EK General exam help for Ocean Navigators from Martin's Marine Engineering Page

Certification Assistance for Canadian Navigators

Canadian Ocean Navigator 
Celestial Navigation Questions

Brought to you by www.dieselduck.net comments to webmaster@dieselduck.net
Transport Canada has ask us to advise users of this webpage to keep in mind that these questions are not the exact questions found in their exams. Martin's Marine Engineering Page - www.dieselduck.net is not affiliated with Transport Canada and these questions have been gathered from various sources.

Authored by Mr. Pete Pedersen. Pete held an ON1 ticket and used to teach the MED courses at PMTI (now BCIT Marine Campus) in North Vancouver. He passed away November 2003, from Lung Cancer. May he rest in peace.

Thank you Walt P. for submitting this material.


Find true Altitude

1/  Jan 3rd., sext. alt., was 47°  32’   index error  1.3 on the arc.  HE  11.5 m

2/ March 19th., sext alt.18°  46’  IE., 1.5’ off the arc.  HE 14.5 m 

3/ April  15th., sext alt.  * Altair was  36°  23.3’  IE  - 2.0’   HE  16.0 m

4/ Sept., 3rd., sext.alt.  Mars was 40°  00.0’, IE +1.0’  HE 5.5 m.

5/ December 21 th.,  08:00 GMT  sext. alt. Moons LL  was 53°  42.5’IE  + 1.2’   HE   9.7 m.

6/ June 21th.,  10:00  GMT sext. alt. Moons UL was 42°  37.5 IE -1.0’  HE  12.3 m.

7/ Find sextant setting for the appropriate meridian altitude of Formulhaut, ( decl., 29°  52.2’S)  for an observer in DR, lat 35° 50.0’ N,  HE 50 feet, IE  3.0’ off the arc., what is the bearing         of the Star?.

8/ Two stars bearing 140° (T) and 240° (T)  gave observed position as lat. 30°  10.0’ N, long 035° 19.0’ W.  Later it was found that the index error of 1.5’ off the arc., had not been applied.

Find true position.

9/ GMT used?. 

10/ Differentiate between Apparent time and Mean time.

11/ What is the equation of time.

12/ Define time zone.

13/ Define LMT.

14/ If LMT is given, how is GMT found.

15/What zone description is long., 108°  14.0’ W in ?.

16/ Z.T. at ship is 14:10 hours  (ZD + 8 ) long., 123°  18.0’ W., find LMT.

17/ about 12:00 ZT., at ship, an observation of the sun gave  60° 00.0’. Chronometer read  07:00:30, on June 1th., what is the declination of the sun at this time.

18/ On May 15 th., at 05:26:00 ZT (Z+2), the observed position by stars was 35° 48.5’N,  41°  38.0’ W, Vessel steamed until 09:15:00 ZT (Z+2), on course 087° (T) for a distance of 57.5 miles by log, when the sext. alt., of the suns LL was 42°  07’, HE 13.4 m, chronometer corrected time  11:14:32. Find ITP., Vessel steamed at 15.1 knots until sextant meridian alt., was  72° 39.0’. find the position of the ship. give position for the 12:00:00 ZT for the deck log.

19/ At about 10:20 (Z+3), on March 3rd., 1958 in EP. lat. 43° 52.0’N, long 054`° 17’ W. Course 274`T speed 14 knots, the sextant altitude of the sun’s LL was observed to be 29°11’ Chronometer read 13h12m33s., Later when the chronometer read 17h57m09s., the sext. alt of       .the sin’s LL was 31°12.7’ .  The chronometer was  8m32s., slow on GMT. HE 35 feet, IE -1.5.   What was the observed position at  15h05m ZT>.

20/ At about 09:33 (Z+4) on December 14th., 1958,  DR, 44°10.0’N, long 054°05.0W.  The sext. alt., of the sun’s LL was 14°51.3’, chronometer read 13h42m18s. Later at the time of the sun’s meridian passage, the sext. alt., of the sun’s LL was 21°37.4’     bearing south. The chronometer was 9m34s fast on GMT., IE.-1.4’, HE 28 feet. Course 346° T, speed 17 knots. Find the observed position at the time of the Meridian Passage..

