The Scorpius constellation

The Scorpius constellation

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.45).

#find North, #finding North, #direction, #by stars, #Scorpius, #Antares, #Sagittarius, #Ara, #navigation, #constellation.

Celestial navigators who do not use declination and right ascension begin their navigation by learning the various bright, easily identifiable constellations in the sky (There are no more than 10 to learn.). The Scorpius is usually chosen to be the second constellation to be learned since it is as large as Orion and is useful when Orion is out of sight.

The Scorpius is a crowded, large Southern constellation of June. Part of it is always seen in the sky of June for the whole night, attains its highest elevation (or altitude) about midnight and is immediately South of the most Southern point of the Ecliptic. Scorpius can be seen on the rising side before sunrise in January, seen for the whole night in May and seen on the setting side after sunset in November.

It has the size of 30 degree (in angle) and has the shape of a hook oriented 55 degree clockwise from the great circle arc through the Celestial poles. Arabian sky watchers see a resembling to the body and tail of a (now declawed) scorpion and gave it the name Scorpius.

The brightest star of Scorpius is Antares but it is so close to the ecliptic that it is often outshone by the Moon and bright planets traveling on the ecliptic. Antares often requires extra care for proper identification. Identifying Antares give a good practice to star identifying.

1. The Scorpius on a Mercator sky-map.

mercator8gc30.jpg

Figure 1: The Scorpio constellation is in the shape of a hook, is close to the ecliptic and one third from the left edge of this Mercator sky-map.

Figure 2: A common Asian scorpion.

The Scorpius has too many stars and its brightest star Antares can even be over-shone by planets wandering near to it. Therefore its identification often requires additional care.

An observer in the Southern hemisphere can check that the hook shaped stinging tail of the Scorpius is just touching the great circle arc (drawn in yellow) through the two Pointers to the Southern Cross.

Figure 3: The Scorpius is seen as a hook in the top left quadrant of this Polar Inversion map of the Southern hemisphere. Its hook shaped stinging tail is just touching the great circle arc (drawn in yellow) through the two Pointers to the Southern Cross.

2. An alternative method of recognizing stars in the Scorpius

Figure 1: Scorpius Sagittarius and Ara are easily recognized together.

I found that it is easier to recognize the bright stars of three constellations Scorpius, Sagittarius and Ara together. They resemble a tree with two side roots rising at right angle from a ground line.

The two brightest stars of all three constellations are Antares and Shaula in the Scorpius.They are separated by 17 degrees in angle. They line up with two other dim stars to form a straight line (delta Scorpius, Antares, Shaula and kappa Scorpius) which is slightly longer.

The South-trailing end of this line continues to be the bisector of a right angle line formed by five stars zeta Sagittarius, Kaus Australis, Shaula, theta Scorpius, alpha Ara.

The line of two brightest stars looks like a tree sticking up at right angle to the ground line formed by dimmer stars in line with alpha and epsilon Ara. The tree has two side roots (Shaula-Kaus Australis. and Shaula-theta Scorpius-alpha Ara) originating from Shaula and each is at 45 degree from the tree trunk.

After the bright stars have been identified, each constellation can be identified using its conventional map as given in [1] and [2].

3. Taking photos of the Scorpius.

The Scorpius is adequately bright and its photos can be taken using a smart phone such as a Samsung Galaxy Note 2 with no extra attachment.

Figure 1: A photo of the Scorpius Constellation taken with a Samsung Galaxy Note 2. This photo was added on 2018Feb26 and has been digitally enhanced.

The Scorpius constellation is in the center of this picture. There are four brightest dots on the top half of this picture. The far right and far left dots are very bright and are two planets traveling on the ecliptic. The planets on the ecliptic sometimes make it hard to identify this constellation. (This added photo was taken on 2018 Feb 26).

Scorpius

Figure 2: Photo of the Scorpius Constellation taken with a Samsung Galaxy Note 2. The original photo was taken prior to 2017Jan09 and has been digitally enhanced.

Scorpius

Figure 2: Another photo of the Scorpius Constellation taken with Samsung Galaxy Note 2. The original photo was taken prior to 2017Jan09 and has been digitally enhanced. There are three bright dots in a straight line at the top of the first photo. The two on the left are two planets on the ecliptic. The third one on the right is delta Scorpius. Antares is the bright dot under the three in line.

4. Easy identification of Scorpius by a slide sky map.

starmap18april0130c.jpg

Figure 1: The Scorpius position by the Mercator slide sky map, with an altitude grid for an observer on 10 deg North (South of India, Thailand, Malaysia, South of Vietnam, the Phillipines, Central America) .

Observers who are not quite familiar with the Scorpius constellation can use the slide sky map described in reference [2] to confirm its identity. The latitude of the observer, time, and North direction are required for identification using a slide sky map. The figure here gives its altitude (elevation) and its orientation at the time of the first photo of the preceding section.

References.

[1]. tonytran2015, Finding North and time by stars in the tropics, survivaltricks.wordpress.com,Finding North and time by stars in the tropics, posted on May 25, 2016

[2]. tonytran2015, Slide Sky-Map for displaying tropical stars, survivaltricks.wordpress.com, Slide Sky-Map for displaying tropical stars., posted on October 7, 2016

[3]. tonytran2015, Finding North and time by stars, survivaltricks.wordpress.com,Finding North and time by stars, posted on August 28, 2015

[4]. The Orion constellation., posted December 26, 2016

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posted on October 21, 2016

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The Orion constellation.

​The Orion constellation

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.43).

#find North, #direction, #by stars, #Orion, #Sirius, #navigation, #constellation.

Celestial navigators who do not use declination and right ascension begin their navigation by learning the various bright, easily identifiable constellations in the sky (There are no more than 10 to learn.).

The Orion is usually chosen to be the first constellation to be learned. The Orion is a bright, easily identifiable constellation of December. It stays in the sky of December for the whole night, attains its highest elevation (or altitude) about midnight and is right on the Celestial equator.
It has the size of 30 degree (in angle) and has the shape of a waisted rectangle. Western sky watchers see a resembling to man in an armor vest and gave it the name Orion. Pacific sky watchers see its two brightest diagonal stars as the ends of a large stick in the sky.

It is never blinded by the Moon or any bright planet as the ecliptic is well away from it. As it is quite bright and has easily identifiable shape, it is usually used as the base (anchor marks) to start locating other stars.

1. The Orion on a Mercator sky-map.

mercator8gc30.jpg

Figure 1: The Orion constellation is right on the Celestial Equator and one third from the right edge of this Mercator sky-map.

 



The three dim stars in a straight line starting from the waist band and almost at right angle to it (not shown in this simplified Mercator sky map) are called the Dagger stars. The Dagger is at right angle to the Celestial equator and points along a great arc in the North to South direction on the Celestial sphere.


Rigel or Beta Orionis is bright star at the South leading corner of the waisted rectangle. Betelgeuse is bright star at the North trailing corner of the waisted rectangle. Bellatrix is a less bright star on the North leading corner of the rectangle.

