The Astro Navigation Resource

See the latest post on Meridian Passage.

Although this website aims to promote the Astro Navigation Demystified series of books, it is hoped that it will also provide a useful resource for navigators, scholars and students of the subject.

A wealth of iEARTH AND SUN IN THE SPHEREnformation on the subject of astro navigation can be found under the various headings on the menu bar at the top of the page and in the archives listed down the right. The images below give links to various pages which may be of interest.

Why Astro Navigation?  There is rapidly growing interest in the subject of astro navigation or celestial navigation as it is also known. It is not surprising that, in a world that is increasingly dominated by technology and automation, there is an awakening of interest in traditional methods of using the celestial bodies to help us to navigate the oceans.

Astro navigation is not just for navigators; the subject is an interwoven mix of geography, astronomy, history and mathematics and should appeal to both mariners and scholars alike.

Russia is one of the few countries in the worlaltitude and azimuthd to acknowledge the educational value of astro navigation and to include it as an important part of the school curriculum. In other countries, institutions such as nautical schools and maritime colleges include the subject in their curricula as a subject in its own right while for some independent schools, it provides the perfect theme for integrated studies and open-ended project work.

The question is often asked: ‘how could seafarers navigate the oceans if the global positioning system (GPS) failed? The answer is quite simple; they could revert to the ‘fail-safe’ art of astro navigation. The problem here though, is that we have become so reliant on automated navigation systems that traditional methods are being forgotten.  Even so, there is a very realPZX TRIANGLE danger that the GPS could be destroyed.  During periods of increased solar activity, massive amounts of material erupt from the Sun. These eruptions are known as coronal mass ejections and when they impact with the Earth they cause disturbances to its magnetic field known as magnetic storms. Major magnetic storms have been known to destroy electricity grids; shut down the Internet, blank out communications networks and wipe out satellite systems (including the global positioninplot 3g system).

Couple this danger with that posed by cyber terrorists who could block GPS signals at any time, then it can easily be seen that navigators who rely solely on electronic navigation systems could be faced with serious problems.

cross

 

Unfortunately, many sea-goers are deterred from learning astro navigation because they perceive it to be a very difficult subject to learn. In fact, it is very interesting and easy to learn but sadly, some writers and teachers of the subject attempt to disguise its simplicity by cloaking it in an aura of mystery.

 

 

http://www.amazon.com/Astronomy-Astro-Navigation-Black-Demystified/dp/1511675594/ref=sr_1_2?s=books&ie=UTF8&qid=1446153840&sr=1-2&keywords=astro+navigation+demystified

http://www.amazon.com/Applying-Mathematics-Astro-Navigation-Demystified/dp/1496012062/ref=sr_1_2?s=books&ie=UTF8&qid=1393696809&sr=1-2&keywords=astro+navigation

email: astrodemystified@outlook.com

  1. I am throughly enjoying working through the wonderful book, ‘Astro Navigation Demystified’. At last a well written book on the subject. I was also very pleased to find this accompanying website.

     

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

Posted in Uncategorized

Meridian Passage Long Method

Links:  Understanding Meridian Passage,   Meridian Passage Short Method,  Short Distance Sailing Formulae,  What is the point of meridian passage?         Zone Time,    Local Hour Angle and Greenwich Hour Angle,   Converting GMT to GHA ,  Altitude Corrections

Outline Method

If a vessel is under way, its position at the time of meridian passage will not be known beforehand.  However, it is necessary to calculate the approximate time of meridian passage before it occurs so that the altitude measurements can begin in time.  This is achieved by calculating the time of meridian passage at the present D.R. position a few hours before noon and then estimating what the vessel’s new position will be at that time.  The approximate time of meridian passage can then be recalculated for the new position.

To calculate the new position, we use the Short distance sailing formulas which are fully explained in my book ‘Celestial Navigation – The Ultimate Course’. Short distance sailing is a term which is applied to sailing along a rhumb-line for distances less than 600 nautical miles.  Of course, we could simply extend our dead reckoning track for the required distance on a mercator chart.  However, mercator charts, which do not allow for the curvature of the Earth, are not very accurate for plotting tracks which cross high latitudes or which are predominately east-west.  Therefore, for the sake of accuracy, the meridian passage long method employs the short distance sailing formulas for calculating the new position.

Greenwich Mean Time Versus Universal Time. The nautical almanac lists the times of events such as mer. pas. in terms of universal time (UT); however, since we are dealing with the time that the Sun crosses the Greenwich Meridian, it is more helpful to refer to the time in terms of Greenwich Mean Time (GMT) instead. (Remember the terms Greenwich Mean Time and Universal Time are generally considered to be synonymous).

Refraction.  Since refraction is negligible when the Sun is at its zenith, additional altitude correction for non standard conditions is not necessary when calculating the true altitude at meridian passage.

 Relationship between Altitude and Zenith Distance.

Zenith Distance = 90o – Altitude

and Altitude = 90o – Zenith Distance

 Rules For Calculating Meridian Passage.

  • Latitude and declination same names but latitude greater than declination:

LAT  =  DEC + (90o – ALT)

  • Latitude and declination same names but declination greater than latitude:

LAT  =  DEC – (90o – ALT)

  • Latitude and declination opposite names:

LAT  =  (90o – ALT) – DEC

Nine-Step Proforma. This easy to the follow nine-step proforma has been devised provide a step by step method for calculating a vessel’s position by the Meridian Passage Long Method.  The method will become clear as you work your way through the guided examples below.  A blank copy of the proforma template can be found in appendix 10.

Outline of the 9-step Proforma.

Pre Planning.  At least one hour before noon, preferably two, calculate your vessel’s first DR position.  Busy navigators in ships travelling at speed will need to do this early so that they will have time to calculate what the ship’s  new position will be at the time of meridian passage.

