Finding North by stars for beginners

Finding North by stars for beginners.

by tonytran2015 (Melbourne, Australia).

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

(Blog No.85).

#find North, #finding North, #by stars, #star disk, #star map, #Mercator, #beginner,

Finding North by stars for beginners.

Beginners only need to know few stars to practice finding North by stars.

1. Common viewing instructions for all beginners.

1. From the following three maps select and print the one suitable for your zone.

Sky map Northern 3/4 sphere

Figure: Sky map (Inversion type) of the Northern Celestial 3/4-sphere showing only 20 brightest stars and some constellations. 24hr of R.A. is on the top and R.A. increases in the clockwise direction.

Sky map Southern 3/4 sphere

Figure: Sky map (Inversion type) of the Southern Celestial 3/4-sphere showing only 20 brightest stars and some constellations. 24hr of R.A. is on the top and R.A. increases in the anti-clockwise direction.

star map mercatorx1p6

Figure: The Mercator map of the sky for inhabitants of Tropical Zone. North direction is on its top. 24hr of R.A. is near the center and R.A. increases towards the left (East) of the map. The map is to be read South side up in the Southern hemisphere.

2. Use a shadow stick or a compass to find out the (true) North direction at your location.

shadow stick to tell time and find North

Figure: A shadow stick for finding North and time is drawn here in blue colour. The shadow of its tip always move WEST TO EAST along a conical curve C (drawn in red). The axis of symmetry of the curve C is the terrestrial North-South direction. (Conical curve: Elliptical, parabolic or hyperbolic curve).

3. Find out the latitude of your location.

4. Find out the current date in the calendar year.

5. Use the following simplified instructions to identify the stars at mid-nights.

2. Viewing instructions for inhabitants of Polar and Temperate Zones.

1. Place one of your straightened arm horizontally, pointing to North if you are in Northern hemisphere and South if in Southern hemisphere.

2. Raise your straightened arm by an angle equal to your latitude. Your straightened arm now points to the Celestial pole at your location.

3. Hold the circular star map on the hand of that arm, with its axis pointing to the Celestial pole and the MARKING FOR CURRENT MONTH ON ITS RIM AT ITS BOTTOM.

4. You can now see the images of stars on the map pointing to the actual stars.

sky disk alignment

Figure: Aligning the center of the paper star disk to the Celestial pole in the sky to identify the stars at midnight.

5. Beginners only need to recognize the circumpolar stars for their own hemisphere.

Inhabitants of Northern hemisphere need only to identify Little Dipper, Big Dipper (11hr R.A., 60° declination) and Cassiopeia (1hr R.A., 60° declination).

Figure: Finding North by stars for beginners (Northern hemisphere).

Inhabitants of Southern hemisphere need only to identify Agena, Alpha Centauri (pointer stars) and Acherna in the anticlockwise direction (all at 60° South declination). Acherna is 60 degree from the pair (alpha Centauri, Agena) and is on the opposite side across the Southern Celestial Pole.

Figure: Finding North by stars for beginners (Southern hemisphere).

Extending the line alpha Centauri-Agena by 8 degrees gives the Southern Cross Constellation. Then turning clockwise by 50 degrees and extending by another 50 degrees gives the very bright Canopus star.

In the opposite direction, extending the line Agena-alpha Centauri by about 30 degrees gives the stinger tail of the large, distinctive Scorpius constellation.

6. The knowledge of other stars will follow naturally with time.

3. Viewing instructions for inhabitants of Tropical Zone.

1. Hold the Mercator star map above your head, with North direction pointing to true North.

2. The length of the map corresponds to 13 months. Select and view only 6 month centered on the CURRENT MONTH. The line for the current month is worked out from the markings along the vertical lines of this Mercator map.

3. You can now see the images of stars on the map pointing to the actual stars.

4. Beginners only need to recognize some bright stars near to the Celestial equator: Orion Rigel and Betelgeuse of the large, distinctive Orion constellation, Procyon, Leo Regulus, Spica, Bootes Arcturus, Altair, Antares of the large, distinctive Scorpius constellation. They are associated with various different months of the year.

Equatorial Stars2

Figures: Finding North by stars for beginners (Tropical zone). Click to enlarge figure.

5. The knowledge of other stars will follow naturally with time (see Slide Sky-Map for displaying tropical stars.).

Bright Stars 20 Plus 2

Figure 2: Table of 20 brightest +2 stars in order of appearance.

