Finding North from unclear sky around September.

Finding North from unclear sky around September.

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. 168).

#find North, #finding North, #direction, #by stars, #Altair, #Fomalhaut, #September, #unclear sky,

Finding North from unclear sky around September.

Around September there are some bright stars shining the whole night. They include Deneb close to the Celestial North pole and Fomalhaut in the Southern sky. These stars can be used to locate the Celestial poles in the sky and subsequently the terrestrial principal directions.

1. Celestial poles and terrestrial directions.

Sun on Celestial Sphere

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

To an Earth bound observer, the Earth appears to be enclosed by a large rotating spherical shell called the Celestial Sphere with all stars attached to it. This shell rotates around the Earth nearly one revolution every 24 hous. This rotation leaves unmoved only 2 points on the shell. They are called the Northern and Southern Celestial poles of the Celestial Sphere.

If an observer can locate one Celestial pole then the projection to the ground of the line from him to the pole will be along his terrestrial North South direction.

2. Locating the Northern Celestial Pole in Northern hemisphere.

Figure: Polar Inversion map for the Northern Celestial hemisphere. The map should be read with its September marking on its rim pointing towards the ground as illustrated here.
An observer has to align the polar map with marking for September on the rim (at 6 o’clock position) pointing downward. An observer in Northern latitude above 30 degrees will see the rotation of bright stars Vega, Deneb [1], Cassiopeia constellation, bright star Capella then Big Dipper constellations in that order.

Cassiopeia goes highest around 01am.

The bisector of the M shaped Cassiopeia goes through the Northern Celestial pole. The Northern Celestial pole is almost 30 degree below Cassiopeia.

Sky map Northern 3/4 sphere

Figure 2: Polar Inversion map of Northern Celestial 3/4 sphere.

3. Locating the Southern Celestial pole in Southern hemisphere.

Figure: Polar Inversion map for the Southern Celestial hemisphere. The map should be read with its September marking on its rim pointing towards the ground as illustrated here.

Sky map Southern 3/4 sphere

Figure: Polar Inversion map of Southern Celestial 3/4 sphere.

An observer has to align the polar map with marking for September on the rim pointing downward as illustrated here. An observer in Southern hemisphere or on the tropical zone would see Achernar [1] rising highest around 2am. Southern Celestial pole is the midpoint of Achernar and the two Pointers and is about 30 degree from Achernar.

 

4. Locating the Celestial poles from tropical stars.

A observer in the tropic should already know the two brightest stars Scorpius Antares (at the heart) and Scorpius Shaula (at the stinger end) of the Scorpius [1]. The straight line from Antares to Shaula goes through the bright star Fomalhaut which is of 60 degree distances from both Scorpius Shaula and Altair [1] which is a star of July and is close to the Celestial equator.

Figure 2: 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.

Figure: Fomalhaut and its nearby stars.

The bisector of the angle Shaula, Altair, Fomalhaut points to the Southern Celestial pole.

Southern Celestial pole is is of 90 degree distance from Altair and of equal 60 degree from both Scorpius Shaula and Fomalhaut.

5. Visibility of the stars.

Scorpius Altairs and Scorpius Shaula are stars of June that set close to midnight when viewed from tropical zone. Altair is a star of July that sets close to 02 am. Fomalhaut is visible for nearly the whole night in September.

References.

[1]. tonytran2015, Finding North from unclear sky in April, survivaltricks.wordpress.com, Finding North from unclear sky around July, posted on 2018, May 13.

[2]. tonytran2015, Finding North from unclear sky in April, survivaltricks.wordpress.com, Finding North from unclear sky around April, posted on 2018, April 12.

[3]. tonytran2015, Finding North from unclear sky around New Year, survivaltricks.wordpress.com, Finding North from unclear sky around New Year, posted on 2018, April 05.

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

[5]. , posted on

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

[7].The Scorpius constellation., posted January 8, 2017

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Finding North from unclear sky around July.

Finding North from unclear sky around July.

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.130).

#find North, #finding North, #direction, #by stars, #Vega, #Deneb, #Altair, #July, #unclear sky

Around July there are some bright stars shining the whole night. They include Vega, Altair and Deneb. These three stars can be used to locate the Celestial poles in the sky and subsequently the terrestrial principal directions.