  • Step 1. Using the nautical almanac daily page, find the time of meridian passage for the first DR position
  • Step 2.  Convert the time of meridian  passage from GMT to zone time.  (Remember, zone time will not correspond to the Sun’s apparent time so although meridian passage occurs at noon apparent time, the zone time is likely to be several minutes either side of this).
  • Step 3.  Calculate what the new position will be at the time of meridian passage as calculated at step 2.  (The short distance sailing formulas which are explained in note 15 should be used to calculate the new position).
  • Step 4.  Calculate the time of meridian passage at the new position.
  • Step 5.  Calculate the declination at the new time of local meridian passage.
  • Step 6.  Calculate the Meridian Altitude and note the deck-watch time.
  • Step 7.  Calculate the vessel’s latitude from the values of the meridian altitude calculated at step 6 and the declination calculated at step 5.
  • Step 8.  Calculate the vessel’s longitude from the deck watch time noted at step 6.
  • Step 9.  Summarise position at zone time of meridian altitude.

Example:    Use the Meridian Passage Long method to calculate the position of the vessel in the scenario below by following the nine-step proforma explained above.

Scenario.

Date: 17 December

(zone -9)

DR Position at 1000 (zone time): 41o 15’.0S. 134o 52’.0E.

Course: 030o  Speed: 15 knots.

Sextant Altitude at Mer. Pas. (Meridian Altitude):  72o 18’.2

Index error: +2’.1.

Height of eye: 12m

Deck Watch Time at Meridian Altitude:  02h 59m 10s

DWE 5s fast

Solution:

Pre Planning.

Date: 17 Dec.  Zone Time: 1000(-9).

DR Pos: 41o 15’.0S. 134o52’.0E.

Course: 030o  Speed: 15 knots.

 
Step 1. Determine Time of Mer. Pas. at Greenwich.

From the Nautical Almanac Daily Page for 17 Dec,

Mer. Pas. at Greenwich =  1156 GMT.

Step 2. Estimate time of local mer.pas.at first D.R. Pos.

Starting Data: Long. 134o 52’.0E

 Calculations:

·      Convert Long. to time.

4 x 134o ÷ 60 =  8.93h               =  8h    55m    48s

4 x 52’.0 ÷ 60 = 3.46m                    =  0h    03m    27.6s

= 8h   59m    15 .6s

·      Estimate zone time of local mer.pas.

Mer. Pas. Greenwich                      11h   56m    00s

Long. (long east GMT least)       –08h   59m    15.6s

Local Mer. Pas (GMT)                   02h   56m   44.4s

=  02h   57m (nearest minute)

Zone (-9)                                        +09h                    (- for GMT, + for ZT)

Zone time Mer. Pas.                       11h   57m

 
Step 3.  Calculate new position at estimated time of Mer. Pas.

Starting data:

Course = 030o Speed = 15 knots.

Zone time at first DR position = 1000

DR Position at 1000 = 41o 15’.0S. 134o 52’.0E.

Estimated zone time of Mer. Pas = 1157

Time elapsed since 1000 = 1h 57= 1.95h

Distance run at 15 knots in 1.95h = 15 x 1.95 = 29.25n.m.

Calculations:

Dep.            = Dist x Sin(course)

= 29.25 x Sin(30)  = 14’.6E

D.Lat.          = Dist x Cos(course)

= 29.25 x Cos(30)  = 25’.3N

New Lat.   = Lat – D.Lat

= 41o 15’.0S – 25’.3N  = 40o 49’.7S

Mid. Lat       = Lat – (D. Lat ÷ 2)

= 41o 15’.0S. – 12’.65N

= 41o 02’.35S.  = 41o.04S

D.Long.      = Dep. x Sec(M.Lat)

= 14’.62 x Sec(41o.04)

= 14′.62 x 1.3258 = 19’.4

New Long.  = 134o 52’.0E + 19’.4

= 135o 11’.4E

Summary:  New Position at 1157 = 40o 49’.7S. 135o 11’.4E.

Step 4.  Calculate time of Mer.Pas. at new position.

Starting data:

New Long. 135o 11’.4E (from step 3)

Calculations:

  • Convert Long. to time.

4 x 135o ÷ 60                       =  9h    00m    00.0s

4 x 11.4’ ÷ 60 = 0.76m           0h    00 m   45.6s

=   9h    00m   45.6s

  • Calculate new time of Mer. Pas.

Mer. Pas. Greenwich:       =   11h    56m   00s        (GMT)

Long (135o 11’.4E):             = –09h    00m   45.6s

Local Mer. Pas (GMT)       =  02h   55m   14.4s

Zone (-9)                               =+09h                   . 

Zone time Mer. Pas.            =  11h   55m    14.4s

=   11h 55(nearest minute)

Step 5. Determine declination at new time of local Mer.Pas.

Starting data:

Date: 17 Dec.

Local Mer. Pas (GMT):      02h  55m 14.4» 02h 55m

Calculations:

Dec Sun (02h):                S23o 21’.2  (d = 0’.1 increasing)

d Correction (55m):                      + 0’.1

Dec Sun (02h 55m):         S23o 21’.3

Step 6.  Calculate Meridian Altitude.

Starting data:

Sextant Altitude: 72o 18’.2

Index error: +2’.1.

Height of eye: 12m

Calculations:

Sextant Altitude:            72o 18’.2

I.E.                                          + 2’.1

Observed Altitude:        72o 20’.3

Dip (12m):                             – 6’.1   

Apparent Altitude:        72o 14’.2

Altitude Correction:         + 15’.9

True Altitude  =             72o 30’.1

(Note deck watch time: 02h 59m 10s (DWE -5s)) 

Step 7. Calculate Latitude

Starting Data:

Estimated Lat = 40o 49’.7S (From step 3)

Estimated Dec = S23o 21’.3 (From step 5)

Altitude = 72o 30’.1 (From step 6)

Rule: Same hemisphere Lat > Dec = rule i

Calculations:

LAT  =  DEC + (90o – ALT) (rule i)

= 23o 21’.3 + (90o – 72o 30’.1)

= 23o.36 + (90o – 72o.5)

= 23o.36 + 17o.5

= 40o.86

Calculated Latitude = 40o.86 = 40o 51’.6S. 