4. Common Identifying instructions.

Sun on Celestial Sphere

Figure: The Sun, the Moon and the stars are attached to a Celestial sphere which encloses the Earth like a giant rotating cage.

1. Beginners should observe the identified stars in subsequent night as well as at various different time.

2. The circumpolar stars will remain visible all year round for cold temperate zones. Beginners only need to know them well.

3. The tropical stars appear in sequences and tropical inhabitants have to associate tropical stars with their months in the year.

4. Tropical constellations are seen upright from Northern Hemisphere and upside down from Southern Hemisphere

References.

[1]. tonytran2015, Shadow-stick-navigation-and-graph-of-solar-paths, posted on August 19, 2016.

[2]. wiki, Astronomical_ceiling_of_Senemut_Tomb.

[3]. Suchow map, http://www.adlerplanetarium.org/exhibits/planetary-machines.

[4]. wiki, Chinese_star_maps

[5]. tonytran2015, Finding directions and time using the Sun and a divider, survivaltricks.wordpress.com , Finding directions and time using the Sun and a divider., posted on May 6, 2015.

[6]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon, survivaltricks.wordpress.com, Finding North direction and time using the hidden Sun via the Moon . Posted on July 6, 2015.

[7]. tonytran2015, Finding North direction and time by stars, survivaltricks.wordpress.com, Finding North and time by stars. Posted on August 28, 2015

[8]. tonytran2015, Finding accurate directions using a watch, posted on May 19, 2015 .

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Time keeping without using watches

Time keeping without using watches

by tonytran2015 (Melbourne, Australia).

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

(Blog No.84).

#find North, #find time, #finding time, #time keeping, #timekeeping, #shadow stick, #star disk, #aiming rod, #equatorial mount, #sundial, #true North.

Time keeping without using watches.

Whenever an expedition camp is set up there is always a need for time keeping in the camp. Time keeping is required to get everyone back to base at the same time for meals or for camp activities. In the Eastern World, people had practiced reasonably accurate time keeping WITHOUT USING WATCHES since more than 2000 years ago. Their technique has been fairly accurate and is explained here so that it can be appreciated and be useful to modern campers when separated from their watches.

1. The vertical shadow stick for finding time and finding North.

In the old-time in Eastern World, each castle has a time-keeper. It is interesting to learn the tricks of such a timekeeper. His main instrument is the vertical shadow stick the operation of which is described here

shadow stick to tell time and find North

Figure: A shadow stick for finding North and time is drawn here in blue colour. The shadow of its tip always move WEST TO EAST along a conical curve C (drawn in red). The shadow of the whole stick is a straight line joining its base to the shadow of its tip on the curve C. The axis of symmetry of the curve C is the terrestrial North-South direction.

A. The timekeeper/navigator first sets up a rigid vertical rod firmly buried in a level ground. The movement of the shadow of its tip gives time as well as directional information. That is it tells both time and the North-South direction.

B. He then draws many concentric circles on the level ground around the base of the stick. He then marks the position of the shadow of the tip on the ground, joining them to make a curve (which can be shown by geometry to be a “conical curve”). The symmetry axis of this curve is the true North-South direction at the location and the point on the curve closest to the base of the vertical stick corresponds to Local Noon (which differs significantly from Zonal Noon due to difference in Longitude and the variable speed of the Sun on the Celestial Sphere, the effect of the latter is known as the effect of the Time Equation). The shadow of the tip always moves WEST TO EAST and does so accurately near to NOON. Near to noon the shadow of the tip moves Eastwards by a distance of 1/4 of its distance to the tip every hour.

The timekeeper/navigator gives daily instructions to camp inhabitants on the time to come back to camp for meals/activities. The time for coming back is selected by his predetermined ratio of the length of the vertical stick to that of its shadow. When leaving the base camp, each inhabitant has to make his own portable vertical stick to keep track of the approaching time for returning to base.

C. The vertical stick has a drawback that is the shadow of its tip travels at non-constant speed on a curve that changes slowly during the year.
One example of the disadvantages of the vertical shadow stick is that it cannot help dividing daylight duration into six intervals of equal duration for guard duties.

D. Equal intervals of time are determined from burning incense sticks, reciting prayers, filling containers with dripping water, boiling water pots, etc… Near to noon the shadow of the tip moves Eastwards by a distance of 1/4 of its distance to the tip every hour (During one hour the Sun moves along an arc which is nearly 15 degrees long and sin 15° is nearly 1/4.).

