Finding North in the polar zones using Equatorial Stars and the Sun.

by tonytran2015 (Melbourne, Australia).

#find North, #finding North, #polar zone, #arctic zone, #Equatorial stars, #Sun, #Viking, #navigation .

Finding North in polar regions using Equatorial Stars and the Sun.

The general principles in Finding North still apply for each familiar method. However Finding North direction in polar regions has its own problems and it is not as simple as for temperate zones due to difficulties caused by steep magnetic lines not pointing to rotational poles, by the closeness of the upper Celestial pole to the zenith, by long extended day time, by aurora light, by aurora interference with radio wave receivers in GPS units.

When those familiar methods encounter problems the method of Finding North by Tropical stars and the Sun can still work and maintain its precision. The Viking may had used this technique in their long sea voyages many centuries ago.

1. The two polar zones

The two polar zones  cover any area with absolute value of latitude higher than 66°33′. That is all their points are less than 23°27′ from one of the two poles. The Northern polar (arctic) zone covers parts of Greenland, Iceland, Sweden, Norway, Finland, Russia, U.S. Alaska, Canada with many of their cities. The Southern polar (antarctic) zone covers parts of Antarctica continent (with Argentinian stations, UK Rother station, etc …).
The ratio of the lengths of Day versus Night varies with a yearly cycle on any point of the Earth. In Arctic zone, it reaches 0-100 for some period centered on Winter solstice (on 21 December ) when the Solar path is totally below the horizon. The ratio then varies from 1-99 to 99-1. It then reaches 100-0 for some other period centered on Summer solstice (on 21 June ) when the Solar path is totally above the horizon. The ratio then varies from 99-1 to 1-99 and reaches 0-100 again.
It is similar for Antarctic zone except for the 6 months time difference between the two polar zones.

2. Finding North by GPS.

Find North by a GPS

Figure: A GPS screen.

The easiest way to find North in a polar region is to use the GPS apps on smart phones or on purpose made GPS units.

GPS compass directions are calculated from the change in terrestrial coordinates when you move. The minimum movement distance is only about 5m. 

GPS compass directions are true directions and are different from and independent of magnetic compass directions.

However, GPS units may run out of battery, be non-operational during war times, be under heavy interference from polar aurora storms. A non-GPS back up method is still necessary.

3. Finding North by a magnetic compass.

Find North by a compass

Figure: A magnetic compass.

3a. The magnetic poles are not exactly at the North and South poles of the Earth. They are currently in Canada and near to New Zealand respectively. Users of magnetic compasses should know how to compensate for this.

3b. Magnetic lines are also nearly vertically inclined in polar regions making normal compasses sticky with their needles and they may have to be replaced by cruder magnetic rods hung on wire threaded through holes near to their mid-points.

3c. Aurora in the sky changes very slowly and can be used as overhead navigational marks juat like permanent clouds.


4. Finding North using Polaris.

Find North using Polar skymaps

Figure: The Northern and Southern Polar skymaps are represented by two circular discs here.

A real dipper versus Big and Little Dipper constellations

Figure: Photo of a real dipper. Inset: The Big Dipper and Little Dipper constellations.

4a. Polaris in the Little Dipper is right on the North Celestial pole. The North Celestial pole is in the Northern direction of all vertical plumb lines. If the star can be obscured by any plumb line then you eye is exactly on the South of the line. Near to the pole, Polaris is close to the upper extension of any vertical plumb line and it is hard to obscure it by some vertical plumb line.

4b. The altitude of Polaris is most easily read with a Bubble Sextant (Aircraft Sextant) or with a Theodelite (for higher accuracy). The direction with smallest value of altitude of Polaris is Northern direction.
The method is easily applicable at night time but Polaris cannot be seen during day time and during aurora storms.

5. Basis of finding North by Tropical stars.

Find North with Orion Equatorial stars

Figure: Panoramic view of the Celestial Equator and the Tropical band from the Arctic zone in December. Stars travel from Front Left to Front Right. The directions and Solar times corresponding to the scale on the bottom of the picture are N(0hr)-E(06hr)-S(12hr)-W(18hr)-N(24hr).

5a. Any point on the Earth sees exactly half of the Celestial Equator above its horizon. The angle between the plane of this half circle and the horizontal one is equal to (90°- latitude).
The Celestial Equator is inclined to the ground and is below the horizon in the North direction in the Northern hemisphere.

5b. Equatorial stars such as the Central Belt Star of the Orion travel along this circle once every day. They rise and set exactly in the exact East and exact West directions respectively.