Step 8.  Calculate Longitude From Deck Watch Time.

Starting Data:

Estimated Longitude = 135o 11’.4E (from step 3)

Deck Watch Time = 02h 59m 10s   (from step 6)

DWE = -05s

Calculations:

  • Calculate time difference.

Deck Watch Time:        02h 59m 10s

DWE:                                            -05s

GMT/UT:                       -02h 59m 05s (Longitude East, GMT Least)

Local Apparent Time:   12h  00m 00s  (midday)

Time Diff:                      -09h  00m 55s

  • Convert Time to Arc.

9=  9 x 15                  =      135o 00’  00”

0m                                          =         0o 00’  00”

55s = 55 ÷ 4                  =        0o  13’  45”

=    13513’  45”  = 13513’.75E

Calculated Longitude at 02h 59m 05s GMT = 13513’.75E 

Step 9.  Summarise position at zone time of meridian altitude.

Starting Data:

GMT of meridian altitude:  02h 59m 05(from step 6)

Zone: -9

Calculated latitude:  40o 51’.6S.  (from step 7)

Calculated longitude: 13513’.75E (from step 8)

Calculate zone time of meridian altitude:

GMT of meridian altitude             =    02h 59m 05s

Zone correction                               =  +09h

Zone time of meridian altitude    =    11h 59m 05s  ≈ 11h 59m

 Summary:

Observed Position at 1159 (zone time)  = 40o 51’.6S. 135o 13’.75 E

This position would be consistent with sailing for 1 hour 47 minutes on a course of 030o @ 15 knots from the 1000 D.R. position of 41o 15’.0S. 134o 52’.0E.

 Where to buy books of the Astro Navigation Demystified series:

Celestial Navigation at Amazon.com

Celestial Navigation at Amazon.uk

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

Posted in astro navigation, astronomy, celestial navigation, Marine Navigation, navigation, trigonometry | Tagged , , , , , ,

Meridian Passage Short Method

Meridian Passage Methods. 

Short Method.  In the case of stationary or very slow moving vessels, it is acceptable to use the Meridian Passage Short Method which involves calculating the time of meridian passage at the current DR position.

Long Method.  For vessels that are making good headway, the long method should be used.  The long method involves calculating the time of meridian passage at the present position an hour or so before noon and then plotting a new DR position for that time.  In this way, the time of meridian passage at the new DR position can then be calculated in advance.

Note.  Since the calculations for position by meridian passage involve the Greenwich Hour Angle and the longitude, the base line for both of which is the Greenwich Meridian, it would seem appropriate to refer to Greenwich Mean Time instead of Universal Time in those calculations. Since the terms GMT and UT are generally considered to be synonymous, no loss of accuracy will arise.

Links:  Understanding Meridian Passage,   What is the point of meridian passage?         Zone Time,    Local Hour Angle and Greenwich Hour Angle,   Converting GMT to GHA ,  Altitude Corrections

Meridian Passage – Short Method.

As we learned in ‘Understanding Meridian Passage’, meridian passage (mer. pas.) occurs when a celestial body crosses the observer’s meridian of longitude and at that instant, it will reach its greatest altitude above the observer’s horizon.  We also learned that if we measure the Sun’s altitude at local meridian passage and use the result together with the Sun’s declination, we can calculate our latitude.

The short method is used for stationary or very slow moving vessels and involves calculating the time of meridian passage at the current DR position.

Rules For Calculating Latitude at Meridian Passage. The following rules were fully explained in ‘Understanding Meridian Passage’ but need to be reiterated here:

  1. Latitude and declination same names but latitude greater than declination:          LAT  =  DEC + (90o – ALT)
  2. Latitude and declination same names but declination greater than latitude:        LAT  =  DEC – (90o – ALT)
  3. Latitude and declination opposite names:        LAT  =  (90o – ALT) – DEC

 Short Method Outline. The short method involves calculating the time of local meridian passage at the vessel’s present geographical position shortly before noon and then measuring the Sun’s altitude as that time approaches.

Outline of the Six-Step Proforma for the Meridian Passage Short Method. This easy to follow six-step proforma can be used for calculating a vessel’s position by the Meridian Passage Short Method.

Pre Planning.  As the time approaches noon, calculate your vessel’s geographical position (DR or EP) and note the zone time at that position.

  • Step 1.  Using the nautical almanac daily page, find the time of meridian passage (mer. pas.) for today’s date (in GMT).
  • Step 2.  Convert the time of mer. pas. from GMT to zone time. (Remember that zone time will not correspond to the Sun’s apparent time so although mer. pas. occurs at noon apparent time, the zone time is likely to be several minutes either side of this).
  • Step 3.  From the nautical almanac daily page, find the Sun’s declination at the time of Mer. Pas.  (Note, when correcting declination for the ‘d’ increment, care should be taken to check the daily page to see if declination is increasing or decreasing).
  • Step 4.  Measure the altitude of the Sun’s lower limb at mer. pas. and calculate the corrected Meridian Altitude.
  • Step 5.  Calculate the vessel’s latitude from the meridian altitude and the Sun’s declination using the rules for Mer. Pas. as explained earlier.
  • Step 6.  Calculate the vessel’s longitude by converting the time difference between Mer. Pas. and GMT.

Example.  This example demonstrates the application of the above method of calculating latitude by the meridian passage short method.

Task.  Use the meridian passage short method to calculate the position of the vessel in the scenario below by following the six-step proforma above.