2. Star disk for time keeping at night.

Time keeping at night can be carried out accurately using the stars.

Any star-gazer (ancient timekeepers/navigators had to be star gazers) in temperate zones can easily see that all stars on the Celestial sphere rotate around the stationary Polar star (when observed from Northern hemisphere) or a stationary black point (from Southern hemisphere). It appears as if all circumpolar stars have been stuck on a heavenly disk pivoted on the Celestial pole in the sky and the disk rotates slowly during the night.

The stars have certainly been drawn on an Egyptian Senenmut star map since before 1473BC (https://en.m.wikipedia.org/wiki/Astronomical_ceiling_of_Senemut_Tomb)

220px-Senenmut

Figure: The double wall mural of the tomb of Senenmut, (https://en.m.wikipedia.org/wiki/File:Senenmut.jpg), the image has been released into Public Domain.

on China Suchow map about 1190BC, and on walls of tombs in the land of present China, wiki, Chinese star maps

Figure: Suchow map, from Wikipedia. Used under Common Creative License conditions.

The rotation of the disk can be used to tell time. The rotation seems to be at constant speed as equal angles of rotation seem to always correspond to the same duration of time for burning incense sticks, reciting prayers, filling containers with dripping water, boiling water pots, etc…

Figure: A circular disk with the drawing of bright Northern circumpolar stars as well as other bright stars visible in the sky.

To tell time accurately, the time-keeper can draw the bright circumpolar stars (including the Little and Big Dippers) on a paper disk, hold the paper disk in the direction of the Celestial pole in the sky and rotate the paper disk to align the drawing to the actual star. The slow rotation of the paper disk indicates the passage of time. The accuracy of the method depends on the size of the disk and the accuracy of its alignment to the real stars in the sky.

star disk alignment

Figure: Aligning the center of the paper star disk to the Celestial pole in the sky to determine its rotation during the night.

This method does not require the determination of meridional crossing of dim stars. Ancient time keepers may have used this method to keep accurate time at night using only bright stars..

3. Time divisions by meridional passing of selected stars.

A star makes a meridional passing when it passes the vertical plane in the North-South direction. That is when it is vertically on top of a wire strung in the North-South direction.

A time-keeper may use the meridional passings of selected stars as markers for division of time (into many known recorded unequal parts) during night-time.

Based on those markers a time-keeper can divide the night into nearly equal intervals.

4. Improved Star disk for time keeping at night.

A bigger disk can be aligned more accurately, its rotation can be more accurately measured, but is harder to be held up in the sky. Making a bigger disk mounted in air for improved accuracy is therefore an expensive design.

star disk for equatorial mount on ground

Figure: A star disk on equatorial mount on the ground, to be read from its upper surface.

A better design is presented here and it is to make a big star disk on equatorial mount so that it will be parallel to the paper disk in the air but is mounted on the ground like a tilted round table top, with an aiming rod mounted at its center pointing to the Celestial pole. The star map engraved on the big disk here is a mirror reflection of the image of stars in the sky. An imaginary observer underneath the disk would see through it the image of the stars in the sky. Markings will be drawn accurately on the rim of the big disk for the positions of the engraved stars (which are drawn for a designated night of the year). There will also be regularly spaced markings for measuring the rotation of the observed stars from their engraved standard positions. A time-keeper will only require access to the upper surface and the rim of this large star disk mounted on the ground.

star disk for mounting on the ground

Figure: A star disk for installing on an equatorial mount on the ground. The map here is a mirror reflection of the image in the sky. This disk is aligned for September Equinox.

With this type of large star disk and its central aiming rod, a time-keeper can tell where a star is relative to its position engraved on the disk. The disk is engraved with drawing of the stars on one designated night which may be either the spring equinox night or the winter solstice night.

The spring equinox night has the advantage of accuracy of date in the year, it is the night when the Sun rises and sets exactly in the East and West principal directions. The winter solstice night has the advantage of having the longest duration to observe stars.

On the designated date for the disk, the rotation of any star from its engraved position directly gives the time from midnight. On any other night an offset can be worked out using only a string placed along the perimeter of the circular disk. For every night subsequent to the designated night the stars move forward by nearly 1/365 of the perimeter.