1. Celestial poles and terrestrial directions.

Sun on Celestial Sphere

Figure: The Sun, the Moon and the stars are attached to a Celestial sphere which encloses the Earth like a giant rotating cage.
To an Earth bound observer, the Earth appears to be enclosed by a large rotating spherical shell called the Celestial Sphere with all stars attached to it. This shell rotates around the Earth nearly one revolution every 24 hous. This rotation leaves unmoved only 2 points on the shell. They are called the Northern and Southern Celestial poles of the Celestial Sphere.

If an observer can locate one Celestial pole then the projection to the ground of the line from him to the pole will be along his terrestrial North South direction.

2. Locating the Northern Celestial Pole in Northern hemisphere.

Figure: Polar Inversion map for the Northern Celestial hemisphere. The map should be read with its July marking (at 4 o’clock position) on its rim pointing towards the ground.
An observer has to align the polar map with marking for July on the rim (at 4 o’clock position) pointing downward. An observer in Northern latitude above 30 degrees will see the rotation of three bright stars Vega, Deneb, Capella then Big Dipper constellations in that order.

Vega and Deneb go highest around 24 hr.

The bisector of the line Vega Deneb goes through the Northern Celestial pole. The pole is almost of equal distances of 45 degrees from each of them.

3. Locating the Southern Celestial pole in Southern hemisphere.

Figure: Polar Inversion map for the Northern Celestial hemisphere. The map should be read with its July marking (at 8 o’clock position) on its rim pointing towards the ground.
An observer has to align the polar map with marking for July on the rim (at 8 o’clock position) pointing downward. An observer in Southern hemisphere or on the tropical zone would see the Southern Cross Pointers highest around 18 hr, then Antares around 20 hr. Achernar is seen rising before Sunrise. The midpoint between the Pointers and Achernar is almost the Southern Celestial pole.

4. Locating the Celestial poles from tropical stars.

A observer in the tropic should already know the very bright star Bootes and the bright star Antares in the Scorpius constellation used in April.

Figure 1: Photograph of Spica (near the bottom edge), Bootes Arcturus (near the right edge) and Antares (1/8 of the width from the left edge) forming a triangle. Celestial North is at 01 o’clock position (30 degree clockwise from vertical) in this photo. There is a very bright planet (1/2 from left edge, 1/3 from bottom) traveling on the Ecliptic in this photo.

Figure 2: 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.

On the trailing side of Bootes Arcturus and Antares, (click the above Mercator map for details) there is a bright star of equal distances of 60 degrees to both of them. This star is Altair, which is as bright as Antares.

Following the line Antares to Bootes Arcturus, turning anti-clockwise by 90 degrees at Bootes Arcturus and traveling for 60 degrees takes us to Vega, which is as bright as Bootes Arcturus. The line (Antares, Arcturus) is nearly at right angle to the almost straight line (Spica, Arcturus, Vega).

The line (Bootes Arcturus, Antares) is nearly parallel to the line (Vega, Altair) which lie slightly nearer to Bootes Arcturus.

Vega is as bright as Bootes Arcturus while Altair is as bright as Antares.

Sky map Northern 3/4 sphere

Figure 3: Polar Inversion map of Northern Celestial 3/4 sphere. The line (Vega, Altair) is 30 degrees long and is nearly parallel to the line (Bootes Arcturus, Antares) which is 60 degrees long.

Rotate the line (Altair, Vega) about Altair by 10 degrees counter-clockwise give the great circle through the two Celestial poles. Northern Celestial pole is nearer to Vega and is 80 degrees from Altair. Southern Celestial pole is nearer to Altair and is 100 degrees from Altair.

Trailing 2 hour behind Vega is the bright star Deneb (see the Mercator star-map). (Vega, Altair, Deneb) is known as the Summer Triangle. The bisector of the angle Vega, Altair, Deneb points to the Northern Celestial pole.

Bright Stars 20 Plus 2

Figure 4: Table of 20 brightest +2 stars in order of appearance.

5. Visibility of the stars.

Altair is visible for nearly the whole night in July. The Summer Triangle is visible for nearly the whole night in July. Click on the Mercator map for details.

6. CAUTION with planets
The Moon and planets travel on the Ecliptic. Observers should take care not to mistake any planet for Antares in the Scorpius constellation.
A planet is always brighter than any star, including Sirius, moves from night to night, and does not twinkle in clear sky.

References.

[1]. tonytran2015, Finding North from unclear sky in April, survivaltricks.wordpress.com, Finding North from unclear sky around April, posted on 2018, April 12.