Scenario:  Date:  22 June

Zone Time: 1140 (+4)

Zone:  +4

DR Position:  320 30’N.  610 55’W.

Speed negligible (Fishing vessel hauling nets).

Sextant altitude at Mer. Pas.: 80o 55’.8

Index Error (I.E.): -0′.2

Ht. of eye:  2.5m.

Deck Watch Time (DWT) at Meridian Altitude: 16h 08m 25.1s

Deck Watch Error (DWE): 5 sec fast (-5)

Solution.

Pre Planning.

Date: 22 June.  Zone Time: 1140 (+4).  DR Pos: 320 30’N.  610 55’W

Step 1. Determine Time of Mer. Pas. at Greenwich.
From the Nautical Almanac Daily Page for 22 June,

Mer. Pas. at Greenwich =  1202 GMT.

Step 2.  Calculate time of Mer.Pas.at D.R. Pos.

(DR Longitude = 610 55’W.)

  • Convert Longitude to time.

Long: 61o 55’W

4 x 61o ÷ 60  = 4.066h      =  4h    04m    57.6s

4 x 55’ ÷ 60 = 3.66m                 0h    03m   39.6s

=                                               4h    07m   37.2s (≈ 37s)

  • Estimate zone time of Mer. Pas.

Mer. Pas. Greenwich     =     12h   02m   00s (GMT) (from daily page)

Long (61o 55’W):             = + 04h   07m   37s (Longitude West, GMT Best(+))

Local Mer. Pas (GMT)    =    16h    09m   37s

Zone (+4)                           =  –04h                     (+4 for GMT but -4 for zone time).

Zone time Mer. Pas.         =   12h    09m   37s        ≈ 1209 (nearest minute)

Step 3. Determine Declination at Time of Local Mer.Pas.

Local Mer. Pas (in GMT): 16h  09m 37» 16h 10m

Dec Sun (16h)                        =    N23o 25′.9  (from Daily Page)  (d = 0′.0)

d correction                           =                0′.0 (from increments table)

Dec Sun (16h 10m GMT):      =    N23o 25′.9  (= N23o.43)

Step 4.  Calculate Meridian Altitude.

Sext. Altitude:                80o 55’.8

I.E.:                                         – 0’.2

Observed Altitude:        80o 55’.6

Dip (2.5m):                            – 2’.8   

Apparent Altitude:         80o 52’.8

Altitude Correction:           + 15’.8

True Altitude:                  81o 08’.6      (= 81o.143)

Step 5.  Determine Latitude.

DR Latitude = 320 30’N.

Declination = N23o.43 (from step 3)

Altitude = 81o.143 (from step 4)

(Lat and Dec same hemisphere; Lat > Dec = rule 1)

Therefore LAT  =  Dec + (90o – ALT) –   (rule 1)

= 23o.43 + (90o – 81o.143)

= 23o.43 + 8o.857

Therefore LAT  =32o.287N = 32o 17’ 13″.2 N

Step 6.  Calculate Longitude  (from DWT at meridian altitude).

(DR Long = 610 55’W.)

  • Calculate time difference.

Deck Watch Time             =    16h 08m 25.1s

DWE:                                   =                -05s

GMT/UT:                             =  16h 08m 20.1s

Local Apparent Time:        =  12h  00m 00s (midday)

Time Diff:                             =+04h 08m 20.1s   ( Longitude West = GMT Best)

  • Convert Time to Arc

4= 4 x 15  =        60o 00’  00”

8m = 8 ÷ 4  =           2o 00’  00”

20.1s = 20.1 ÷ 4 =   0o 05’  01″.5

=  6205’  01”.5

Therefore Long = 6205’ 01″.5 W

 

Therefore, observed position at zone time 12h 09m (local Mer Pas)

= 32o 17’13″.2N.      62o 05’ 01″.5W.

(For comparison DR Pos. at 11h 40m (zone time) was 320 30’N. 610 55’W.)

Where to buy books of the Astro Navigation Demystified series:

Celestial Navigation at Amazon.com

Celestial Navigation at Amazon.uk

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

Posted in Uncategorized

Understanding Meridian Passage (Mer Pas)

Meridian Passage occurs when a celestial body crosses the observer’s meridian of longitude and at that instant, it will reach its greatest altitude above the observer’s horizon. The following diagrams will help to explain how the latitude can be calculated from the Sun’s declination and altitude at Mer. Pas.

Consider the following diagram:

image001

NOS  represents the horizon.

O represents the position of the observer.

X represents the position of the Sun.

Z represents the zenith which is an imaginary position exactly above the observer so that OZ is perpendicular to NOS.

Angle XOS represents the altitude of the Sun.

Angle XOZ equals 90o – Altitude.

There are three cases to consider:

Firstly, consider this diagram:

image002

In this diagram where both latitude and declination are in the same hemisphere but latitude is greater than declination, the following is true:

Latitude = Declination + (90o-Altitude).

Now consider this diagram:

image004

In this case, where latitude and declination are in the same hemisphere but declination is greater than latitude, the following is true:

Declination  =  (90o – Altitude) + Latitude

Therefore, Latitude =  Declination – (90o – Altitude)

The third case is represented by this diagram.

image005

In this case, where latitude and declination are in opposite hemispheres, the following is true:         Latitude + Declination  =  (90o – Altitude)

Therefore, Latitude = (90o – Altitude) – Declination.

 The rules for the three cases are summarised as follows:

(i)  Latitude and declination same names but latitude greater than declination:

LAT  =  DEC + (90o – ALT)

(ii)  Latitude and declination same names but declination greater than latitude:

LAT  =  DEC – (90o – ALT)

(iii) Latitude and declination opposite names:

LAT  =  (90o – ALT) – DEC

Example 1.

DR Latitude = 320 30’N.