Rotating the line Betelgeuse – Rigel by 90 degree in the anti-clockwise direction gives the line Betelgeuse – Aldebaran, (Aldebaran is also called alpha Tauri).

Extending the line Bellatrix-Aldebaran by another 50% makes it reaches Pleiades group of stars (not shown on this simplified Mercator sky map). This group has millions of stars fitting within an area as small as the area of the Moon (The area is equal to that of a fingernail on a fully extended arm). Most people can see a brush shape made of 7 brightest stars of this group.

On the trailing side of Orion lies the brightest star in the sky. It is Sirius. Rigel -Betelgeuse – Sirius form an almost equilateral triangle on the trailing side of the line Rigel – Betelgeuse.

Betelgeuse is the star of December 20th and the December solstice occurs on the 21st of December, on the following night .

The night when the brightest star Sirius attains its highest altitude at midnight is the first night of a new (Roman) calendar year (Is it a coincidence?).

2. Taking photos of the Orion.

Orion Constellation

Figure 2: Photo of the Orion Constellation taken with a Samsung Galaxy Note 2. The original photo has been digitally enhanced. Sirius is the brightest star on the lower half. Rigel, Betelgeuse and gamma-Gemini are in line (from bottom to top) and almost equally spaced.

Figure 3: Photo of the Orion Constellation taken with a Samsung Galaxy Note 2. The original photo has been digitally enhanced. On this night there was a bright object (planet ?) on the elliptic near to the leading shoulder of Orion.

The Orion is quite bright and photo can be taken using a smart phone such as a Samsung Galaxy Note 2 with no extra attachment.

Notes: The photos have been updated in March 2018.

References.

[1]. tonytran2015, Finding North and time by stars in the tropics, survivaltricks.wordpress.com, Finding North and time by stars in the tropics, posted on May 25, 2016

[2]. tonytran2015, Slide Sky-Map for displaying tropical stars, survivaltricks.wordpress.com, Slide Sky-Map for displaying tropical stars., posted on October 7, 2016

[3]. tonytran2015, Finding North and time by stars, survivaltricks.wordpress.com, Finding North and time by stars, posted on August 28, 2015

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Identifying moderately bright navigational stars.

Identifying moderately bright navigational stars

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. 27).

#find north, #navigation, #survival, #moderate stars, #bright star, #Antares, #Fomalhaut, #direction, #distance, #great circle, #navigation, #stars, #neighbour stars, #sky map

Introduction.

Some navigational stars are only moderately bright although they are in the top 20 brightest stars. Antares and Fomalhaut are two such stars. They are used for navigation from September to November but are not easy to identify among their nearly as bright neighbours. The method for identifying them is to relate them to brighter neighbours which have been identified in previous periods of the year.
(GPS navigation cannot be relied on during periods of uncertainty. Traditional methods of navigation is still a necessary skill.)

Using an identifying map.
Knowing the date or even only the month of a star help locating parts of the sky where it may be found. The map giving distances and angles to its more distinctive neighbours then help its identification.

The maps are to be held such that its shown Celestial pole is pointing close to that actual Celestial pole whether it is in the sky or below the ground. The map is thus to be held in the star direction but oriented either upright or up-side-down.

Examples:

Figure 1: Antares in Scorpii with its neighbours. The centering mark is the Southern Celestial pole.

Figure 2: Fomalhaut with Alpha, Beta Grus and their neighbours. The centering mark is the Southern Celestial pole.

ariessmallc30.jpg

Figure 3: Hamal in Aries and its brighter neighbours. The tail of the inverted Little Dipper in the North is the North pole.

The first two maps make easy the confusing identification process of these two Southern navigational stars for October.

The third map makes easy the identification process of the dim Northern star Hamal in Aries for November.

References.

[1]. tonytran2015, Finding North and time by stars in the tropics, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2016/05/25/finding-north-and-time-by-stars-in-the-tropics/, posted on May 25, 2016

[2]. tonytran2015, Finding North and time by stars, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/28/finding-north-and-time-by-stars/, posted on August 28, 2015.

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, posted on May 06, 2015 .

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Finding North direction and time accurately from the horn line of the Moon. Posted on August 12, 2015. This is my novel technique.

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Finding North direction and time using the Moon surface features. Posted on July 1, 2015.

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

Finding North and time with unclear sky. Posted on October 17, 2015.

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, posted July 22, 2016

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Slide Sky-Map for displaying tropical stars.

Slide Sky-Map for displaying tropical stars

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, #by stars, #Mercator, #sky map, #star map, #slide sky map, #navigation, #tropic, #declination, #right ascension.

slide sky map

Figure 1: Illustration of the Slide Sky-Map using the mask for 15 degree North latitude.
Slide Sky-Map for displaying tropical stars (blog No. 26).

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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 tropical night sky with current commercially available circular star maps as they have a lot of distortion for tropical 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 curve should be nearly circular around the zenith point.

The device given in this posting gives the desired displays with low distortion for the tropical night sky and has been designed for use with latitudes between the two tropical lines. I give it the name Slide Sky-Map (which is similar to the name Slide Rules of similar looking mathematical devices before the age of calculators).

It is made of Mercator map of stars and of the viewing grids to give elevation and azimuth angles of stars to observers located near to 0 degree, 15 degree North and 15 degree South in latitude.

It will be useful to tropical people who want to learn the stars by themselves or need to refresh their nightly knowledge of the sky before going out. It is inexpensive, light weight, small, flexible, durable and quite portable. If made from waterproof materials, it may also be used as a low cost standby star map for travelers, hikers and seamen traveling in the tropic (my is made from waterproof sheets).

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

1. Making the maps for the core.

mercatorx1p6

Figures 1a: The Mercator map for the front of the core of the Slide Sky-Map.
star map mercatorx1p6

Figures 1b: An alternative Mercator map with star names for the front of the core of the Slide Sky-Map

mercator8fx1.6polarc30.jpg

Figures 2: The map on the reverse side of the core.

The map on the front of the core of the slide sky-map is a Mercator map with continuation by its repeat copy. The map here wraps around the Celestial equator by 600 degrees, meaning that it has about 1.7 times the width of the minimal Mercator map. The extra length allows the slider covering 180 degree in the East-West direction to be centered on any given longitude.

The two inversion maps of the North and South polar regions of the Celestial sphere are overlaid at the two ends of the same Mercator map and the combined map is placed on the reverse side of the core. The two insets represent the two polar regions of the Celestial sphere not displayed on the Mercator map. They help visualizing the two polar zones of the Celestial sphere, they can be easily joined to the polar sides of the Mercator map using shared common constellations present in both types of maps as stitching guides.

The core maps are to be printed on both sides of a thick sheet of A4 waterproof paper. This thick sheet of paper forms the core fitting inside the sleeves of next few steps. Alternatively the core maps can be printed on waterproof A4 papers and glued onto the opposite sides of a piece of thick waterproof board used as the core.

 

2. Making azimuth and elevation masks for the slider

mercator grid 00deg mask

Figure 1: The grid mask for 0 degree latitude.

mercator grid15d N.jpg

Figure 2: The grid mask 15 degree North latitude.

mercator grid 15d S.jpg

Figure 3: The grid masks for 15 degree South latitude.