21/ At about 14:10 hours (Z-9) on August 20th., in DR. lat 43°6’S, long 138° 05.0 E

The following observations were taken: Chronometer  05h05m07s   sext. alt. sun’s LL  25° 16.8’ Chronometer  05h07m32s    sext. alt Moons LL  48° 49.9’ Chronometer   was 2m18s slow, IE +1.5’, HE 36 feet,  Course 052`  speed 20 knots. Find position at time of second sight

22/  At about 04:50 hours (Z-4) on October 3rd., 1958, in DR. lat 40° 41.0’N long 062° 28.0’E, the following observations were made;

           Chronometer.                         Body.                      Sextant Altitude

              00h52m20s                        Diphda.                          23°  41.7’

              00h55m18s                        Procyon                         36° 50.3’

              00h58m05s                        Mars                               25°  42.1’

          Chronometer error  7m51s., fast, HE 26 feet, IE +0.5’, course 225° (T)

           Speed 14.5 knots.

            Find the observed position at the time of the last sight.

23/ At about 16:39 (Z+1) on January 20th., 1958, in DR. lat  45°  15.0’N, long. 14°  32.0’W, sextant alt. of  Polaris was 46° 18.2’ when chronometer showed 17h54m18s, chronometer was 15m10s fast on GMT. IE -1.2’, HE 42 feet. Find observers latitude.

24/ Find the zone time of morning civil twilight, sunrise and sunset at Halifax, lat. 44°  40.0’N, long. 063° 35.0’W, June 18th., 1058.

25/ At true sunrise on July 30th., 1958 in DR. lat. 47°15.0’N,  long.033° 12.0’W, the bearing of the sun was 064° (T)  What was the gyro error.

26/ In DR. lat. 27°  50.0’N, long. 028°  14.0’W, on April 14th., 1958, find the time of Moon Rise.

27/ January 8th., in long. 150° W, sext. alt.,” meridian “, of star Alioth below the pole was 15°  08.0’North of the observer, IE 1.6 off the arc, HE 10 m. required latitude.

28/  On June 22nd., in lat. 48°  04.0’ S., long 120°  E. Compute the approximate sext.alt. of the star Achernar below the pole, IE 1.5 on the arc., HE 8.5 m.

29/ On January 12, in long.020° E., the sext. meridian alt. of the star Canopus below the pole was 14° 12.5’  bearing south, IE1.3 off the arc.,HE 39 feet. Required latitude.

30/ On June 15, in ling.020° W., the sext. alt. of star  Deneb when on the meridian below the pole was 17°  40.3’ North of observer, IE.,2.0’n the arc.,He., 24 feet. Required latitude.

31/ On December 22 in latitude by account 49°  52’N., long. 170° 00.0’ E., compute the approximate sext. meridian alt. of the star Duhbe below the pole. sextant has an error of 1.8 on the arc, HE., 33 feet.

32/ On September 19 in lat. by account  51°  10.0’ S., long  160°  00.0’ W, Compute ( approx. )  the sext. alt., of the star Atria when on the meridian below the pole, as a   guide to setting the sextant for observation. IE., 1.5’ off the arc., HE 39 feet.

Answers to question 27 to 32, inclusive. 

27,    lat. 48°  49.5’ N.
28,    lat  15°  40.6’ S.
29,    lat. 51°  23.3’ S.
30,    lat.  62°  22.7’ N.
31,    Alt.,  21°  59.8’
32,    Alt.   30°  13.7’

33/ July 17th., vessels noon position was 45°  57.0’ N,  long. 24°  07.0’ W Course 245°  T,  speed 10 knots, (Z+1). At midnight clocks were retarded one hour, At 1040 ZT,  the suns LL was observed, chronometer  12h39m12s, which was 32seconda slow on GMT, alt. 60°  52.5’  IE 1.5’ off the arc, HE 25 feet. Later the sext. meridian alt. was 66°  46.3’. Find position of vessel.