[2]. tonytran2015, Finding North from unclear sky around New Year, survivaltricks.wordpress.com, Finding North from unclear sky around New Year, posted on 2018, April 05.

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

[4]. , posted on

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

[6].The Scorpius constellation., posted January 8, 2017

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Finding North from unclear sky around April.

Finding North from unclear sky around April.

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.124).

#find North, #finding North, #direction, #by stars, #Spica, #Bootes Arcturus, #Antares, #April, #unclear sky
Around April there are some bright stars shining the whole night. They include Spica, Bootes Arcturus and Antares. These three stars can be used to locate the Celestial poles in the sky and subsequently the terrestrial principal directions.

1. Celestial poles and terrestrial directions.

Sun on Celestial Sphere

Figure: The Sun, the Moon and the stars are attached to a Celestial sphere which encloses the Earth like a giant rotating cage.
To an Earth bound observer, the Earth appears to be enclosed by a large rotating spherical shell called the Celestial Sphere with all stars attached to it. This shell rotates around the Earth nearly one revolution every 24 hous. This rotation leaves unmoved only 2 points on the shell. They are called the Northern and Southern Celestial poles of the Celestial Sphere.

If an observer can locate one Celestial pole then the projection to the ground of the line from him to the pole will be along his terrestrial North South direction.

2. Locating the Northern Celestial Pole in Northern hemisphere.

Figure 1: Stars in the Northern hemisphere rotates anticlockwise around the North pole.

An observer in Northern latitude above 30 degrees will see the rotation of three bright stars Vega, Deneb, Capella then Big Dipper constellations in that order.

Big Dipper constellation goes highest around 22 hr.

3. Locating the Southern Celestial pole in Southern hemisphere.

Figure 1: Stars in the sothern hemisphere rotates anticlockwise around the North pole.

An observer in Southern hemisphere or on the tropical zone would see the Southern Cross Pointers for the whole night.

4. Locating the Celestial poles from tropical stars.

Figure 1: 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.

An Earth bound observer in Southern hemisphere or on the tropical zone can identify the forward swept broom (or a duck foot (?), a bird foot (?) or a tree with 3 upper branches (?)). formed by the brightest star Sirius and four surrounding bright stars Canopus, Orion-Rigel, Betelgeuse and Procyon. The line Canopus to Sirius make the 35 degrees long broomstick handle and three lines from Sirius to each of the other three stars form three branches of the forward swept broom head (see the star maps). Sirius to Procyon is the trailing branch of the (three branched) broom head.
Doubling the travel from Sirius to Procyon takes us to another bright star named Pollux.

Two thirds of the line from Procyon to Pollux is a point on the Ecliptic (the great circle containing the.Sun and all planets). Turning anticlockwise 100 degrees at this point and traveling by a distance of 40 degrees takes us to a less bright star Leo Regulus. Keeping the direction from that two thirds point to Leo Regulus and travel for another 50 degrees takes us to a brighter star Spica. Spica is 90 degree in distance from the that two thirds point. (Observers from the Southern Hemisphere may also see that the great circle arc going through the long axis of the Southern Cross goes by 50 degrees to get very close to Spica. Draw the line from Southern Cross to Spica and then turns 30 degrees anticlockwise and continue for another 30 degrees to reach Bootes Arcturus.)

Turning clockwise by 90 degrees at Spica to leave the Ecliptic and traveling by 30 degrees takes us to a much brighter unmistakable star Bootes Arcturus.

Instead of turning right toward Bootes Arcturus, traveling along the Ecliptic for another 50 degrees take us to a bright star Antares in the Scorpius (Observers from the Southern Hemisphere may also see that Antares is 45 degrees clockwise and 45 degrees distance from the direction of dim Pointer to bright Pointer.).

Figure: Antares is the bright star in the Scorpius constellation which has the shape of a declawed scorpion. Two bright objects on the third top of the photo are planets traveling on the Ecliptic. Northern Celestial pole is from the top left (11 o’clock) direction of the photo.

The stars Spica, Bootes Arcturus, Antares form an arrow-head pointing North.

The midpoint of the great circle arc from Spica to Bootes Arcturus is almost on the Celestial equator. Rotating this arc clockwise by 30 degrees makes its extension goes through both Celestial poles. Northern Celestial pole is 90 degrees from the midpoint and on the side of Bootes Arcturus. Southern Celestial pole is 90 degrees from the midpoint and on the side of Spica.

