# Finding direction, distance and navigating to a distant base by stars, fine reading of latitude (Part 2).

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

#find North, #finding North, #direction, #time, #star, #sky map, #sky disk, #declination, #right ascension, #fine reading, #celestial, #distance, #find, #latitude, #navigation, #no instrument, #polynesian, #zenith,
This is applicable to navigation in an ocean or in a large desert with clear, flat horizontal skyline. It uses the complementary stars touching the horizon instead of stars traveling directly over the zenith of the navigator. It is more suitable for sea travel with readily available horizon but unsteady travel platform. It is a useful trick to return to a base (e.g. a Polynesian island) when having no measuring instrument.

## Step 1: Basis of the method.

Figure: The trajectory of the complementary star touches or nearly touches the horizon. Figures: Horizon for an example latitude of 30degrees North projected onto North and South Celestial hemispheres respectively.

Stars travel along constant declination circles drawn on the Celestial sphere. If the base city is at latitude L then the constant declination circle of 90°-L on its same (North or South) hemisphere will be seen touching the horizon and the lowest position of the complementary star will be right on the horizon and in the principal Northern/Southern direction. When the (complementary) stars of declination 90°-L is at its lowest point near the horizon, unaided human eyes can easily tell its elevation accurate to 1/4 Moon’s diameter (1/8 of a degree).

If bright complementary stars are unavailable for any latitude, users of this method have to identify some constellations having dim complementary stars for that latitude and use these stars instead.

## Step 2: Preparation at base for this method.

Figures: 20 brightest stars and their positions in the sky represented in Northern and Southern 3/4 spheres. Dimmer stars beyond this list may have to be used by this method for traveling to any arbitrarily given latitude.

1. Work out the latitude of the chosen city.
2. Work out the complementary angle for that latitude.
3. Use a list of bright stars (in reverse order of brightness) to choose a star or stars having declinations being equal or greater than the complementary angle by less than 2 degrees (the difference is less than 2degrees or 4 Moon’s diameters). The less bright stars may have their declinations closer to required values but their poor visibility may make them unsuitable. The chosen star may slightly dive under the horizon but its neighbouring stars can indicate how far it has dived.
4. Practice identifying the complementary stars in all imaginable conditions.

Step 3: Field application

5. Travel North or South until the lowest position of the complementary star touching or slightly above the horizon by the so determined adjustment of less than 4 diameters of the Moon.
6. On attaining that latitude, only travel along a parallel circle to maintain the latitude.

Step 4: Examples.

Figure: The trajectory of the complementary star for London touches or nearly touches the horizon when viewed at the latitude of London.

London is at (0°5′ longitude, 51°32′ latitude), choose Vega (18hr 37 RA, +38.8deg declination). Around midnight of Dec. 25th, the star Vega travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 51°32 + 38.8° – 90° = 0.3°.
This angle is half the diameter of the Moon and can be judged accurately by unaided eyes.

Berlin is at (13°25′ longitude, 52°30 latitude), choose Vega (18hr 37 RA, +38.8deg declination). Around midnight of Dec. 25th, the star Vega travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 52°32 + 38.8° – 90° = 1.3°.
This angle is 3 diameters of the Moon and can be judged accurately by unaided eyes.
Manila (120°57′ longitude, 14°35′ latitude), choose a dim star Beta Ursae Minoris, (Kochab, 14hr51RA, +74.3deg declination). Around midnight of Nov. 07th, the star Kochab travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 14°35 + 74.21° – 90° = -1.3° (under the horizon by 1.3degrees. This angle is 3 diameters of the Moon and cannot be seen but its visible neighbouring stars in the Ursa Minoris group can indicate how far this star is below the horizon.).
Mecca(39°45 longitude, 21°29 latitude) choose Gamma Ursae Minoris (Pherkad Major, 15hr 21RA, +71.8° declination). Around midnight of Nov. 16th, the star Kochab travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 21°29 + 71.8° – 90° = +3.3°. This angle is 7 diameters of the Moon and can be judged accurately by unaided eyes using fingerwidths on a stretched arm.

Tonga Capital city is Nukuʻalofa (175°12′W = 184°48′ longitude, 21°08′S latitude). Choose the star Beta Carinae (Miaplacidus 09hr 13 RA -69.7decl). Navigators may have to identify the constellation Carina containing the bright star Canopus in order to identify a not quite bright Beta Carinae. Around midnight of Aug. 10th, the star Beta Carinae travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 21°08′ + 69.7° – 90° = +0.8°. This angle is 1 and 1/2 diameters of the Moon and can be judged accurately by unaided eyes.