A grid mask is placed on top of the core map to read the azimuth and the elevation of the stars drawn on the map. An observer must use the mask drawn for his latitude.

Description:
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. 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 concentric nearly circular curves represent the constant elevation circles in the sky. They are placed at 30, 60 and 90 degrees from the zenith. The curve 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.

There are 3 grid masks given for this design. Select one that is based on a latitude nearest to your current latitude.

For latitude between 8 degree North and 8 degree South select the mask based on 0 degree latitude.

For latitude between 7 degree North and 23 degree North select the mask based on 15 degree latitude North.

For latitude between 7 degree South and 23 degree South select the mask based on 15 degree latitude South.

You can make all three 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 transparent sheet. Print the selected grid on a 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.

3. Making the slider (improved design, 2017, August 31).

slideskymap00

Figure 1: Photograph of an actual Slide Sky-Map fitted with the mask for the equator.

BrightStars20Plus2

Figure 2: Table of bright stars for the back side of the double layered slider sleeve.

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 right side and R.A. increases towards the left (East) of the map.

The slider consists of a double layer white sleeve fitted with a transparent rectangular strip carried between its front layers.

Wrap a waterproof, white, thick sheet around the rectangular core map to make a white sleeve of no less than 360 degree along the East West direction of the core map (that is wrapping no less than two third of the length of the core map). The core should fit snugly inside the white sleeve and should be able to slide smoothly along its East West direction inside the white sleeve.

Cut a rectangular window on the front center of this white sleeve to reveal 180 degree width of the core map. The back of this white sleeve should be glued or taped to make it a proper sleeve.

Wrap another layer of the same waterproof, white material around the inner sleeve just made to make a white outer sleeve that fits snugly on the inner sleeve. The sleeve has now two layers.

Make sure that there is SUFFICIENT GAP between the two sleeves so that the core map can also be inserted into and can also slide in the GAP between the two front layers of the double layered slider.

Make the two layers stick together on their back sides by tapes or glue. Then cut the window through the outer layer so that the core map can be observed through the front window as if the slider sleeve was made of only a single layer.

Figure: The sleeve has two layers.

You may like to add the table of bright stars (Fig. 3) to the (uncut) back side of the double layered white sleeve to facilitate calling star names.

Choose the transparent sheet with the printed mask for your latitude. Cut it into a rectangular shape with 2 long arms extending from the East and West sides of the transparent grid mask. The rectangular transparent sheet has its width slightly wider than the width of the core map.

Insert the rectangular transparent sheet BETWEEN the two FRONT LAYERS of the double layered slider sleeve. Align the printed window of the transparent sheet to the cut window of the double layered sleeve. The East-West arms of the mask should be trimmed so that they only protrude slightly out of the double layered sleeve just enough to make easy insertion and removal of the mask.

In this way, any of the transparent mask can be fitted into or removed from the double layered sleeve whenever the user requires a new mask for his new latitude.

4. Final assemblage.

slideskymap15s

Figure 1: Front view of a Slide Sky-Map fitted with the mask for 15 degree South latitude.

slideskymap2backc100.jpg

Figure 2: Back view of a Slide Sky-Map.
Slip the core map into the inside of the double layered sleeve. The core map is now behind the transparent grid mask.

5. Usage.

The sky at night is represented by the core map going toward its west under the transparent window (that is it goes from left to right under the viewing window).

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

2/- The four vertical lines for equinoxes and solstices are printed on the core map. Other date lines are interpolated from them.

Place the center of the sliding window on the current date to see the mid-night sky for the date.

3/- Then slide the core map by half a division (15 degree on the equator or half a month) to the east or to the west for every hour ahead of or after midnight.

4/- The latitude for the grid not being exactly that of the observer and the true time at the location is not being equal to the zonal time causes the stars inside the smallest circle around the zenith to have slightly inaccurate position relative to the grid. However the lines joining these stars still give accurate directions and the stars still help identifying other stars near the horizon. The stars near the horizon have their values of azimuth and elevation angles given more accurately by the Slide Sky Map.

6. Record of a previous design.

(For reference only, do not use this obsolete design).

The slider consists of a white inner sleeve and a transparent outer sleeve tightly fit together.

Wrap a waterproof, white, thick sheet around the core (printed with maps) to make a white sleeve of no less than 360 degree along its East West direction (that is wrapping no less than two third of the length of the core map). The core should fit snugly inside the white sleeve and should be able to slide smoothly along its East West direction inside the white sleeve.

Cut a rectangular window on the front center of this white sleeve to reveal 180 degree width of the core map. You may like to add the table of bright stars (Fig. 3) to the (uncut) back side of the white sleeve to facilitate calling star names.

Choose the transparent sheet with the printed mask for your latitude. Cut it into the shape of a cross with 4 long arms extending from 4 sides of the transparent grid rectangle window. Each arm has its width equal to the size of the corresponding side of the adjoining window. Its North and South arms will be joined together to make a second, transparent sleeve fitting tightly outside the white sleeve, its long East and West arms will be slipped into the inside of the white, inner sleeve to anchor it on the white, inner sleeve. The East-West arms should protrude slightly out of the inner sleeve to make easy insertion of the sliding core into the white sleeve.

Wrap the transparent sheet tightly outside the inner sleeve and tape its North and South arms together to form a transparent sleeve with its grid right on the cut window of the inner sleeve. The East and West arms of the transparent sheet are slipped into the inside of the inner sleeve to lie along the East West direction underneath the white layer to anchor the transparent sheet on the white, inner sleeve.

In this way, any of the transparent outer sleeve can be fit into or removed from the inner sleeve whenever the user requires a new mask for his new latitude.

Slip the core map into the inside of the cardboard sleeve. Make sure that it goes behind the two transparent arms inside the sleeve so that it can travel fully from East to West.

Reference.

[1]. tonytran2015, Finding North and time by stars in the tropics, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2016/05/25/finding-north-and-time-by-stars-in-the-tropics/, posted on May 25, 2016

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Navigating with an AM MW radio receiver, posted January 17, 2017, The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food., Using GPS in off-grid situations, Shadow Stick Navigation, posted on 19 Aug 2016

, posted on

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. Posted on May 25, 2016

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Slide Sky-Disks with grid masks showing azimuths and altitudes, posted on 03 Nov 2016 ,

, posted July 22, 2016DirectionTimeByStars

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Finding North direction and time by any bright star.

NorthByKnownStar

Finding North direction and time by any bright star

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, #find, #direction, #time, #bright star, #Sun, #divider, #navigation.

Find North Direction and time by any bright star.

Most people living in the Northern temperate and arctic zones know how to find the star Polaris to find North direction and can even tell time by the orientation of the Little Dipper (part of the Little Bear). But Polaris is not an easily seen bright star and may even be hidden from view for people in Tropical zone and in Southern Hemisphere.

This posting shows how to use ANY arbitrarily known star to find North direction and time, and is useful to non-users of Polaris star. The method is similar to that given previously using the Sun [1] and is useful when only one bright star is visible in an unclear sky (affected by thick clouds or pollution).