The internal bisector of the angle formed by (Spica, Bootes Arcturus, Antares) points to the Southern Celestial pole while its rearward extension points to the Northern Celestial pole.

Figure: Photograph of Spica (near the bottom edge), Bootes Arcturus (near the right edge) and Antares (1/8 of the width from the left edge) forming a triangle. Celestial North is at 01 o’clock position (30 degree clockwise from vertical) in this photo. There is a very bright planet (1/2 from left edge, 1/3 from bottom) traveling on the Ecliptic in this photo.

Bright Stars 20 Plus 2

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

5. Visibility of the stars.
Orion constellation, Sirius and its surrounding stars are visible after Sunset. Spica, Bootes Arcturus and Antares are all visible for nearly the whole night in April.

Figure 1: Azimuth and elevation angles of stars for equatorial observers.

Figure 2: Azimuth and elevation angles of stars for observers on 30 degrees North latitude.

Figure 3: Azimuth and elevation angles of stars for observers on 30 degrees South latitude.

6. CAUTION with planets
The Moon and planets travel on the Ecliptic. Observers should take care not to mistake any planet for a navigational bright star.
A planet is always brighter than any star, including Sirius, moves from night to night, and does not twinkle in clear sky.

References.

[1]. tonytran2015, Finding North from unclear sky around New Year, survivaltricks.wordpress.com, Finding North from unclear sky around New Year, posted on 2018, April 05.

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

[3]. , posted on

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

[5].The Scorpius constellation., posted January 8, 2017

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Finding North from unclear sky around New Year.

 

Finding North from unclear sky around New Year.

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.121).

#find North, #finding North, #direction, #by stars, #Sirius, #Canopus, #Orion-Rigel, #Capella, #New Year, #unclear sky
Around New Year there are some bright stars shining the whole night. They include Sirius, Canopus, Orion-Rigel and Capella. These four stars can be used to locate the Celestial poles in the sky and subsequently the terrestrial principal directions.

1. Celestial poles and terrestrial directions.

Sun on Celestial Sphere

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

To an Earth bound observer, the Earth appears to be enclosed by a large rotating spherical shell called the Celestial Sphere with all stars attached to it. This shell rotates around the Earth nearly one revolution every 24 hours. This rotation leaves unmoved only 2 points on the shell. They are called the Northern and Southern Celestial poles of the Celestial Sphere.

If an observer can locate one Celestial pole then the projection to the ground of the line from him to the pole will be along his terrestrial North South direction.

2. Locating the Northern Celestial Pole.

Orion by Samsung GN2

Figure: Photo of the Orion constellation (Photo added 2018 May 09). Northern Celestial pole is from the top direction of this photo.

An Earth bound observer in Northern hemisphere or on the tropical zone can identify the Orion constellation around New Year. The front foot of the hunter represented by this constellation is the bright star Orion-Rigel. The trailing shoulder of the hunter is the bright star Betelgeuse.

The brightest star in the sky is Sirius. The great circle arc Sirius to Capella is 70 degrees long with Betelgeuse being close to its midpoint.
Extending the great circle arc Orion-Rigel to Capella to 100 degrees long bring us practically to the Celestial North pole.

star map mercatorx1p6

Figures 1a, 1b: The Mercator maps 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.

3. Locating the Southern Celestial pole.

An Earth bound observer in Southern hemisphere or on the tropical zone can identify the Orion constellation around New Year. Sirius is the brightest star in the sky and it is behind the trailing foot of the hunter.
Canopus is the next brightest star within 45 degrees of Sirius. The great circle arc Sirius to Canopus is nearly 35 degrees long. Doubling this arc bring us practically to the Southern Celestial pole.

Bright Stars 20 Plus 2

Figure 2: Table of 20 brightest +2 stars in order of appearance.
4. Visibility of these four stars.
The four stars appear on the meridional line (the North South line through the zenith of the observer) near midnight of New Year.
They appear two hours earlier for each additional calendar month after that date.
Example:
In April, they appear on the meridional line at about 24 hr – (2 hr)×(4th-1st) = 18 hr. After 18 hr they slowly move to the setting (Western) side.

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Finding North and time with unclear sky

Finding North and time with unclear sky

by tonytran2015 (Melbourne, Australia).

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

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).

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Figure 1: Bright stars about Southern Celestial pole.

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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.

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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.

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

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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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