Slide Sky-Map for displaying tropical stars.

Slide Sky-Map for displaying tropical stars

by tonytran2015 (Melbourne, Australia).

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#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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Finding North and time by stars in the tropics

Finding North and time by stars in the tropics

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

This posting gives a method of using stars in the tropics under adverse effects of high skyline and bright sky. It is applicable whenever more than 30% of the night sky is seen.

It is based on the traditional tropical Oriental country methods, with the added improvement by using accurate data on dates and angular distances between stars for their identification. It is useful when the sky is unclear and restricted such as in cities with high skyline and bright sky.

1. Identifying bright stars in the tropics.

BrightStars20Plus2

Figure 1: Table of 20 brightest stars plus two additional easily identifiable stars for navigation in the tropics.

People in the tropics learned using stars differently from people in the temperate zones.

In the tropics it is difficult to see the polar and circumpolar stars to start identifying stars. Traditional (not influenced by Western astronomical knowledge) country methods by tropical people ignore the polar stars and rely on the dates of tropical stars and their order of succession in the sky to identify them.

Any tropical star is visible nightly (either from Sunset to its setting or from its rising to Sunrise) for more than 10 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.

Mercator star map

Figures 2,3: 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. Click to enlarge figure.

The table of this step shows the stars in their order of appearance in the year. The date of a star is the night when the star attains its highest elevation at mid-night (when the hidden Sun has the most negative elevation) and it is visible for that whole night.

2. Identifying stars positively using patterns in the map.

mercator8gc30.jpg

Figure 1: Sky map for the tropic. It is a Mercator map of the central strip of the night sky for printed side down reading. An observer looking up will see that the continuous strip made up of this map and its identical copies slowly and repeatingly moves from its left (aligned to rise on the East of the sky line) to its right (aligned to set on the West of the sky line).

The bright stars for the date near to the current date are then joined to its neighbours of similar brightness to reveal their relative directions and distances. These directions and distances form shapes and sizes to positively identify the stars.

As only the 20 brightest stars are used with large unique patterns in the sky, there is no possibility of having two similar patterns with equal sizes. A user of this method matches the observed shapes in the sky and compare them with those given in the map to identify stars positively.

The map of this step (for printed side down reading) shows the stars in a central strip of 120 degree width going across the sky starting from the Eastern horizon and ending at the Western horizon. An observer lying on his back, looking upwards vertically will see a part of a long continuous strip made up of the map in this step joined by its identical copies slowly rises from the Eastern horizon, moves across the sky (the right hand side of the map leads, left hand side trails) then sets on the Western horizon. He can only see those stars of this map within a window of 12 hours width (in the direction of left to right on the map) when there is no sunlight. The window remains stationary while the continuous strip, being the map here followed by its identical copies, moves across the sky (the right hand side of the map leads and left hand side trails). This is illustrated in the following four maps of the tropical mid-nights and their four approximate zenithal maps to be found at the end of this section.

Merc12

Figure 2: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Dec. 21st from the equator.

Merc03

Figure 3: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Mar. 21st from the equator.

merc0621b

Figure 3: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Jun. 21st from the equator.

Merc09

Figure 3: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Sep. 23rd from the equator.

The users of this method should keep in their minds that some bright planets (especially the outer planets Mars, Jupiter, Saturn) may wander on the ecliptic (drawn on the map) and cross some area under observation to confuse the identification of stars and constellations. The positions of those such slowly moving bright planets should be noted when observation condition is favourable.

Example:

For May 15th, the star to use is Antares (of May 29th) in the Scopii. The nearby stars to use are

Spica (201.3 deg R.A., -11.1 deg decl.),

Arcturus (213.9 deg R.A., +19.2 deg decl.),

Antares (247.3 deg R.A., -26.4 deg decl.),

Vega (279.2 deg R.A., +38.8 deg decl.).

3. Mercator maps and the distances on them.

Zenith12

Figure: Approximate zenithal map of the tropical midnight sky for December 21st. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

Zenith03

Figure: Approximate zenithal map of the tropical midnight sky for March 21st. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

Zenith06

Figure: Approximate zenithal map of the tropical midnight sky for June 21st. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

Zenith09

Figure: Approximate zenithal map of the tropical midnight sky for September 23rd. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

The map in the preceding step uses a Mercator projection to preserve angles. This projection specifies that

(Vertical distance to equator on Mercator map)/(dist. to equator by rectilinear scale) =

(180deg/3.14159rad) × ln((1+tan(0.5×decl.))/(1-tan(0.5×decl.))) / declination.

The projection makes small shapes look similar to the original shapes on the Celestial sphere. Equatorial shapes on the Celestial sphere are faithfully represented. However shapes near the polar regions of the Celestial sphere are enormously overstretched by this type of maps. The distortion can be easily seen by comparing the Mercator map given here and the two polar maps given in reference [2].

The equator line of a Mercator map can be used as a scale to measure distances between stars near to the equator. The vertical lines for of Right Ascension divides it into hours. Each hour of R.A. corresponds to 15 degrees on the Equator line.

The distance between two close stars anywhere on the map is their distance measured on the map multiplied by the cosine of the declination angle of their midpoint.

When the two stars are widely separated, the great circle arc joining them is divided into (about 3) small segments and their distances are added together to give the total distance.

Example:

The distance between Sirius and Canopus on the map of step 2 is measured (using the equator line as a scale) to be nearly 47 degrees in length.

Their midpoint is nearly at 40 degrees (in absolute value) in declination.

Their great circle distance on the Celestial sphere is therefore nearly

47deg X cos(40deg) =36 deg.

This is reasonably close to the actual distance of 36 degrees deduced from the values obtain from their declination and R.A. values given in the table of step 1

4. Measuring the angle between any two stars.

The actual angular distance between any two stars in the sky can be measured using a compass divider with each leg pointing to a star and their angle measured on a protractor.

The two legs of the compass divider can be substituted by two stretched fingers on one hand. The protractor can be substituted by a 12h clock face with each hour marking representing 30 degree angle separation.

(Instrumental navigators use sextants for highly accurate measurements of angles between stars and they can quickly decide on the identity of stars.)

5. Finding time with stars.

On its date, a star reaches its meridian at midnight. Every month before/after that the star reaches its meridian plane two hours later/earlier.

The user of the method should add the difference between zonal time and local time (when noon is at 12am) to obtain the zonal time.

6. Conclusions.

1/- I have tested this method in Saigon, a city with unclear sky and high-rise buildings and found it to be applicable in 80% of the non-rainy nights.

2/- Users of this method should take care not to mistake planets for dimmer stars along the ecliptic.

Reference.

[1]. tonytran2015, Finding North direction 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.

Added after 2018 July 20:

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

[3]. http://www.ancient-wisdom.com/zodiac.htm

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