Declination = N23o.43

Altitude at Mer. Pas. = 81o.143

(Lat and Dec same hemisphere; Lat > Dec = rule i)

LAT  =  Dec + (90o – ALT) –   (rule i)

= 23o.43 + (90o – 81o.143)

= 23o.43 + 8o.857

             =32o.287N = 32o 17’ 13″.2 N

Example 2.

DR Latitude = 60 10’N  = 60.166N

Declination = S22o.82

Altitude at Mer. Pas. = 61o.55

(Opposite hemispheres = rule iii)

LAT  =  (90o – ALT) – Dec   (rule iii)

=  (90o – 61o.55) – 22o .82

= 28o.45 – 22o.82

= 5o.63

=05o 37’.8N

Example 3.

DR Latitude = 20 10’N. = 20.1N

Declination = N11o.86

Altitude at Mer. Pas.= 80o.2

(Same hemisphere; Dec. > Lat = rule ii)

LAT  =  Dec – (90o – ALT) –   (rule ii)

= 11o.86 – (90o – 80o.2)

= 11o.86 – 9o.8

=2o.06N = 2o 3’.6N = 2o 3’ 36″N

Links:  Meridian Passage Methods,   What is the point of meridian passage?   Time,   Zone Time,    Local Hour Angle and Greenwich Hour Angle,   Converting GMT to GHA , Altitude Corrections

Where to buy books of the Astro Navigation Demystified series:

Celestial Navigation at Amazon.com

Celestial Navigation at Amazon.uk

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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Altitude Corrections For The Moon

Continuing the series on the Moon.

When a navigator measures the altitude of the Moon, there are several corrections that he has to make to the readings.

Corrections For The Moon’s Semi-Diameter.  The point on the Moon’s circumference nearest to the horizon is called the lower limb and the point furthest from the horizon is called the upper limb.  When the Moon is not full, sometimes only the upper limb will be visible and sometimes only the lower limb.  From the diagram below it can be seen that sometimes, depending on the phase of the Moon, either the upper or the lower limb cannot be seen.

image057

It should be noted that whether the Moon’s upper or lower limb is visible is dependent not only on its phase but also on the relative altitudes of the Sun and the Moon.  For example, if, one morning, a crescent or gibbous moon is visible in the eastern sky and the Sun is at a higher altitude, only the upper limb will be visible but if, in the evening of the same day, the Moon is visible in the western sky and the Sun has set below the western horizon, only the lower limb will be visible.

In navigational practice, the altitude that we measure is that of the lower limb; however, when the lower limb cannot be seen, we have no choice other than to measure the altitude of the upper limb.   Regardless of which limb we use, what we really need is the altitude of the Moon’s centre so we must either add or subtract the value of its semi-diameter.  The following diagram shows why the semi-diameter must be added when the altitude when the lower limb is measured. Based on the assumption that the lower limb will normally be used for altitude measurements,  30’ is added to the corrections during compilation of the Moon altitude tables to allow for semi-diameter.   Therefore, when the upper limb is used,  the 30’ must be subtracted.

 lower limbAs the Moon travels around its orbit and its distance from the Earth changes, so the value of the visible moon’s semi-diameter will change.  The value of the Moon’s semi-diameter for each day is given in the daily pages of the Nautical Almanac.

 Corrections For Refraction.  When a ray of light from a celestial body passes through the Earth’s atmosphere, it becomes bent through refraction and causes the apparent altitude to be greater than the true altitude.  Since the sextant measures the apparent altitude, a correction for refraction must be applied to find the true altitude.  Refraction is at its greatest when the altitude is small (i.e. when the celestial body is near the horizon) and becomes less as the altitude increases.  The effects of refraction are illustrated in the diagram below.

refraction

O is the observer’s position and Z is the zenith at that point.  OH is the horizon.  XOH is the true altitude of the Moon from the observer’s position.  However, due to refraction, the celestial body appears to be at Y and so YOH becomes the observed altitude and a correction will have to be made to compensate for this.

Corrections For Parallax. We measure the altitude of a celestial body from our position in relation to our visible horizon; this is known as the observed altitude.  However, when calculating the true altitude, measurements are made from the Earth’s centre in relation to the celestial horizon.  The displacement between the observed position of an object and the true position is known as parallax.

 parallax

Parallax corrections for the Moon.  Because the Sun and the Moon are relatively close to the Earth, parallax will be significant and so a correction has to be made.  These corrections are included in the altitude correction tables in the Nautical Almanac.

Horizontal Parallax. Parallax error is greatest when the celestial body is close to the horizon and decreases to zero as the altitude approaches 90o.  It is negligible except in the case of the Moon which is close to the Earth in comparison with the other celestial bodies.  Because horizontal parallax is significant in the case of the Moon, a separate correction has to be applied.  The hourly values of horizontal parallax for the Moon are listed in the daily pages of the Nautical Almanac.

Links:    Lunar Distance       Phases of the Moon     Tidal Effects of the Moon.  

Survival – Finding Direction From The Moon

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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The Tidal Effects of the Moon

Continuing the series on the moon.

If it were not for the gravitational attraction of the Sun and the Moon, the water level of the seas and oceans would be kept at equal levels by a combination of the Earth’s own gravity pulling it inwards and centrifugal force pushing it outwards.  However, the gravitational force of the Moon is strong enough to attract the water towards it and cause a bulge beneath it.  As the Earth rotates and the Moon orbits around it, the bulge follows the Moon causing high tides in its vicinity.