The divider compass in this posting is only for instructional purpose and is not needed in actual application. The user may use any two of his fingers instead.

1. Requirements by the method.

To apply this method you need:
1. Your current latitude,

2. The current date in the Solar Year,

3. An unmistable bright star,

4. Its Declination and its Right Ascention already converted to Date of that Star in the Solar Year (see the details on the Conversion in the following section).

2. The date of a star.

BrightStars20Plus2

Figure: Table of bright stars with their approximate dates .

The date of a star should be known, even only approximately by the month, if the user wants to tell time from that star.

The date is obtained from the linear conversion:

a. 00:00 hr of R.A. —-> Sep 23 in Date

b. 06:00 hr of R.A. —-> Dec 21 in Date

c. 12:00 hr of R.A. —-> Mar 21 in Date

d. 18:00 hr of R.A. —-> Jun 21 in Date
Any star is visible nightly (either from Sunset to its setting or from its rising to Sunrise) for more than 9 months each year. The visibility cycle for each star begins with the star seen rising near the Eastern horizon few minutes before Sunrise. On subsequent days, the star rises earlier and earlier, it travels gradually towards the West and remains for longer and longer duration in the night sky until one day it stays for the whole night. The star is therefore called a star of that date. After that day, the star is seen setting in the West in the night. On subsequent days, its lead on the Sun gradually increases and it sets on the West at earlier and earlier time. Near the end of the cycle, the star is visible above the Western horizon for only few minutes after Sunset. It then sets on the West. At the end of this cycle, the star is too close to the Sun to be visible in the sky. The cycle then repeats from the beginning.

Example:

Boote Arcturus is a star of April 25th with declination 19 degree N. Step 6 of reference [2] shows how to easily identify it.

It reaches its highest elevation at mid-night of that date and remain visible for that whole night.

In February it rises about 4 hr after Sunset and has not enough time to complete the journey to the West. On April 25th it rises at about Sunset to complete the journey to the West about Sunrise. In June it is seen already high in the sky at Sunset and set on the West 4 hr before Sunrise.

3. Selecting a star for current month in the year.

PolrNorthNC20const8

Figure: Sky map (Inversion type) of the Northern Celestial 3/4-sphere showing only 20 brightest stars and some constellations.

polrsouthq3c60.jpg

Figure: Sky map (Inversion type) of the Northern Celestial 3/4-sphere showing only 20 brightest stars and some constellations.

Select a bright star of a date in the year near to your current date (or month) and read its declination from any source such as the internet, your own tables or the two star maps supplied here. If you use the star maps, its declination is read from the constant declination circles and its date from the rim on the opposite side (that is also the point closest to the Sun on the elliptic circle).

This method requires POSITIVE IDENTIFICATION of your chosen star. To positively identify it, you may need to see

1/- either neighbouring bright stars, their relative distances and orientation

2/- or surrounding dimmer stars making up the constellation containing it.

When that star is the only visible one in the sky you may have to identify it relying on its appearance details in previous nights such as:

1/- Continuity of its characteristics from previous nights (or hours),

2/- its elevation after Sunset,

3/- its relative directions from the setting Sun or the (moving) Moon,

4/- its ranking as the few brightest objects in the sky after Sunset.

Stars near to the elliptic may sometimes be confused with much brighter planets and their use involves extra cares.

If you are away from the two polar zones and always can see an unobstructed sky (nearly half of the Celestial sphere), you only need to find one of the 3 stars Orion Rigel, Boote Arcturus and Altair to apply this method.

4. Rules for turning to lower Celestial pole.

divider43.jpg

Figure: The rule for finding North by any chosen star is similar to the rule illustrated here for the Sun.

Be certain of your hemisphere and whether the star is rising (early star) or setting (late star) to turn the second leg of the divider to the left or to the right. This is similar to the requirement for finding North using the Sun.

Then apply all the steps of the next section.

5. Steps to find North direction and time using a star.

DirectionTimeByStars

Figures: Summary of steps to find North direction and time by any known star.

When any star is used on its date in the year, the Sun leads it by exactly 12 hours. For every month after that, the lead by the Sun is reduced by 2 hours (or every 12 months by 24 hours). The last figure of the illustration shows the Sun leading the star by about 5 hours on the Celestial clock face.

Example 1:

In December, January, February use Sirius if you can see it.

Sirius is a star of Jan 1st with declination 17 degree S. Step 8 of reference [2] shows how to find it.

On Jan 1st the time determined by Sirius is 12 hours behind the time by the Sun.

On April 1st, the time determined by Sirius is 6 (=12-3*2) hours behind the time by the Sun.

Example 2:

In March, April, May use Boote Arcturus if you can see it.

Boote Arcturus is a star of April 25th with declination 19 degree N. Step 6 of reference [2] shows how to identify it.

On April 25th the time determined by Boote Arcturus is 12 hours behind the time by the Sun.

On May 25th, the time determined by Boote Arcturus is 10 (=12-1*2) hours behind the time by the Sun.

On June 25th, the time determined by Boote Arcturus is 8 (=12-2*2) hours behind the time by the Sun.

References.

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

[2]. tonytran2015, Finding North and time by stars, survivaltricks.wordpress.com, posted on August 28, 2015.

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

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.

BStarsN20Vega8C

wpid-30naugplrnc-.jpg.jpeg

wpid-30naugplrsc.jpg

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.

BrightStars0b

polrnorthqrefc60.jpg

polrsouthq3c60.jpg

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.

BStarsN20Vega8C2.jpg

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 ( viking ships , [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.

[2]. viking ships , http://www.hurstwic.org, http://www.hurstwic.org/history/articles/manufacturing/text/norse_ships.htm

Added after 2018 July 20:

[3]. https://misfitsandheroes.wordpress.com/2012/08/28/ancient-navigators/

[4]. https://www.abc.net.au/news/science/2021-09-23/polynesia-settlement-pacific-islands-genome-dna-rapa-nui-history/100471492

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Finding direction, distance and navigating to a distant base by stars (Part 1)

Finding direction, distance and navigating to a distant base by stars (Part 1)

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, #celestial, #distance, #find, #latitude, #navigation, #no instrument, #polynesian, #zenith

polrnorthqrefc60.jpg

Figure: The sky map for use in Northern hemisphere.

The method here uses stars for finding base city at a distance between 1000km to 9000km and for traveling to that base using constant latitude for final path.
It uses the stars passing overhead the base city and accurate time to tell those moments. Direction and distance to that city are directly observed from the stars. If no current longitudinal information is available and longer travel distance is acceptable then the user can also use this method to aim for base city on the final constant latitude part of the travel.
This is a back up or emergency method for people who may need to find out their direction to base and how to arrive there even when having no landmarks for current position. This is the case for:
A. People who are lost in the ocean or in a large desert with no reliable landmark. They need some method of orientation using minimal number of tools.
B. People drifted to an isolated island in the ocean after a tsunami !
C. Installers of long distance or satellite communication antennas wishing to aim their devices when not having any map.
Required information:
1. Selected star(s) for the chosen base city with the target point(s) underneath the star(s) reasonably close to the base city.
2. Longitude of the base city and time signal announcing GMT time to show the time at base city. The time signal may come from Broadcast or Marine Band Weather Radio.
3. or an accurate watch that allows determination of the true (not zonal) time of base city (Each minute earlier or later than intended time may cause a longitudinal error of 0.25 degree that is about 27km near the equator.).