The Northern tip of Iceland is at 66°30′ (see the map from viking ships , [2]). Choose the Sun at its June 21st solstice. Around midnight of Jun. 21st, the center of the Sun travels to its lowest point on a circle glancing the horizon. Its center is exactly on the horizon when the navigator is on the latitude of the Northern tip of Iceland. The upper rim of the Sun is just touching the horizon on Jun. 21st when the navigator is on the latitude of Northern Iceland. Keeping this latitude brings the navigator to Iceland on a journey of 900km from Norway.

Step 5: Notes on terminal homing of journeys.

Near to the end of his journey, an ocean navigator may release island spotting birds.
If the birds can attain a height of 800m, they can spot land (even without using cloud features) at distance of 110km away (60 nautical miles, or 1 degree of arc or 2 Moon’s diameters).
If the birds can attain a height of 250m, they can spot land (even without using cloud features) at distance of 55km away (30 nautical miles, or 0.5 degree of arc or 1 Moon’s diameter).
If the birds can attain a height of 62m, they can spot land (even without using cloud features) at distance of 28km away (15 nautical miles, or 0.25 degree of arc or 0.5 Moon’s diameter).

Alternatively the navigator may note the presence of nautical birds from the island ( , [2]). The navigator can also use currents, winds and even smells in this phase.
The error of this navigation method is thus well within the operational range provided by the spotting birds.

References

[1]. tonytran2015, Finding direction, distance and navigating to a distant base by stars (Part 1). Additional Survival tricks, wordpress.com,
Posted on January 27, 2016.

Added after 2018 July 20:

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Finding North and time by stars. Posted on August 28, 2015

# Finding time to Sunrise with star maps

Finding time to Sunrise with star maps

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

#determine, #find, #find North, #time, #Sunset, #Sunrise, #time to Sunrise, #time to Sunset, #sky disk, #star disk,
Finding time to Sunrise is needed for traveling across deserts as the travellers may want to be on time to avoid excessive heat and coldness. It is also needed by long distance traders and country people who have to schedule their peak activities around Sunrise time.
Finding time to Sunrise is harder than to Sunset because the Sun is not seen before Sunrise (for people in tropical and temprate zones)! This method relies on the symmetry between Sunset and Sunrise to work out the time to next Sunrise using a circular sky map.

1. Mark the direction to the setting Sun

Use two rocks or a stick lying on the ground to mark the direction of the setting Sun.

2. Start a stop-watch.
The interval from Sunset to alignment of star maps may be significant (See the note at the end of step 5.).

3. Aligning stars and the Sun to star map

Figure 1: Aligning the sky map to the stars and Celestial axis OP. Figure 2: Constructing the half-plane containing the Celestial axis OP and the half-line pointing to Sunset position. Figure 3: The intersection between the sky map and the Sunset half-plane gives the radial line OC.

Accurately align one of the star maps (such as of this article) to the stars and align its axis to the Celestial axis so that it points to the upper Celestial pole P. Work out the half-plane of constant R.A. containing the Celestial axis and the Sunset direction half-line. This half-plane intersects the polar sky map along a radial line which is often non-horizontal. Use a paper clip to mark the intersection C of the rim of the star-map disk and the half-plane.

4. Stop the stop watch.

Figure 1: The sky map for use in Northern hemisphere. Figure 2: The sky map for use in Southern hemisphere.
Stop the stop watch and note the time from Sunset to time of alignment of the sky map. This time varies from 5 minutes in the tropic to nearly one hour in the cold temperate zones (See the note at the end of step 5.).

5. Adjustment of alignment of the Sun
Use the stop-watch reading to determine the small amount of time from Sunset to the successful alignment of the star map. The paper-clip on the rim should be moved to a new position toward the bottom of the sky map by an angle corresponding to the time interval given by the stop-watch.
The paper clip should now be on the R.A. half-plane containing the Celestial axis and the Sun. The Sun has moved further down under the horizon corresponding to the rotation of sky map since Sunset to alignment time.
The stop-watch of steps 2, 4 and 5 is not necessary if the rotation of the Celestial sphere during that time interval can be worked out by any other mean such as from the rotation of an early Moon which is visible both before and after Sunset.
6. Coarse time to Sunrise.
The rising Sun will be the left-right reflection image of the setting Sun through the true North-South plane . So are the two corresponding positions of the paper clip. The sky map will rotate during the night and the paper clip will move through the position for Sunrise. The time to Sunrise is the time for the sky map to rotate between its current position and Sunrise position. (One full circle is 24 hours).

