### Self Assessment 8

#### § 29 – 31

Use the ANC N.A. pamphlet extracts and Sight Reduction Tables for Marine Navigation NP 401 (H.O. 229) Vol. 4 where appropriate. For Plotting question use the ANC Sight Form and Astro Plotting Sheets.

THE MOON AND *POLARIS

106. With reference to the Moon, explain the meaning of:—

a. Lunation

A Lunation (or Lunar Month) is the time taken by the Moon to complete one revolution round the celestial sphere with reference to the Sun, and is the interval between successive New Moons. Because the Sun moves eastward about 1° and the Moon 13° per day across the celestial sphere, the daily separation amounts to about 12° (12°.2). A lunation therefore takes 360/12.2 days approximately and its average value is 29 days, 12 hrs, 44 mins (although this can vary as much as 13 hours.

b. Barycentre

The barycentre is the common centre of gravity around which the Earth and the Moon both revolve. It lies about 1000 miles inside the Earth on the line joining the centres of the Earth and the Moon.

c. Terminator

The Terminator is the curved line which separates the illuminated from dark sector of the Noon as seen from Earth.

d. Perigee

Perigee is the point on the Moon’s orbit which lies closest to the Earth (about 222,000 miles) as opposed to apogee, the point furthest from the Earth (where the Moon is about 253,000 miles distant).

107. Again with reference to the Moon, explain the difference between conjunction and opposition.

The Moon is in conjunction when both the Sun and the Moon are on the observer’s upper meridian (New Noon) and the Moon’s illuminated hemisphere is directed away from the Earth. It is in opposition when the Moon is on the observer’s upper meridian, the Sun is on the observer’s lower meridian and the Moon’s illuminated hemisphere is facing the Earth (Full Moon).

108. When it is not immediately apparent which limb of the Moon should be observed for determining the altitude, how would you decide which limb to observe?

To decide which of the Moon’s limbs to observe, bear in mind: that a straight line which joins the ends of the terminator [see l(c) above] is at right angles to the direction of the Sun from the Noon, and you should always observe the limb nearest to the Sun, and when the Moon’s age is between 0 and 14 days (between New and Full Moon) the western limb should be observed, and when its age is between 14 and 28 days, the eastern limb should be observed.

109. In correcting the Moon’s obs. Alt., explain why it is necessary to take account of:

a. the augmentation of the Moon’s semi-diameter, and

Because of the Moon’s proximity to the Earth it is perceptibly closer to an observer when at the observer’s zenith than when on the horizon, so that its apparent diameter at the zenith appears larger than when on the horizon and proportionately so at intermediate altitudes. The value tabulated as the Moon’s semi-diameter in the NA is the angle at the Earth’s centre subtended by the radius of the Noon, which is always less than the semi-diameter observed from the Earth’s surface. This error can be adjusted by a correction called the Augmentation of the Moons Semi-Diameter in all volumes of Nautical Tables.

b. the reduction of the Moon’s horizontal parallax for the terrestrial spheroid.

The horizontal parallax of the Moon is tabulated in the NA as the angle subtended at the Moon’s centre by the equatorial radius of the Earth. Because the Earth’s equatorial radius is greater than the polar radius, the Moon’s HP is greatest on the equator and decreases with Latitude. A correction for this discrepancy can be found in Nautical Tables as Reduction of the Moon’s Horizontal Parallax.

c. Explain why *Polaris is not readily identified at morning and evening twilight and how you would overcome this difficulty.

Because *Polaris is not a very bright star (2.2 mag) it cannot easily be seen by eye when the horizon is sufficiently distinct for an accurate observation. To locate *Polaris, set the DR or EP Latitude as altitude on the sextant and sweep the northern horizon until the star is found. More accurately, add 1° to the DR Latitude and subtract correction ao from the Pole Star Tables in the N.A. for the approximate altitude to set on the sextant.

SPECIAL OBSERVATIONS

110. On Jan 02nd 199X on a yacht bound from Rhodes to Alexandria in D.R. Lat 32°55’N, Long. 28°27’E a compass bearing of the Sun at true Sunrise gave 115°C. Find the compass error and the Deviation for the vessel’s heading if the Variation was 5°E.

111.   On Jul 04th 199X between Cape Horn and Buenos Aires in D.R. Lat 45°10’S, Long.059°54’W, At 22:44 (Zone +4) a compass bearing of *Spica gave 285°C at 02h 44m 07s D.W.T.. Find the compass error and Deviation for the vessel’s heading if the Var = 2°E.

112.  On Jan 21st 199X from a small craft in the Baltic Sea in DR Lat 55°47’N, Long 19°55’E, the D.W.T. was 07h 11m 56s when the sextant altitude of *Polaris was 55°18′.2 and its compass bearing was 356°C.

a. Find the vessel’s Latitude if the deck watch was correct on G.M.T., the I.E. of the sextant was 1′.5 on the arc. and the HE of observer was 4.6 metres.

b. Find the compass error and Deviation for the vessel’s heading if the Variation was 1°E.

The Sight Form Calculation for these two observations is shown in fig. 61-5 and the Plot for the observed position is shown on fig. 61-6-7. Clearly, since the L.H.A. of Mars ♂ was zero, the planet was on the meridian at the time of this observation.

Observed Position At 17:56 (Z+4) = 50° 20’S, 058° 22’W

113.  Shortly after sunset on Sep 16th 199X the skipper of a yacht north of the Falkland Islands in E.P. Lat 50°25’S, Long. 058°15’W observed the sextant altitude of the Moon’s lower limb ☾ 51°47′.1 at D.W.T. 21h 53m 52s and Mars ♂ 65°58′.3 at DWT 21h 56m 04s. Find the yacht’s observed position at 1756 (Z +4) if the I.E. of the sextant was 1′.5 off the arc, the D.W.E. 49s slow and the H.E. 3.9m.

114.  At approximately 03:45 (Z+2) Jul 04th 199X a yacht bound from Bermuda to Plymouthwas in D.R. Lat 45°01’N, Long. 023°59’W steering 060°T and making good 6 knots in a current setting 100° at ¾ knot. The sext alt of the Moon’s upper limb when on the meridian was found to be 37°10′ when the Log read 102. At 0645 (Z +2), Log reading 118, the sext alt of the Moon’s upper limb was found to be 24°41′.0 when the chronometer which was 15s fast at noon 2 June 199X and gaining 0.7s daily, read 08h 46m 00s. The I.E. of the sextant was -2′.1 and the observer’s H.E. 3.1 metres.

a. At what time was the meridian altitude of the Moon observed?

b. Plot the yacht’s position at 06:45 ZT

The Sight Form calculation for the 06:45 observation is shown in fig: 61-5 and the Plot for the Observed Position at 06:45 is given in fig: 61-7.

The Observed Position at 06:45 is  Lat 45° 05’N Long 23° 29’W

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