Step 1: Preparation before expedition

polrsouthq3c60.jpg

Figure: The sky map for use in Southern hemisphere.
1. Search from the list of brightest stars (in descending order) for the brightest identifiable star that can closely pass overhead the base city (with acceptable error distance) and the approximate date for it to be seen in at midnight.
Examples:
London is at (0°5′ longitude, 51°32′ latitude). In June, choose Eltanin (Gamma Draconis, 17hr 57′, +51.5° declination) target point underneath the star is 0km from base.
Berlin is at (13°25′ longitude, 52°30 latitude). In June, choose Eltanin (Gamma Draconis, 17hr 57′, +51.5°declination), target point underneath the star is nearly 110km South of the city while the zenith of the city is 2 Moon’s diameter from the star and toward the Celestial North . In December choose Gamma Persei (03hr05RA +53.5degrees declination, app magn 2.91) target point underneath the star is nearly 110km North of the city while the zenith of the city is 2 Moon’s diameter from the star and toward the Celestial South.
Mecca(39°45 longitude, 21°29 latitude) choose ArcturusBoote (213.9RA, 19.2° declination) nearby location underneath the star is 230km South of the city while the zenith of the city is 4 Moon’s diameter from the star and toward the Celestial North.
Manila (120°57′ longitude, 14°35′ latitude) choose Regulus, (Alpha Leonis, 10hr08’RA +12.0°declination) nearby location underneath the star is 280km South of the city while the zenith of the city is 5 Moon’s diameter from the star and toward the Celestial North.
2. Work out the day for the star to be highest at midnight. The day is the same for all locations. It is almost Sep23rd plus the RA of the star multiplied by (365.25days/360°).
Example:
Gamma Persei is nearly overhead at midnight of
Sep23 + 3hr05*(365.25days/24hr) =
Sep23 + 46.92days = Oct23 + 17d = Nov 09.
3. Learn by heart how to identify in the sky the stars associated with the base city. The accuracy and speed of this ability is essential to avoid mistakes under adversed circumstances. Users should not confuse between stars near the ecliptic and wandering planets nearby.
4. Practice determining the time when the star passes the vertical North-South plane at the base city on that date. It is midnight minus the local advance on GMT, which is equal to longitude multiplied by (24hr/360°).
Example:
Gamma Persei passes near Berlin (longitude 13°24′) on that date ahead of mid – night GMT by (13°24′)/(15°/hr) = 0.89hr, that is at
24hrGMT – 0.89hr = 23.11hrGMT = 23hr07GMT.
5. Every day later/earlier than that date, the star passes the location (60minx24/365.25) = 3.942 min of time earlier/later. This earliness is observable at all locations including your current one. When observing the star on another day, the earliness adjustment is needed.
6. If the Sun crosses the North-South vertical plane earlier/later than at base, the chosen star also crosses the North-South vertical plane earlier/later than at base by the same amount of time.
Step 2: Field application

BrightStars0b

List of 20 brightest stars. Additional, dimmer stars are also needed to travel closer to any arbitrarily given latitudes.

7. Identify the star and obtain the time signal from GMT. Work out the instant the star is overhead the base. (Alternatively, the moment the chosen star passes overhead the base can also be determined with an accurate watch from the time it passes the North-South vertical plane of current location and the advancement or retardment of local Noon relative to Noon at base.)
8. At that moment, the star is above the nearby spot close to the base. Every degree from your zenith is 111km distance from you. The direction to the star projected onto the ground gives direction to the chosen nearby location. To obtain more accurate direction to your base when the star does not pass its zenith, you can imagine another star at some diameters of the Moon on either North or South side of the RA circle from the chosen star and use it instead. Alternatively you can add some adjustment based on the differentials on a spherical surface to obtain the exact direction to your base.
Step 3: Navigating by only stars.
9. To travel to the target location, aim for a location on the same latitude but more in the North-South direction of the current point. This makes the travel distance longer but ensures that the target is not missed in the final part of the travel. When arriving at that target latitude, aim at the target location. Keeping the selected star on the East West line when it has highest altitude will ensure that the traveler does not miss the target.
This method suggests a possible way used by desert travelers and an alternative for refinement of Polynesian method of navigation.

4. How to find the zenith point.

The navigator has to hang a long plumbing line from a point higher than his eye level, stand away from it and look at the projection of the line onto the sky. The projection is a great circle arc through the zenith.

Looking at the plumbing line from many directions gives many great circle arcs intersecting at the zenith point in the sky. The navigator may have to note its relative distances to familiar stars and draw it and the stars on a piece of paper for future reference and cross checking.

This method requires a steady plumbing line and is suitable for ground travelers when resting at night.

5. How to locate any chosen bright star in the sky.
1. Find out its position relative to the 20 brightest stars by plotting it on the star maps here from its RA and declination.
2. Work out steps starting from identifiable top 10 brightest stars to positively identify it through progressively nearer, easily identifiable, bright neighbours .
3. Use the sky maps here to practice finding it in the sky.
4. Examples.
4.1 Locating Eltanin:
Eltanin is found from star charts and the sky maps here as the brightest star near to the point of one third of the way from Vega to Dubhe (There is no brighter star in the vicinity.).
4.2 Locating Regulus:
The broom shaped group of stars (Sirius, Canopa, Orion-Rigel, Betelgueuse, Procyon) identifies their elements. Betelgueuse-Pollux forms the hypotenus of the isoceles right triangle (Procyon, Betelgueuse, Pollux, Procyon, counter-clockwise) with Procyon at the right angle. Regulus is then one distant vertex of the rhombus (Procyon, Betelgueuse, Pollux. Regulus, Procyon, counter-clockwise).

6. Notes.
1. The local true time at the base city has the Sun crossing the North-South vertical plane at 12am. The zonal time (broadcasted by local radio and TV stations in the winter) is the true time advanced or retarded so that it differs from GMT by a whole number of hours.
2. The Sun crosses the North-South vertical plane before or after 12am zonal time by the difference between the local true time and zonal time. This amount is due to the excess or shortage of longitude to the nearest multitude of 15 degrees chosen for zonal time.
3. With an accurate watch still showing the zonal time at the base city, the longitudinal increment from that of base city can be worked out by the increment in the earliness of the crossing of the North-South vertical plane by the Sun. Each increment of 15 degrees in longitude corresponds to 60 minutes advancement in noon time.
4. Near to the end of the journeys, overland navigators may apply terminal homing using mega-features such as familiar city silhouettes, mountain peaks, rivers, rock and soil formation, permanent cloud formations, existing or ancient tracks, vegetation boundaries or even smell from plants. Some traditional land travelers may even release trained eagles to home on prairies while some traditional ocean travelers may release islands spotting birds to home on islands.
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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

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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Finding North and time with unclear sky

Finding North and time with unclear sky

by tonytran2015 (Melbourne, Australia).

