinoctial system (as given in ‘The Nautical Almanac’) with its position using the horizon system (as observed by the navigator).
The parts of the PZX triangle are:
Side PX : the Polar Distance or arc of a celestial meridian between the celestial body and the elevated pole.
Side ZX : the Zenith Distance or angular distance of the celestial body from the observer’s zenith measured on the vertical circle through the body.
Side PZ : the Co-Latitude or arc of a celestial meridian between the observer’s zenith and the elevated pole.
Angle P (ZPX) is the Local Hour Angle (LHA) or the observed body.
Angle Z (PZX) is the Azimuth of the observed body.
70. How can a navigator find the value of each of the three sides of the PZX triangle?
The values of the PZX triangle sides are found as follows:
Side PZ (Polar Distance) = 9O° ± Declination (as found from the Nautical Almanac)
Side ZX (Zenith Distance) = 90° — True Altitude of observed body
Side PZ (Co—Latitude) = 90° — Latitude (of vessel’s EP or DR position)
TRUE ALTITUDES AND LATITUDE BY MERIDIAN ALTITUDE
71. On Dec 03rd l99X sextant measurements of the Sun’s diameter gave 33′.3 on the arc and 31′.7 off the arc. Later that day using the same sextant the altitude of the Sun’s upper limb was found to be 47° 10′.0 when the height of eye (HE) was 2.3m. What was the Sun’s true altitude at this time?
72. For each of the sextant altitudes and celestial bodies given below, find the observed altitude, apparent altitude and true altitude.
a. Sun’s lower limb 35° 15′.5, IE 3.1’ off the arc, HE 4.6m, Feb 05th .
b. Planet Mars ♂ 29° 14′.9, IE 0.7’ on the arc, HE 2.7m, May 06th .
c. Sun’s upper limb 12°46′.7. IE -2.2’, HE 3.9m, Sep 05th .
d. *Vega 67° 53′.0, IE +2.1’, HE 3.7m, Dec 09th .
e. Planet Venus ♀38° 17′.3. IE + 1.1’, HE 2.3m, Feb 09th .
73. Find the Geographical Position of:
a. the Sun at 15h 09m 23s GMT on Jan 20th 199X.
b. Venus ♀at 07h 45m 39s GMT on Jul 04th l99X.
74. Draw a figure on the Equidistant Projection showing the diurnal path of a circumpolar body of Declination 57° N if the observer’s Latitude is 48°N.
Diurnal path of circumpolar body of Declination 57º N for an observer in Latitude 48 Nº.
75. For each of a-b-c below find the GMT of meridian passage, the vessel’s Latitude, and draw a figure on the equidistant projection to illustrate the problem.
a. Jan 21st l99X, East of Japan in EP Lat 40° 17’N, Long 156° 11’E sextant mer alt ☉ 29°3O’.1, IE + 1′.5, H of E 3.7 metres.
b. Jul 05th 199X, approaching New York in EP Lat 41° 10’N, Long 55° 00.0’W Sextant mer alt ☉ 71° 19′.5, IE — 1′.3, H of E 12ft.
Jan 03rd 199X, in the South Pacific Ocean in EP Lat 8°55’S, Long 178° 12’E sextant mer alt 76° 22′.3, IE nil, H of E 4.6 metres.
76. Find the GEOGRAPHICAL POSITION of: –
a. The Sun at 15h. 09m. 23s. G.M.T. on Jan 20th 199X
∴ G.P. ʘ = Lat 20º 04.2’ S Long 44º 33.7’ W
b. Venus ♀at 07h. 45m. 39s. G.M.T. on Jul 04th 199X