7. Alternative coarse time to Sunrise by the late Moon.
A late Moon remains in the sky until Sunrise. The shape of the Moon indicates the direction of the out-of-view Sun. The Celestial axis can be determined from the declination of the Sun and the local latitude. So time for the Sun to reach the horizon can be estimated. This method has been given previously.
8. Fine time to Sunrise.

Observe the identifiable stars near the 90 degree Eastern horizon. They always rise up at the same angles (along the constant declination lines) from the same terrestrial directions on the horizon. Before the stars fade at Sunrise, pay attention to those that have risen about 1 to 5 degree from their rising positions and take notes of their travel (at angle to the horizon, along the constant declination lines) from the initial rising positions on the horizon. The stars rise 1 additional degree early for each subsequent day and new stars will appear to take their role. Using these stars close to the Eastern horizon, the time to Sunrise on subsequent days are determined with better accuracy.
Notes.
1. The motion of a new or early Moon in the sky can be used to time the interval from Sunset to alignment of the star map (by checking its rotation with the sky map). A stop-watch is not required in such a case.
2. If a large sky map is drawn on a wheel mounted on its axis aligned along the Celestial axis then a time keeper only needs to align the sky map to the stars at night and the paper clip to the Sun during day time to read fairly accurate local time from the travel of the rim of the wheel. The paper clip will make one complete rotation everyday and its position on the sky map needs adjustment by only 1 degree each day.
References

[1]. tonytran2015, Finding North direction and time by stars, Additional Survival Tricks, http://www.survivaltricks.wordpress.com/, posted on Aug 28, 2015
[2]. tonytran2015, Finding North and time with unclear sky, Additional Survival Tricks, http://www.survivaltricks.wordpress.com/ , posted Oct 17, 2015.
[3]. tonytran2015, Finding time to Sunset with bare hands, Additional Survival Tricks, https://survivaltricks.wordpress.com/2015/11/11/finding-time-to-sunset-with-bare-hands/, posted Nov 11, 2015.

[4]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon, Additional Survival Tricks, http://www.survivaltricks.wordpress.com/ , posted Jul 06, 2015.un/, posted May 24, 2017,

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# Finding time to Sunset with bare hands

Finding time to Sunset with bare hands

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

#bare hands, #determine, #find, #find North, #time, #Sunset, #Sunrise, #time to Sunrise, #time to Sunset.

Finding time to Sunset with bare hands (Blog No. 11).

There are times when you have no watch or when it is not practical to carry a watch (such as when going for a swim in the sea) and you need to know the time from Sunrise or to Sunset. This time can be determined reasonably accurately using only your bare hands.

1. Hand postures

Figure. Hand posture for determining time to Sunset in the Northern hemisphere.

Cup your hand as if about to hold water. Position the wrist to have the thumb on top with four fingers horizontal and close together. Then stretch your arm, keeping all fingers at right angle to the stretched arm. Stand with your chest facing the Sun but DO NOT LOOK INTO THE SUN. Interpose the bent fingers on your stretched arm between the Sun and your aiming eye on the same half of your body. Twist the stretched arm to have the bent fingers forming with the horizon an angle equal to the local latitude angle and the contact line between middle finger and ring finger being on the same plane with the Celestial axis (Tilting the fingers from the horizontal by an angle equal to latitude angle is close enough).
The Sun will travel at right angle to your fingers to its setting position on the horizon .
Count the finger widths from the Sun to its setting position. Each finger width is about 1.5 degrees distance and is equal to 1.5×4 = 6 minutes of time to setting on equinoxes or is equal to 6.6 minutes of time to setting on solstices.
(At solstices, the length of the trajectory of the Sun is only (6.24radius)x cos(23.5degrees), so each 1degree of length corresponds to 4.4minutes of time).
For example, four finger widths to setting point gives 4×1.5×4 minutes of time to setting at equinoxes or 4×1.5×4.4 minutes of time to setting at solstices.

2. Notes

1/- In the Northern hemisphere the Sun moves to the right (North) when setting.
2/- In the Southern hemisphere the Sun moves to the left (South) when setting.
3/- The Sun is between the middle and ring fingers if any small gap between them let through strong rays of light.
4/- Your finger width on your stretched arm may sustain an angle different from 1.5 degree. You need to check it against the diameter of 0.5 degree of the rising or setting Moon.
5/- In Northern hemisphere, the Sun rises to the right (South).
6/- In Southern hemisphere, the Sun rises to the left (North).

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