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Blog post No. 09

#find North, #finding North, #direction, #time, #bright stars, #unclear sky, #sky map, #by stars, #sky disk, #declination, #right ascension,

Finding North by stars with unclear sky requires determining the Celestial poles mostly from the 10 brightest stars. They are, in descending order of brightness, Sirius, Canopus, Alpha Centauri, Arcturus, Vega, Capella, Rigel, Procyon, Achernar and Betelgeuse.
The projection to the ground of the Celestial axis gives the terrestrial North – South axis.
The method described here uses only brightest stars with high elevations and is suitable for people living in areas with naturally hazy skies, with brightened skies such as in cities or with high horizons such as in valleys.

1. Locating the Celestial poles.

Figure: Finding a Celestial pole using two chosen known stars.

The traditional method uses easily identifiable group of stars such as the Big Dipper or Cassiopeia to locate the next group of star, Little Dipper, which straddles a Celestial pole. One of the stars of this group of star, Little Dipper, is fortuitously quite close to the Northern Celestial pole and is used as that Celestial pole.

This traditional method is quite good for Northern polar and temperate zones but is not applicable to the other zones. In the Southern hemisphere, there is no group of stars straddling the Southern Celestial pole while in the tropical zone, the visibility of the Celestial poles are usually obstructed on the horizon.

Here two additional novel methods of finding North are also used. The first method is my method of “Finding North direction and time from the Sun using bare hands” [2], with the star replacing the Sun. The second method is based on geometry and is my generalization of the traditional method (which is applicable only to groups of stars directly overhead users) used by tropical people who pay little attention to neither Polaris nor Southern Cross.

In the second method (illustrated in the figure), two identifiable bright stars are chosen, one of them is called the pivoting star of the method. A flat cardboard is then used to see the great circle through the pair. The card board is then rotated around the line of sight of the pivoting star by some angle to become the plane of the great circle through the pivoting star and two Celestial poles. The declination of the star determines the directions of the Celestial poles. The Celestial axis is then projected onto the ground to give terrestrial North direction. The error of this method is minimal when the pivoting star has the same elevation as the upper Celestial pole.

Example A:

A1. Choose the pair of brightest stars OrionRigel (pivoting star) and Betelgueuse of the Orion group. Their identifying features are three regularly spaced Orion belt stars in a short straight line bisecting the line joining them .

A2. A flat cardboard is then used to see the great circle through the pair. The card board is then rotated 30 degrees clockwise (this angle is easily read from the sky maps) around the line of sight of OrionRigel to become the plane of the constant RA plane through OrionRigel.

A3. The North and South Celestial poles are respectively 90+8 and 90-8 degrees from OrionRigel.

A4. The error in this example is minimal when OrionRigel has the same elevation as the upper Celestial pole.

Example B:

B1. Choose the pair of very bright stars ArcturusBoote (pivoting star) and Spica. They are the pair of brightest stars 35degrees apart, straddling the Celestial equator, attaining their highest elevation in April.

B2. A flat cardboard is then used to see the great circle through the pair. The card board is then rotated 30 degrees clockwise (this angle is easily read from the sky maps) around the line of sight of ArcturusBoote to become the plane of the constant RA plane through ArcturusBoote.

B3. The North and South Celestial poles are respectively 90-19 and 90+19 degrees from ArcturusBoote.

B4. The error in this example is minimal when ArcturusBoote has the same elevation as the upper Celestial pole.

2. In the Northern hemisphere, over 40 degrees North. (outside tropical zone)

image

Figure 1: Bright stars about Northern Celestial pole.

BrightStarsDatesF

Figure 2: List of brightest stars.

About Northern Celestial pole there is a quadrilateral of bright stars (Vega(0.03), 25 degrees distance, Deneb(1.25), 75 degrees, Capella(0.08), 50 degrees, Dubhe(1.79), 65 degrees, Vega(0.03), in clockwise order). The vertices (accompanied by apparent magnitudes in brackets) are cited with their distances between them. This quadrilateral rotates in the counter-clockwise direction with time.

The quadrilateral has almost the shape of a trapezium with the long base being Capella – Dubhe and the short base being Vega – Deneb. Dubhe is the least bright of the four stars. It is the bright Pointer star (aUMa) of the Big Dipper, close to the dimmer Pointer star (Merak, bUMa) which is on the mid-point of the line Capella – Arcturus Boote.
The North Celestial pole is nearly of equal distances to the three long sides of the quadrilateral, also on the bisector of (Vega, Altair, Deneb), on the extension of Ori Rigel – Capella and almost on the bisector of (Dubhe, ArcturusBoote, Vega). The line Vega-Celestial pole is 12 degrees clockwise from and 60% of the length of the 95 degrees long line Vega Capella. Extending the line OriRigel – Capella by an additional 80% gives the great circle arc through three points OriRigel-Capella-Celestial pole.

Note.

There is a very large, right triangle of brightest stars (Vega(0.03), 90 degree distance, Capella(0.08), 105 degrees, Arcturus Boote (-0.04), 55 degree, Vega, in clockwise order). The vertices (accompanied by apparent magnitudes in brackets) are cited with their distances between them. It could be thought that the triangle would allow easy identification of its three vertices and consequently nearby stars. However the triangle is too large for most observation locations and the whole of it can be seen continuously only from locations above 75 degrees N and can be seen for fractions of 24 hours from locations above 15 degrees N. Therefore identifying Northern stars has to rely on less bright stars forming smaller polygons.

Traditional method for clear sky.

The Big Dipper is a group of 6 mid-bright stars and 1 low-bright star that outlines the corners of a dipper of 30 degrees long. It spreads between 30 and 40 degrees from the Celestial pole. During the nights of May, the Big Dipper stands upright (its deep cup opening pointing upright with the vertical handle on its right) while the dim Little Dipper stands almost upside down on the tip of its curved handle and the deep cup opening pouring outwardly to the right. The tip of the handle of the Little Dipper is the mid-bright star Polaris which is right on the Northern Celestial pole and is in line with the Pointers (of the Big Dipper) and 30 degrees from the Pointer stars (The Pointers of the Big Dipper are 5.5 degrees distance apart and they point from the dimmer to the brighter star towards the Northern Celestial pole.). Both Dippers are in the sky all year round but only the Big Dipper is easily visible.

3. In the Southern hemisphere, over 40 degrees South (outside tropical zone).

image

Figure 1: Bright stars about Southern Celestial pole.

BrightStars20Plus2

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

About Southern Celestial pole there is a triangle of bright stars (aCen(-0.01), 63 degrees distance, Achernar(0.46), 30 degrees, Canopus alpha(-0.72), 60 degrees, aCen(-0.01), in counter-clockwise order).The vertices (accompanied by apparent magnitudes in brackets) are cited with their distances between them. This triangle rotates in the clockwise direction with time.