34/ On July 14th.,  at 1200 hours, (Z-1) vessels position was 49°  51.0’W find the great circle distance from the last position, find mercator course and distance to a position in 09° 24.5 N, 79°  55.0’W (Z+5). Calculate the ETA for the complete voyage at 10.5 knots.

35/  Two stars bearing 140` (T) and 240° (T) gave observed position of 30° 10.0’N, and 035° 10.0’W. If the index error of 1.5’ off the arc had not been applied, find the true position of the ship.

36/   July 15th.,  1234 ZT  vessels DR. position was 48°  51.0’N,  012° 25.0’W, an observation of the suns LL  near the meridian gave an altitude of 62°  12.0’, HE 25 feet. Find the direction of the position line and the position through which to draw it.

37/ On September 29t., in DR. lat., 47°  30.0’ N, long. 052°  10.0’ W, the sext. of the sun’s  LL on the meridian was 39°  57.4’, IE 1.5’ off the arc, HE 14 m. Find the latitude.

38/  On October 4th., in DR latitude 40° 15.0’ N, longitude 145° 20.0” E, the sext. alt. of the moons LL was 67° 22.4’., IE 2.5 off the arc, HE 10.5 m. Find latitude.

39/  On Sept., 29th., in DR position, lat. 41° 37.0’ S, long. 178°  30.0 W, is to take an  observation of the planet Venus at the meridian passage, FIND:-  A) the zone time of meridian passage. B) the appropriate sextant altitude at the meridian passage, HE 11m, IE+2.2’ C) the latitude, if the sextant altitude was 39°  27.5’ at transit.

40/  On October 4th., an observer in DR position long. 130°  27.0’ W, is to take an observation of the star Vega at meridian passage. FIND:-  A) the LMT of meridian passage.  B)  the latitude, if the sextant altitude was 51°  29.0’ N at transit, HE 8m, IE 2.0’ on the arc.


hs *  =  51°  29.0’ N
IE     =         -2.0’
h      =  51°  27.0’
dip   =         -5.0’
ha     =   51°  22.0’
corr. =          -0.8’
ht.   =     51°  21.2’N
~      90°  00.0’
CZD =     386°  38.0’ S
decl. =     38°  46.2’ N
lat.  =      001°  07.4’ N..........

41/  January 8th., in longitude 150° W, sext. meridian alt. of  * Alioth, below the pole was 151° 08.0’ N of observer, IE 1.6’ off the arc, HE 10 m,  required latitude.

42/ on June 22nd., in lat. 48°  04.0’S, long. 120° 00.0’ E. Compute the approximate sext. alt. of the star Achernar below the pole, IE 1.5’ on the arc., HE 8.5 m.

43/  On January 12th., in long. 020° 00.0 E, the sext. alt. of the  *  Canopus below the pole was 14° 12.5’ bearing south, IE 1.3’ off the arc, HE 39 feet. Required latitude.

44/ A vessels consumption of coal is 30 tonnes per day, at 12 knots, required her consumption at a reduced speed of 10 knots

45/  In bad weather a vessel makes 10 knots for 4 days of 24 hours each on 25 tons of coal per day and finds she has 1000 miles to go and only 80 tons of coal left. Find the  reduced speed to enable her to reach port under the same weather conditions.

46/ The average speed is 12 knots, on 40 tons of coal a day. After 10 days steaming there is 350 tons of coal left and 3000 miles to go. Required, the reduced speed to reach port.

47/ From “A” in  51°  25.0’ N, 009°  29.0’W to “B” 40°  43.0’ N, 074°  07.0’ W. Required Great       Circle; dist., initial Co.,  final Co., latitude and long. of the vertex, and lat. of point where 60°  00.0’ W, crosses point.

48/  “A” in lat. 41°  30.0’S, to “B” 56°  10.0’S,  067°  30.0’W.  max. lat., 56° 10.0’ S.  Required: initial Co., total dist., and lat of point in 130°  00.0 W.