The combined effects of the Earth’s rotation and the Moon’s orbit around it, cause the ‘bulge’ to move around the Earth in 24 hours and 50 minutes and so it would seem at first sight that we would get high tides only at that time interval.  However, other forces are at play.  On the opposite side of the Earth to where the ‘bulge’ occurs, the Moon’s gravitational pull is at its weakest and this allows the Earth’s centrifugal force to push the water outwards and so cause another bulge there giving us two high tides a day.  This means that the time between high tides is approximately 12 hours and 25 minutes and the time between high tide and low tide is 6 hours 12.5 minutes in deep ocean areas. This can change dramatically owing to a variety of factors such as the topography of the ocean floor, local currents, varying water depths and the declination of the Moon.

bulge

The height of the tides vary during the course of a month because the Moon is not always at the same distance from the Earth due to its elliptical orbit.  As the Moon comes closer to the planet, its gravitational pull increases and this leads to higher tide levels.  Likewise, when the Moon’s orbit takes it further away from the Earth, the tides become lower. When the Moon is at its closest distance to the Earth, its gravitational pull increases by as much as 50% and this leads to higher sea levels on Earth.  When it is at its furthest distance, sea levels are much lower,

Tidal Effects of the Sun. The Sun also affects the rise and fall of the tides on Earth.  The gravitational attraction of the Sun pulls the ocean water towards it but at the same time, the effect of the Earth’s rotation around the Sun creates a centrifugal force which pushes the water outwards on the side facing away from the Sun.  The combined effect of these two forces creates a tidal bulge on the side of the Earth facing away from the Sun.  However, this effect of the Sun is less than that created by the Moon which is much closer to the Earth.

Spring Tides.  When the Sun, the Moon and the Earth are in syzygy, that is when they are lined up as during a Full Moon or New Moon, the combined tidal effect of the Sun and Moon is at its greatest and causes what is known as Spring Tides.  This has nothing to do with the season of Spring but to do with the saying that the water ‘springs’ higher than normal.

Neap Tides.  When the directions of the Sun and the Moon in relation to the Earth are at right angles, as during a Half Moon, the combined effects of their gravitational pull is less and so the height of the tides is much lower and are known as Neap Tides.

Links:    Lunar Distance       Phases of the Moon     Altitude Corrections for the Moon.

Survival – Finding Direction From The Moon

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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The Moon

My recent article ‘Finding Direction By The Moon’, sparked off a flurry of correspondence on the topic of the usefulness of this celestial body in navigation and in response, the next few articles will be on this subject.

PHASES OF THE MOON.

The diagram below shows, that as the Moon completes its 27.3 day orbit around the Earth, we see it pass through various phases of illumination.   It goes from New Moon, to Full Moon and back to new Moon again.moon phases

The Phases.

New Moon.  When the illuminated side of the Moon is facing away from the Earth.  The Moon and the Sun are lined up on the same side of the Earth, so we can only see the shadowed side.  During a new moon, we can see the reflected light from the Earth, since no sunlight is falling on the Moon – this is known as ‘earthshine’.

Waxing Crescent – The waxing crescent moon is the first sliver of the Moon that we can see after the new moon. From the northern hemisphere, the crescent moon has the illuminated edge of the Moon on the right. This situation is reversed for the southern hemisphere.  “Waxing” means that the Moon becomes more illuminated night-by-night,

First Quarter – This occurs when the Sun and the Moon make a 90-degree angle compared to the Earth.   Although it’s called a quarter moon, we actually see it as half illuminated.

 Waxing Gibbous – This phase of the Moon occurs when more than half of the Moon is illuminated but it is not yet a full Moon.

Full Moon – This is the phase when the Moon is brightest in the sky. The Moon and the Sun are lined up on opposite sides of the Earth, so from our perspective here on Earth, the Moon is fully illuminated by the light of the Sun.

Waning Gibbous – In this lunar phase, more than half of the Moon is illuminated but it is not yet a full moon. The term “waning” means that it’s getting less illuminated each night.

Last Quarter – At this point of the lunar cycle, the Moon has reached half illumination again. Now it is the left-hand side of the Moon that’s illuminated, and the right-hand side is in darkness (from a northern hemisphere perspective).

Waning Crescent – This is the final sliver of illuminated moon we can see before the Moon goes into darkness again.

Links:    Lunar Distance       Tidal Effects of the Moon.     Altitude corrections for the Moon

Survival – Finding Direction From The Moon

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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Survival – Finding Direction From The Moon.

Just as the Sun can help us to find our general bearings during the day, so can the Moon at night.

Moonrise and Moonset.  As in the case of the Sun, the Moon will rise between north east and south east and will set between north west and south west.  The exact bearing will depend on the observer’s latitude, and the Moon’s declination but in a survival situation, this is not important; all we need to know is that the Moon will rise in the east and set in the west.

MOON TIPSMoon Tips.   A crescent moon can provide us with a quick and easy method of finding the directions of north and south.  If you imagine a line that joins the tips of the crescent and extend this line down to the horizon, it will point roughly south for observers in the northern hemisphere.  In the southern hemisphere, the line will point to the north.

 

SHADOW STICK EW MOONShadow Stick. Sometimes, the Moon will be bright enough to cast a shadow and when this happens, we can use the same shadow stick method that we use for the Sun to find the directions of east and west.

Method

  1. Place a stick in the ground and mark the end of the Moon’s shadow with a stone or some other object.
  2. Wait for half an hour or more and then mark the point that the tip of the shadow has moved to.
  3. Scratch a line in the ground to join the two marks. (If the terrain is not suitable for this or the line cannot be seen clearly, use a piece of string or a straight pole etc.).
  4. Because the Moon moves from east to west, the line that you have made will also point east and west.

 waxing waningWaxing / Waning Moon.   If we are out in the open in a survival situation, we will have plenty of opportunity to study the night sky and so we will probably know if the moon is waxing or waning and this knowledge can help us to find the directions of east and west.

When the Moon is waxing (between the new moon and the full moon) it follows the Sun as it crosses the sky from east to west  and so, as we look at it from the Earth, its western side will face the Sun and will therefore be illuminated.