The South Celestial pole is inside the triangle, nearly of equal distance to the 3 vertices and at 2 degrees distance to the mid-point of the line aCen – Acherna. It is also at the mid point of bCen-Achernar, on the bisector of the angle (aCen, Altair, Acherna) and is the reflection of Sirius across Canopus alpha on the extension of the line Sirius – Canopus alpha (Canopus alpha is almost the mid-point of the 75 degree long line Sirius-Celestial pole.).

Traditional method for clear sky.

The very bright Pointers and very bright Acherna are both about 30 degrees from the Celestial pole. During the nights of April, the Pointers lies horizontally with the very bright star (alpha Centauri) trailing the bright star (beta Centauri) by 4.5 degrees. The dimmer Southern Cross group of stars ahead of them is used for their identity confirmation. Southern Celestial pole is on the bisector line of the Pointer stars, on the right of the Pointers’ direction (from very bright pointer to bright pointer) and 30 degrees distance from it.
Southern Cross is group of stars (group of 3 mid-bright and 1 low-bright stars forming the 4 extreme points of a Christian cross, with the low-bright star at the extremity in the leading direction). The shaft length of this Cross is about 6 degrees, cross bar length 4 degrees.

4. Between 40 degrees North and 40 degrees South

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Figure 1: Example of Northern sky map (Celestial pole above horizon) for 30 degrees North latitude in August.

image

Figure 2: Example of Southern sky map (Celestial pole below horizon) for 30 degrees North latitude in August.

The method described here assumes that observer’s view is obstructed below both Celestial poles. An observer needs to use bright stars with elevation of more than 10 degrees.

An observer in this zone see only slightly more than half of one sky map and slightly less than half of the other sky map. The division line are nearly straight circular arcs going close to the poles on the sky maps. If the observer see a circular disc centered on one pole he will not see the disk of the same size centered on the opposite pole. Any tropical star is visible nightly (either from Sunset to its setting or from its rising to Sunrise) in the tropical zone for more than 11 months each year.

When not able to see the poles the observer has to use identifiable bright stars around the Celestial poles in turns as they circle around the poles when the sky maps rotate.

About Northern Celestial pole there is a quadrilateral of bright stars (Vega, Deneb, Capella, Dubhe, Vega, in clockwise order).

About Southern Celestial pole there is a triangle of bright stars (aCen, Achernar, Canopus alpha, aCen, in counter-clockwise order)

In March there are Big Dipper pointing to N. Celestial pole and (Southern) Pointers giving S. Celestial pole.

Vega is brightest, reaches its highest elevation at mid-night of July 1st. Vega-Deneb is horizontal at midnight of August 1st. The triangle (Vega, 25 deg, Deneb, 32 deg, Altair, 35 deg, Vega, in counter-clockwise order) is known as the Summer triangle and is highly visible in Northern Summer .

From May, use Vega and Deneb to locate Northern Celestial pole. The line Deneb – NCelestial pole is 45 degrees long and 90 degrees counter-clockwise from Deneb-Vega, 150 degrees counter-clockwise from Deneb – Altair, 30 degrees clockwise from Deneb – Capella.

From September, use bright, setting Altair and very bright Acherna to locate S. Celestial pole. The line aCen-Acherna is 63 degrees long and is 105 (180-75) degrees in the clockwise direction from the Southern Pointers’ direction. The line Acherna-Celestial pole is 30 degrees long, originating from Acherna and is 90 degrees clockwise from Acherna-Altair, 70 degrees anti-clockwise from Acherna-(very bright) aCanopus.

When Vega has set, the angled line Deneb – Capella (Goat Star) -Orion Rigel is used to locate the North Celestial pole. The angle (Deneb, Capella, Orion Rigel) is 150degrees clockwise. The line Deneb – Capella is 75 degrees long, originating from Deneb and is 120 degrees anti-clockwise from Deneb – Vega .

The line Capella-Celestial pole is 45 degrees long and 30 degrees counter-clockwise from Capella – Deneb, 50 degrees clockwise from Deneb – Arcturus Boote. The line Capella-Orion Rigel points in the opposite direction, away from the North Celestial pole.

The line Capella-Boote Arcturus is 100 degrees long, originating from Capella and is 70 degrees anti-clockwise from Capella-Deneb. Half-way on this line (at 50 degrees distance from Capella) is the dimmer (Merak) of the two Pointer stars Dubhe and Merak of the Big Dipper. They point at Polaris, 110 degrees in clockwise direction from the line Capella – Pointers.

The line Dubhe – Vega (bright Pointer – Vega) is 65 degrees long, originating from Dubhe and is 45 degrees anti-clockwise from Pointers’ direction. The three stars (Vega, 55 degrees distance, Arcturus Boote, 50degrees distance, Dubhe, 65degrees distance, Vega) are the vertices of an almost equilateral triangle.

The line Vega-Celestial pole is 50 degrees long and 30 degrees counter-clockwise from Vega – Dubhe, 50 degrees clockwise from Vega – Deneb.

The bisector from Altair of the Summer triangle (Vega, Deneb, Altair) goes very near to the North Celestial pole. The pole is 82 degrees from Altair.

When Altair sets on the Western (at about (270+8) degrees) horizon Ori Rigel has risen from the opposite direction, at (90+8) degrees East and the Orions group is already high in the sky.

Near to Orion group, on its South-Trailing (South-Eastward) side, is Sirius, the brightest star in the sky. Sirius simplifies the identification of its 4 neighbours which are in the top 10 brightest stars. Sirius is at the center of a broom shape, surrounded by 4 neighbours outlining the extremities of the broom. Canopa is at the end of the handle and then, in the counter-clockwise direction, are 3 bright stars Orion-Rigel, Betelgueuse, Procyon almost equally spaced on a 120 degree circular arc of 25degree radius centered on Sirius. The handle line Canopa-Sirius is 30degrees clockwise from the line Sirius-Procyon and 30degrees anticlockwise from Sirius-Betelgueuse.

(Sirius, Ori Rigel, Betelgueuse, Procyon, Sirius, in anticlockwise direction) are the vertices of a rhombus. The line Sirius-Procyon joining two very bright stars is also oriented 30 degrees anticlockwise from its RA arc.

When the Orion constellation begins to set in the Western direction the whole Big Dipper near to Northern Celestial pole and Arcturus Boote and the two Southern (Centuri) Pointers near the Southern Celestial pole have all risen for 3 hours. The method is continued with these stars taking their turns.

5. In tropical zone.

mercator8gc30.jpg

Figure 1: Mercator map of brightest stars and great circle arcs to their neighbours.

image

Figure 2: Northern polar (inversion) map of brightest stars and great circle arcs to their neighbours.

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Figure 2: Southern polar (inversion) map of brightest stars and great circle arcs to their neighbours.

The horizon of a tropical navigator looks like a straight arc going near to the center of each polar sky map. Stars near the Celestial equator rise and set 12 hours apart. Initially any star is first seen setting at the beginning of the night; it rises earlier each subsequent night to appear for the whole night; finally it is so early that it is seen setting at the beginning of the night; it is then invisible for about one month and can be seen again setting at the beginning of the night. The whole cycle takes exactly one year. Their rising and setting time for any day of the year can be read directly from the edge of the sky map and can be used to identify them.