5. Star disk for time keeping in the day.

The nights with partial Moon show that the Moon moves around the aiming rod at nearly the same speed as the stars. The days with partial Moon also show that the Moon and the Sun move around the aiming rod at nearly the same speed.
Therefore any time-keeper with an inclined star disk will find that the Sun, the Moon and the stars all move together around the aiming rod with nearly the same speed. This would lead to his use of the inclined star disk for time keeping, with the advantage that the shadow of the aiming pole moves on the rim of the inclined disk at constant speed! So the inclined star disk also work as an equatorial mounted sundial (meaning the sundial disk is parallel to the equatorial plane.).
(This knowledge has given rise to the description of Solar position in the Zodiac. The shifting of the Zodiac by precession shows that the association of solar position with the Zodiac has begun thousands of years ago.)

So far I had been able to find only equatorial mounted sundial with no engraving of stars. One such a sundial can be seen in Beijing. This disk has only time markings and can be read on both sides.

Figure: A sundial in the Forbidden City, or Imperial Palace, in Beijing. https://commons.wikimedia.org/wiki/File%3ABeijing_sundial.jpg, Date 26 February 2003, Author User: Sputnikcccp~commonswiki .Figure used under the Creative Commons Attribution-ShareAlike License.

During Winter months, a flat cardboard can be used to find the intersection of the shadow of the aiming stick and the rim of the large disk if it has no accessible lower surface.
Using the equatorial sundial during the days gives the advantage of fast determination of time with no required large seasonal adjustment. With the help of an equatorial mounted sundial, a time-keeper can divide time into any number of equal intervals and can also work out the ratio of a vertical stick to its shadow at any time of the day.

6. Timing wires used in remote areas.

Similar to the central rod of an equatorial mounted star disk, any taut wire strung parallel to the Celestial axis can be used to time intervals of 24 hour. The shadow of such a wire under a strong Sun comes back to its previous position after every 24 hours. Clock makers in the 1800’s, when radio receivers were not widely used, have been using this trick to time the clocks under their repairs .

7. Time keeping with an unclear sky.

Burning of incense is used to complement time keeping using star disk in days of poor visibility.

Time keepers have incense sticks for short-term timing or incense coils which last up to three days for long-term timing.

Time keepers also have other methods for timing, they are reciting prayers, filling containers by dripping water, boiling water pots.

On ancient ships, time keepers can count repetitive actions such as the rowing cycles of oars, the food items made by a kitchen, etc…

8. Announcing time to surrounding area.

The time-keeper may use drums or low pitch horns to announce the time to his surrounding area.

On receiving the signal for time, surrounding institutions such as nearby pagodas synchronize their own activities and then may sound their own gongs as secondary level time signals.

The population around the castle use these time signals to open their shops, prepare their predawn cooking etc…

The whole community relies on those signals to synchronize their interacting activities.

9. Natural time keepers.

There are natural time keepers, they are the animals and plants in the areas.

Certain types of birds tweets ar some fix time intervals before sunrise. Each type of tweets has its own fix interval before sunrise. The tweets by different types of birds follow one another in the same sequence every day.

Chickens’ roosting have been used as reliable time signal foe imminent sunrise.

Chameleons’ croaking have sometimes been used by some people in Vietnam as reliable Noon time signal.

There are some plant flowering at some certain time during the day. The Vietnamese plants “HOA MƯỜI GIỜ” (meaning “Ten o’ clock flowering plants”) flowers at a constant time near to 10 AM.

References.

[1]. tonytran2015, Shadow-stick-navigation-and-graph-of-solar-paths, posted on August 19, 2016.

[2]. wiki, Astronomical_ceiling_of_Senemut_Tomb.

[3]. Suchow map, http://www.adlerplanetarium.org/exhibits/planetary-machines.

[4]. wiki, Chinese_star_maps

[5]. tonytran2015, Finding directions and time using the Sun and a divider, survivaltricks.wordpress.com , Finding directions and time using the Sun and a divider., posted on May 6, 2015.

[6]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon, survivaltricks.wordpress.com, Finding North direction and time using the hidden Sun via the Moon . Posted on July 6, 2015.

[7]. tonytran2015, Finding North direction and time by stars, survivaltricks.wordpress.com, Finding North and time by stars. Posted on August 28, 2015

[8]. tonytran2015, Finding accurate directions using a watch, posted on May 19, 2015 .

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Slide Sky-Disks with grid masks showing azimuths and altitudes.

Slide Sky-Disks with grid masks showing azimuths and altitudes

by tonytran2015 (Melbourne, Australia).