When the Moon is waning (between the full moon and the new moon) it leads the Sun across the sky and so its eastern side will face the Sun and be illuminated.

The Pointing Method. The pointing method that we use with the Sun to keep us on course during the day can be used with the Moon during the night.  The method is explained below:

  1. Face the direction in which you plan to travel and point in the direction of the Moon.
  2. Hold this position for a few seconds until the Moon’s direction relative to your body is imprinted in your mind.
  3. Set off on your chosen course keeping the Moon in the same relative position.
  4. Stop every ten to fifteen minutes to reacquaint yourself with the Moon’s relative position.

Survival Links:  Astro Navigation in a survival situation.  Latitude from the midday Sun. Find your longitude.   Latitude from the North Star  Calculating declination.   Declination table.    The Survival Sundial

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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Survival – The Daytime Star

Just as the stars can be your compass at night, there is another star to guide you during the day and that of course is the Sun.

Sunrise/Sunset.   We are taught that the Sun rises in the East and sets in the West; well that is true on only two days of the year, the Vernal and Autumnal Equinoxes.  During the rest of the year, sunrise will be between north east and south east while sunset will be between north west and south west; however, all we really need to know in a survival situation, is that sunrise is approximately east and sunset is approximately west.

Between Sunrise and Sunset.  Fine, we can find east and west at dawn and dusk and from there we can align ourselves with north and south but how do we manage between these times?  Well, there are several methods that we can use depending on whether we are on the march or we have time to stop.

The Watch Compass  If you are lucky enough to have an analogue watch, this can serve as a substitute compass.

watch compassMethod.

  1. Make sure the watch shows the time for your locality (standard time if on land or zone time if at sea).
  2. Point the hour hand towards the Sun.
  3. Imagine a line from the centre of the watch face to the 12 o’clock position and then imagine an angle between that line and the hour hand as shown in the diagram. When in Daylight Saving Time (Summer Time) use the 1 o’clock position instead of 12 o’clock).
  4. Next imagine a line bisecting this angle as represented by the dotted line in the diagram,
  5. If you are in the Northern Hemisphere, the line bisecting the small angle will point towards the South and the line bisecting the large angle will point towards the North. If in the Southern Hemisphere, it will be the other way round.

Notes.

  1. This method is based on the ‘True Sun’ (the Sun we see in the sky). However, clock time (mean time or standard time) does not keep in step with the True Sun and so the watch compass will not always exactly indicate true south or true north but it is close enough for survival purposes.
  2. If you are in the tropical zone (23.5o north to 23.5o south), you may have difficulty with this method because the Sun will sometimes be to the north, sometimes to the south and sometimes, exactly over your latitude.
  3. Never look directly at the Sun as this can seriously damage your eyes. A piece of smoked glass can easily be made for use as a light filter; simply hold a piece of glass in the smoke of a candle or oil lamp until it is covered in a layer of smoke residue.

Shadow Stick  If you do not have an analogue watch, you can still use the Sun to find your direction as long as you have time to stop in one place for a while and if there is sufficient sunlight to make a shadow.

East / West Shadow Stick Method.

SHADOW STICK EWMOD

Method

  1. Place a stick in the ground and mark the end of the Sun’s shadow with a stone or some other object.
  2. Wait for half an hour or more and then mark the point that the tip of the shadow has moved to.
  3. Scratch a line in the ground to join the two marks. (If the terrain is not suitable for this, use a piece of string or a straight pole etc.).
  4. Because the Sun moves from east to west at 15o per hour, the line that you have drawn will also point east and west.

North / South Shadow Stick Method  At noon, the True Sun will be over the meridian of longitude of your position and will have reached its highest altitude for the day.  Because of this, shadows cast by the Sun at this time will lie from north to south and so indicate those directions for us.

SHADOW STICK NS

Method

  1. Judge when the Sun is approaching the highest point of its path across the sky.
  2. Place a stick in the ground and mark the tip of its shadow.
  3. Draw a line from the base of the stick to the tip of the shadow.
  4. About 5 minutes later, mark the point that the tip of the shadow has moved to and draw a line along the length of the shadow as before.
  5. Repeat this process several times. The shadow will become shorter as the Sun approaches its highest altitude at noon and then it will begin to get longer again.
  6. The shortest shadow occurs when the Sun is at its highest altitude and this line will lie north/south.
  7. In the Northern Hemisphere, the end of the shadow nearest the stick will point to the South at noon and in the Southern Hemisphere, it will point to the North.

Notes

  1. Never look directly at the Sun as this can seriously damage your eyes.
  2. Again, there may be difficulties with this method in the tropics.
  3. If you have a watch but you are not sure of the time, you can set it at noon as indicated by the shortest shadow.

 Survival Sundial.  If you are camped in one place for a day or more, you can make a survival sundial which will not only serve as a clock but also as a compass.  Click here to learn more about the survival sundial.

The Pointing Method.  If you do not have time to stop and you do not have an analogue watch,  you can always use the ‘pointing’ method to keep you on course.

Method.

  1. Face the direction in which you plan to travel and point in the direction of the Sun.
  2. Hold this position for a few seconds until the Sun’s direction relative to your body is imprinted in your mind.
  3. Set off on your chosen course keeping the Sun in the same relative position.
  4. Stop every ten to fifteen minutes to reacquaint yourself with the Sun’s relative position, bearing in mind that it covers 15o per hour as it makes its arc across the sky.

Notes.

  1. If the Sun is obscured by cloud, you can adapt this method by using a tall object such as a church spire or mountain to point at.
  2. You can also adapt the method by noting the direction of your shadow instead of the position of the Sun.