When the star reaches its highest elevation, the angle between the star and the navigator’s zenith reaches a minimum being the difference between its declination and his latitude.

Navigators in the tropical zone can advantageously identify bright equatorial stars by their rising time and their highest elevations and they do not have to bother with polar stars. (Country people and fishermen in Vietnam have been using this method since ancient time).

Examples:

Altair (+9 degrees declination) reaches its highest elevation on midnight (and rises and sets at 18 and 06 hours) on July 15th. It is seen rising before sunrise about 5 months before July and seen setting right after sunset about 5 months after July.

Orion Rigel (-8 degrees declination) reaches its highest elevation on midnight (and rises and sets at 18 and 06 hours) on December 15th.

Navigators can work out the angle from any identified bright star to the lower Celestial pole by remembering its declination (the required angle is equal to 90 degrees plus or minus its declination). Using that only star, navigators can locate the Celestial pole using the method of “Finding North direction and time from the Sun using bare hands” [2], with the star replacing the Sun.

In tropical zone, pairs of stars are useful for finding North.

Boote Arcturus and Vega are two brightest stars in the Northern Celestial hemisphere in May and both are brighter than any other star within 150 degrees distance from both of them. The great arc from Boote Arcturus to Vega is 55 degrees long, attains highest elevation around May 23rd and is 60 degrees in the trailing direction (anti-clockwise) from the intersecting constant RA arc pointing North. Boote Arcturus leads and has only one less bright star Spica close to it (within 35degrees distance). Vega follows and has two less bright stars Deneb and Altair close to it (within 35degrees distance).

In the equatorial sky, Boote Arcturus is at the tip of a V shape formed by (Spica, Boote Arcturus, Antares). This V shape points almost at the Northern Celestial pole.

Any tropical midnight in September has no bright star near to the zenith. Navigators have to use bright stars on the West (including the pair Fomalhaut-Deneb) early in the night and then switch to bright stars on the East late in the night. Fomalhaut and Deneb are high in the sky two hours before midnight.

The star Aris Hamal (of 24 deg. N. declination) of Oct 24th is a 51st brightest star but it is identifiable in this dark area of the Celestial sphere and is often used in this September time.

At midnight of September 7th, a relatively bright Fomalhaut reaches its highest elevation, 30degrees South of the Celestial equator. Deneb and Fomalhaut are separated by about 75 degrees distance, straddling the Celestial equator. The polygonal line (Deneb, 75degrees separation, Fomalhaut, 40degrees, Acherna, 40degrees, Canopa) joining 4 of top 20 brightest stars is almost a great circle arc (straight line) and this unique line can be used to identify these 4 stars. The direction Fomalhaut to Deneb is 30degrees in the leading direction (clockwise) from the North pointing constant R.A. arc.

In October, navigators may have to use a 90degrees long arc joining the bright stars Fomalhaut on the South-West and Aldebaran on the North-East. Fomalhaut-Aldebaran is 60degree in the trailing direction (anti-clockwise) from the North pointing RA arc.

At mid-nights in December, navigators can use the line joining the 1st and 3rd brightest stars in that sky (Sirius and Capella). It is 70degrees long, straddling the Celestial equator. Rotating this line by 15degrees anti-clockwise gives a RA great circle going through the two Celestial poles.

In the nights of December, use Sirius, Canopa and Orion group of stars.

At midnight of January 1st, Sirius, the brightest star of the sky reaches its highest elevation, 16degree South of the Celestial equator..Sirius and Canopa are two brightest in the sky, 36degrees apart and the line Sirius-Canopa points to Southern Celestial pole.The North and South Celestial poles are respectively (90+17)degrees and (90-17)degrees from Sirius.

The line Ori Rigel – Capella is a R.A. arc going through both Celestial poles. The North Celestial pole is 45 degrees from Capella and 98 degrees from Ori Rigel.

The line joining the two brightest stars of Orion (Ori Rigel and Betelgeuse) are about 25 degrees long, has its center on the equator and is oriented 30 degrees anticlockwise from its RA arc. The two shoulder stars of Orion is along a constant declination circle.

In March, before mid-night, use the equilateral triangle (Sirius, Betelgeuse, 25degrees, Procyon, Sirius, in counter-clockwise order). Its center of gravity is less than 2 degrees South of the Celestial equator and its base Betelgeuse-Procyon is a constant declination arc. After mid-night use Spica and Arcturus Boote.

At mid-nights in April, there are one very bright star Arcturus Boote and one bright star Spica. They are 35degrees apart with their mid-point on the 5degrees declination circle. The line from Spica to Boote is 30degrees anticlockwise from the intersecting RA great arc pointing North.

SUMMARY

The stars to use are:

Nov: Aldebaran, O.Rigel (8 deg. S declination), Betelgeuse.

Dec: Capella, O.Rigel, Betelgeuse, Sirius, Canopus.

Feb: Betelgeuse, Procyon, Sirius.

Apr: Spica, Boote Arcturus, Antares.

Aug: Altair (9 deg. N declination), Vega, Deneb, Fomalhaut.

6. Finding time from sky maps.

When a star is used in its date of the year, the Sun leads it by exactly 12 hours. For every month after that, the lead by the Sun is reduced by 2 hours.

Example:

Sirius is a star of Jan 7th. On Jan 7th the time determined by Sirius is 12 hours behind the time by the Sun. On April 7th, the time determined by Sirius is 6 (=12-3*2) hours behind the time by the Sun.

The positions given in the maps here are for mid-night of September 23rd (Autumn equinox time). The maps rotate once every (365/366)*day and the midnight maps rotate once every year. The rotation is counter-clockwise for Northern and clockwise for Southern hemispheres.

Difference in orientation of actual sky and the map gives the time from mid-night of the locality.

In my actual nightly field testings at few suburbs of Melbourne in winter time, it is found that traditional clear sky method is applicable in less than 10% of the times while this bright star method is applicable in about 60% of the times.

7. Preparation for worsening visibility.

divider43.jpg

Figure 1: Aligning the divider along sun rays and the layout of the compass points.

DirectionTimeByStars

Figure 2: Summary of steps for Finding North by any known bright star.

A user has to anticipate which star may remain last visible when visibility worsens. He has to quickly work out its angle to the Celestial pole (which is equal to 90 degrees plus or minus its declination). With only that single visible star, it is still possible to locate the Celestial pole using the method of “Finding North direction and time from the Sun using bare hands” [2], with the star replacing the Sun.

At that moment, the user should also bring out his magnetic compass to check its magnetic declination before relying on it when the last star disappears. Even a button sized compass, provided it is well made, can be quite helpful when Celestial navigation is disabled.

References.

[1]. tonytran2015, Finding North and time by stars, https://survivaltricks.wordpress .com /2015/08/28/finding-north-and-time-by-stars /, Posted on August 28, 2015.

[2]. tonytran2015, Finding North direction and time using the Sun and a divider, http://www. survivaltricks.wordpress.com/, 06 May 2015.

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