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

(blog No.28)

#find North, #finding North, #direction, #time, #slide, #sky, #star, #map, #disc, #disk, #star disk, #slide sky map, #slide sky disk, #slide star disk, #navigation, #declination, #right ascension.
Feature Figure: Illustration of a rotatable Sky map with an overlaid grid mask showing azimuths and latitudes of stars for a user at 40 degree latitude.

(Note: There was a software error which initially set the publication date wrongly on October 19th, 2016. The true publication date is Nov 3rd, 2016.)

It is an advantage to know the arrangement of stars for the nights before engaging in nightly activities such as going to the country side or navigating your way by stars. It is difficult to have a good display of the night sky with current commercially available circular star maps as they are equidistant-azimuthal and have a lot of distortion for visualization whereas easy visualization requires that groups of stars should appears with the same shape as actually observed in the sky and the constant altitude curves should be nearly circular around the zenith point.

The device given in this posting gives the desired displays with low distortion for the night sky. I give it the name Slide Sky-Disk (which is similar to the name Circular Slide Rules of similar looking mathematical devices used before the age of calculators).

It is made of two maps of stars and of interchangeable viewing grids to give elevation and azimuth angles of stars to observers located near to 0 degree, 20 degrees, 40 degrees and 60 degrees in latitude.

It will be useful to people who want to learn the stars by themselves or need to refresh their nightly detailed knowledge of the sky before going out. It is low cost, light weight, small, flexible, durable and quite portable. If made from waterproof materials, it may also be used as a low cost standby star maps for pilots, travelers, hikers and seamen (My is made from CD discs, flexible CD cases and plastic films, they are all waterproof).

The device is made by following instructions in the next 4 steps. PLEASE READ THROUGH ALL STEPS BEFORE STARTING ANY CONSTRUCTION.

Step 1: Making the base maps for the Slide Sky-Disks.

Sky-disk for Celestial Northern 3/4-sphere

Sky-disk for Celestial Southern 3/4-sphere

Figures 1, 2: Two base maps.

The two maps of the North and South regions of the Celestial sphere made by Inversion Projection (Stereoscopic Projection) are used for the Northern and Southern hemispheres respectively.

The maps are to be printed on both sides of a thick sheet of A4 paper to make a base disc. Alternatively they can be printed on ordinary A4 papers and pasted on the opposite sides of a thick disk used as the base disc. I used 2 CD discs and print the maps as their labels.

Step 2: Making rotatable overlaying masks giving azimuth and elevation on the Slide-Sky-Disks.

altitude azimuth grid mask for 00 degrees of latitude

altitude azimuth grid mask for 20 degrees of latitude

altitude azimuth grid mask for 40 degrees of latitude

altitude azimuth grid mask for 60 degrees of latitude

Figures 1, 2, 3, 4: The grid masks for observers at 0 degree, 20 degrees, 40 degrees and 60 degrees in latitude.

A grid mask is placed on top of the base map to read the azimuth and the elevation of the stars drawn on the map. The grid masks must match the type of coordinates used for drawing the Celestial sphere. An observer must use the mask drawn for his latitude.

Description of curves on grid masks:

The smallest circle of each grid is graduated into 12 intervals of 30 degrees each to show the azimuth angle of the star or direction from True North (or True South for Southern latitudes). The curves radiating from the center represent the great circles from the zenith to the terrestrial points of 0 degree (North), 30, 60, 90 degree (East) , 120, 150, 180 degree (South), 210, 240, 270 degree (West), 300, 330 (The North line points toward the map’s center in Northern hemisphere and away from it in Southern hemisphere.). The red circular arcs represent the constant elevation circles in the sky. They are placed at 30, 60 and 90 degrees from the zenith. The circle at 90 degrees from the zenith represents the horizon on flat locations. The graduation can also be read from the horizon circle toward the center to show the elevation angle of the star. The position of any star in the sky can be read against the grid.

Four grid masks are given here for use with both Celestial spheres. You have to select one that is based on a latitude nearest to your current latitude.

For latitude between 0 degree and 10 degree select the mask based on 0 degree latitude.

For latitude between 10 degree North and 30 degree select the mask based on 20 degree latitude.

For latitude between 30 degree North and 50 degree select the mask based on 40 degree latitude.

For latitude between 50 degree North and 70 degree select the mask based on 60 degree latitude.
You can make all four masks as each can be easily fit into and removed from the device as you move to a location with a different latitude.