Survival Links:  Astro Navigation in a survival situation.  Latitude from the midday Sun. Find your longitude.   Latitude from the North Star  Calculating declination.    Declination table.    The Survival Sundial

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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Survival – The Star Compass

“Know The Stars And You Will Always Have A Compass”.

dreamstime_m_5648294In a survival situation, whether at sea or on land, the chances are you may have nothing to navigate by other than the stars in the sky.

Finding the Direction of North.    The Pole Star (otherwise known by various names including Polaris, North Star, Lodestar and the Guiding Star).  As the Earth rotates, the Pole Star, which is almost exactly in line with the Earth’s celestial north pole, does not change its position in the sky unlike the other visible stars. For this reason, it will always indicate the direction of north.  The trick is to find the Pole Star in the sky and for this we need the help of the following constellations of stars.

 Ursa Major (also knowursa major separten as The Big Dipper, the Plough or The Great Bear).  The best known and easily recognizable constellation in the northern hemisphere is the constellation Ursa Major which is also known by various other names such as the Big Dipper and the Plough.  Ursa Major is a circumpolar constellation which means that it rotates around the celestial north pole and never sets below the horizon.  It is visible all year round in the northern hemisphere and in northern regions of the southern hemisphere.

UrsaUrsa minor Minor (also known as the Little Dipper or the Little Bear) contains Polaris, the Pole Star.  Ursa Minor is also a circumpolar constellation and it can be seen throughout the northern hemisphere and as far south as 10oS.

Using Ursa Major and Minor to find the Pole Star.  Ursa major and minor2As illustrated in the diagram below, Ursa Major contains a reference line known as the line of pointers.  The line joining Merak to Dubhe, when extended, will point to Polaris (the Pole Star) which is in the constellation Ursa Minor.  Polaris is not a particularly bright star although it is the brightest star in Ursa Minor.

cassiopeia aloneCassiopeia. The Queen.  Cassiopeia is another circumpolar constellation; it is quite easy to find because of its ‘W’ shape which sometimes hangs upside down as it circles the north celestial pole.  It can be observed throughout the northern hemisphere and down to 20oS.

The star Segin which lies in Cassiopeia can be located along a line of reference from the Pole Star at an angle of 135o to the line of pointers in Ursa Major as the diagram below shows.  As Ursa Major revolves around the Pole Star, so do the five stars of Cassiopeia with Segin always keeping its position 135o from the line of pointers.  Knowing that the  Pole Star always lies between these two constellations provides us with a further way of finding it.

bear to cassiopeia updateFinding The Direction Of South.   The Southern Cross (the constellation Crux)Crux (Latin for cross) it is one of the smallest constellations in the sky but also one of the brightest.  It is not visible north of 20°N in the northern hemisphere but it is circumpolar in the southern hemisphere south of 34°S which means that it never sets below the horizon there.

Crux has four main stars which mark the tips that form the ‘Southern Cross’:

Acrux, the brightest star in the cross.crux

Becrux, the second brightest.

Gacrux, the third brightest.

Palida has variable levels of brightness.

 

 

finding crux with pointers

 

How to find the Southern Cross.  The constellation Centaurus contains two bright stars which make excellent pointers to help us find the Southern Cross.  The Pointers as they are known, are Rigil Kentaurus and Hadar.

 

Finding south by using the Southern Cross.  Whereas the Pole Star coincides with the position

pointerof the north celestial pole, Crux does not coincide with the celestial south pole so we have to rely on other methods of using it to find the direction of South.  There are several methods but the simplest is as follows: Make an imaginary line between Gacrux and Acrux then extend this line from Acrux (the brightest star) for 4.5 times the length of the Southern Cross, as shown in the diagram below. This will take you to the position of the South Celestial Pole in the sky.  From the South Celestial Pole, drop a line down to the horizon. Where this line touches the horizon is the direction of south.

 

Finding The Directions Of East And West. There will be times when neither the Pole Star nor the Southern Cross can be seen for various reasons.  However, this need not be a problem, for if we can find east or west, we can find north and south.  Fortunately, there are at least two constellations that can help us in this respect.

Orion, The Hunter  This easily recognized constellation straddles the celestial equator and for this reason, it always rises in the East and sets in the West.  The stars Alnitak, Alnilam and Mintaka form the belt of the hunter and are easy to find.  Alnilam which is the middle star of the belt and the brightest of the three is almost exactly on the Celestial Equator so it will always rise atorion due east and set at due west.  The bright red star Betelgeuse will rise first and this will give you a warning when Alnilam is about to rise.

After Orion has risen  it moves across the sky in an westerly direction following the Celestial Equator and so, by noting its position at intervals, we can gauge the direction in which it is moving and so find east and west.

Orion is a Winter Constellation.  This means that it is only visible in the night sky during the northern hemisphere’s winter months (summer in the southern hemisphere).  During summer in the northern hemisphere, it is above the horizon during daylight hours so we cannot see it.  However, all is not lost; we have a summer constellation which can help us to find east and west when ‘Orion is asleep’.

Aquila,aquila The Eagle. Like Orion, Aquila sits astride the celestial equator and its brightest star, Altair, rises very slightly north of due east and sets just north of due west.  During the northern hemisphere’s summer, Altair takes the place of Alnilam and becomes our guiding star to the directions of east and west.

 

summer triangle

 

How to find Altair.  Together with Altair, the stars Deneb in the constellation Cygnus, and Vega in the constellation Lyra form an astronomical asterism known as the ‘Summer Triangle’ which is formed by imaginary lines drawn between those stars as shown in the diagram opposite.  As well as being an important navigation aid in its own right, the Summer Triangle helps us to easily find Altair which can, in turn, help us to find the directions of east and west.

 Reference for the quotation “Know the stars and you will always have a compass”: Michael Punk. 2002. The Revenant

Survival Links:  Astro Navigation in a survival situation.  Latitude from the midday Sun.   Find your longitude.   Latitude from the North Star  Calculating declination.    Declination table.    The Survival Sundial

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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