49/ Observer takes a bearing of * Capella of 022 3/4° by gyro. GMT 08h05m, on July 29th.,   DR 57°  21.0.’N,  135° 13.0’W. Vessel's course is 156° gyro. standard heading, 129° (c), variation 271/2° E. : Required gyro error and deviation of the standard compass.

50/  September 29th., in DR., 22°  00.0’S, long. 110°  32.0’E. Find GMT and LMT of the meridian passage of Jupitor. Also approximate sext. alt. at meridian passage, HE 12m, IE 2.0’ off the arc.  If sext. alt at transit was 44° 57.2’, find observed latitude.

51/ Find LMT and GMT at the lower transit of  *  Kochab on November 13th.  (1978)

52/ Required the GMT of the * Achernar on June 10th., in DR. 08° 40.0’N,  0271°  30.0’W at upper passage. 

53/ What selected stars or planets will be above the horizon and less than 10`  00.0’ of hour angle from the meridian of the observer in 30°  00.0’S. 150`  00.0E,  when twilight ends on July 16th.,  (1978)

Formulae's for Great circle Sailing's, Composite Tracks, and Intercept sight reduction.

Great circle;

Distance:  - the angle opposite the side and two other sides must be known.

           Hav AB= Hav P, sin PA, sinPB  +   Hav ( PA-PB )


Course:  - three sides of the triangle must be known

           Hav a = (nat Hav. PB- nat Hav.(( PA-AB )) cosec. PA cosec.AB)


Intercept formulae; Lets take a look at the Great Circle Formulae and compare....



Intercept..          LHA, cos lat, cos decl.         (L~D).

GS.  HavAB = Hav. P, cos PA, cos PB, + Hav (PA-PB)

 As can be seen, only the name of the parts change.


Hav. CZD = Hav LHA, cos lat, cos decl. + Hav. lat~decl

 Azimuth is as follows:

       sin AZ. = sin LHA, cos decl., sec. CZD.


 The ABC Tables may also be used, to find the Azimuth.


The Cosine formulae is in my opinion slightly more accurate, than the Haversine formulae.


To create a Haversine the following formulae is a must:

        (   1 -  cosine / 2 ) (( cosine of the angle ))



Working with logarithms, one have to realize that to add two numbers is like multiplying.

subtracting is like dividing.



the ABC Tables may also be used to do Great Circle Tracks or Intercepts..


ABC Formulae's:


     A = cot. lat.   x  tan. HA

     B = tan. decl  x cosec. HA

     C =  cot. AZ  x  sec. lat.  = ( A ~ B  x sec. lat = cot. AZ)




 Lets look a Composite Track Sailing's.:  Limiting Latitude



Distance..   lat A.   =  log sin.............

                  max lat = log cosec.........

                   =   log cos.


D’long       lat A     = log tan............

                  max lat = log cot............

                   =  log cos.


Initial Co.   lat A    = log sec.............

                  max lat =log cos.............

                  = log sin.


Distance.   lat A     = log sin..............

                 max lat. = log cosec.........

                  - log cos.


 d’long        = Long A~ long V1 =




(also distance is)...   dep.= d’long   x  cos mean lat..



 Mercator:  tan. co. = d’long /  DMP

                  dist.     =  d’lat  x  sec Co.


Mid. lat.  :   d’long  x  cos. mid lat  = tan co.

                    dep / d’lat  =  tan. Co.

                    dist.    =  d’lat  x  sec. Co.


Parallel Sailing.:

                     D’long  =  d’long  x sec. lat

                     Dep.  = d’long  x  cos. lat.

Brought to you by www.dieselduck.net comments to webmaster@dieselduck.net
Transport Canada has ask us to advise users of this webpage to keep in mind that these questions are not the exact questions found in their exams. Martin's Marine Engineering Page - www.dieselduck.net is not affiliated with Transport Canada and these questions have been gathered from various sources.