Make each mask with the CORRECT size and print it at the CENTER of an uncut A4 waterproof transparent film by a photocopier. If this cannot be done you may have to print the mask on an ordinary piece of paper, place a transparent film on top of it and trace the grid lines onto the waterproof transparent film using a pen with waterproof ink.

Step 3: Making the grid holder for a Slide-Sky-Disk.

Figure: The grids holder is made from a flexible CD case.

The grid holder is made from a flexible plastic CD box. The front circular window has been cut for viewing the map. A small rear window is cut for moving the map. A grid is drawn onto a square transparent film and fitted to the front cover. It is to be held in place by the four plastic lugs (visible in the picture). The base map will be fitted on to the holding stub on the back cover and it can be rotated relative to the case and the grid on the front cover.

Step 4: Final assemblage of a Slide-Sky-Disk.
slide-sky-disk

Figure 1: Photograph of an actual Slide Sky-Disk fitted with a mask for 40 degree.

slide sky disc rotated

Figure 2: Photograph with Sky-Disk rotated anti-clockwise by about 25 degrees.
Push the CD with the picture of the chosen hemisphere onto the holding stub of the CD case. Make sure that it can be easily rotated inside the holder. Close the case and the Slide Sky-Disk is ready for use. The disc is rotated by access through the small window on the back cover.

Step 5: Using the Slide-Sky-Disks.

The sky at night is represented by the circular sky map centered on the corresponding Celestial pole under the transparent window carrying the grid showing azimuth and altitude (that is the disc rotates under the viewing window).

1/- Check that the center cross of the grid is on the declination line corresponding to your required latitude.

2/- Rotate the map to place the current date on the opposite side of the window. The map and the grid gives the view of the mid-night sky for the date.

3/- Then rotate the core map by half a division (15 degree on the equator or half a month) to decrease or increase the Right Ascension for every hour ahead of or after midnight. R.A. increases in the clockwise direction for Northern and counter-clockwise for Southern hemisphere.

4/- As the latitude for the grid is not being exactly that of the observer and the true time at the location is not being equal to the zonal time the slide star disk may not give very accurate values of elevation and azimuth angle for the stars within 30 degree of the zenith. However the lines joining these stars still give accurate directions and they help identifying other stars near the horizon. The stars near the horizon can be read from the Slide Sky-Disk with more accurate values of azimuth and elevation angles.

Examples:

The sky of December 21st can be visualized for any latitude using these Slide Sky-Disks in combination with a Slide Sky Map [3] .The view is CORRECTLY ORIENTED WHEN its December marking ON EACH DISK IS AT THE BOTTOM. You may have to click on each image to have a clearer view.

Sky map for Dec 21st at latitude of 60°N

 Sky map for Dec 21st at latitude of 40°N

Figures 1,2: Night sky on Dec 21st at latitudes of 60°N, 40°N, up side down view. The view is CORRECTLY ORIENTED WHEN its December marking ON EACH DISK IS AT THE BOTTOM.

 Sky map for Dec 21st at latitude of 20°N

 Sky map for Dec 21st at latitude of 20°N

Figures 3,4: Night sky on Dec 21st at latitudes of 20°N, upside down view. The view is CORRECTLY ORIENTED WHEN its December marking is AT THE BOTTOM ON THE DISK.

 Sky map for Dec 21st at latitude of 0°

 Sky map for Dec 21st at latitude of 0°

 Sky map for Dec 21st at latitude of 0°

Figures 5,6,7: Night sky on Dec 21st at latitude of 0°N. The view of Figure 5 is CORRECTLY ORIENTED WHEN its December marking is AT THE BOTTOM ON THE DISK.

 Sky map for Dec 21st at latitude of 20°S

 Sky map for Dec 21st at latitude of 20°S

Figures 8,9: Night sky on Dec 21st at latitudes of 20°S.

 Sky map for Dec 21st at latitude of 40°S

 Sky map for Dec 21st at latitude of 60°S

Figures 10,11: Night sky on Dec 21st at latitudes of 40°S and 60°S.



References.

[1]. tonytran2015, Finding North and time by stars. Posted on August 28, 2015

[2]. tonytran2015, . Posted on May 25, 2016

[3]. tonytran2015, Slide Sky-Map for displaying tropical stars, posted on October 7, 2016

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Finding time to Sunrise with star maps

Finding time to Sunrise with star maps

by tonytran2015 (Melbourne, Australia).

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#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

sunrise1

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

sunrise2

sunrise3

sunrise

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.

PolrNorthNC20const8

 

polrsouthp4

 

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.

Sunrise5

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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