Find North with Scorpius Equatorial stars

Figure: Panoramic view of the Celestial Equator and the Tropical band from the Antarctic zone in June. Stars travel from Front Right to Front Left. The directions and Solar times corresponding to the scale on the bottom of the picture are S(24hr)-W(18hr)-N(12hr)-E(06hr)-S(0hr).

5c. Any tropical star (any star which is no further than 23°27′ from the Celestial Equator) travels along one large (but not great) circle in the sky every day. The circle is “parallel” to the Celestial Equator.

5d. The elevation/altitude of the star varies daily with an amplitude equal to (90°-observer’s latitude) about its daily mean (which is nearly equal to its Declination multiplied by the sine of observer’s latitude)

5e. The North Souih line is the bisector of two directions pointing to any two positions having equal elevations of the same star. The common elevation can be conveniently chosen to be the mean of its 24hr values.

6. Solar trajectory on the Celestial Sphere

The Sun travels along one large (but not great) circle in the sky every day. The circle is “parallel” to the Celestial Equator. The circular Solar path drifts to its most Northern position at 23°27′ latitude on 21 June solstice then drifts to its most Southern position at 23°27′ latitude on 21 December.

At equinox times, the Sun is exactly on the Celestial Equator and rises and sets exactly like an equatorial star.

Locating the hidden Sun by polarized lightFigure: Locating the hidden Sun by polarized light from bright patches of the sky.

Knowing the trajectory of the Sun, you can locate it using polarizing sunglasses even when it is hidden and under the horizon (see ref. [5], Using polarized light to locate the Sun when it is hidden from view).

7. Measuring solar altitude with a stretched hand on an extended arm.

A hand with stretched out fingers hold on its extended arm sustains an angle of about 12 degrees and is a very convenient mean for measuring Solar elevation (altitude) angle in polar regions.

8. Variation of Solar altitude/elevation during the day.

Solar elevation/altitude varies daily with an amplitude equal to (90-latitude) about its daily mean (which is nearly equal to Solar Declination of the day multiplied by sine of local latitude).

You can tell where is the Sun on its daily cycle by measuring its altitude with a stretched hand on an extended arm.

As the Sun travels on a known wavy line its altitude gives both its compass direction and the corresponding time of the day.

The directions and times corresponding to the scale on the bottom of the first panoramic picture (for Arctic regions) are N(0hr)-E(06hr)-S(12hr)-W(18hr)-N(24hr).

For Antarctic regions the directions and times corresponding to the scale on the bottom of the second panoramic picture are S(24hr)-W(18hr)-N(12hr)-E(06hr)-S(0hr).

9. Time estimation from Solar altitude

Solar altitude may give a better time estimation near to Sunrise and Sunset.

The time is 6hr or 18hr when the altitude of the Sun crosses its mean value.

10. Distinguishing AM from PM

When using the Sun for navigation, it is important to know whether the Sun is ascending (AM) or descending (PM).

10a.A 24hr sub-dial on a clock face is certainly useful in telling AM and PM.

10b. Ambient air temperature after receiving daylight radiation is also usually higher in PM time than in AM time.

10c. There are different sets of stars in the sky for AM and PM in the night.

10d. Birds activities are different in AM and PM.

10e. Your biological clock (circadian rhythm) may help distinguishing AM and PM.

11. Finding North with a watch in a polar region

Finding North with a watch

Figures: Finding North with a watch for antartic and arctic zones. 

Finding North with a watch needs a modification: If you can travel to the nearest pole in 2hr, you have to remember that the 6-12 line on the watch points along the meridian line of your home city, not toward the Pole of the Earth. Indeed, you can travel around the pole but that 6-12 line keeps its direction along the meridian of your home city.

The watch face can be simply laid horizontally as in the original “Scout method” without generating any noticeable directional error.

Figure: A map of the arctic from National Oceanic and Atmospheric Administration ( All meridional lines converge at the pole.

12. Finding North with a divider in a polar region

solar declination from a watch face

Figure: Estimating Solar declination by drawing a watch face with a subdial.

Finding North by a divider

Figure: Finding North by a divider.

The divider method is still applicable for finding direction and time but requires high accuracy in Solar declination and latitude angle for setting the divider.

A small plumb line hanging from the stem of the divider can improve the accuracy for its latitude angle setting.

With the above additional plumb line, the divider can measure the altitude of the Sun to give a good estimate of time.

13. Finding North with an AM Broadcast radio receiver in a polar region

AM radio usable for Finding North direction

Figure: An AM Broadcasting radio receiver wirh an internal ferrite rod antenna.

The method of finding direction using an AM radio receiver tuned to nearby broadcasting ([8]) is useful near to cities with AM broadcasts  in polar regions. The transmission is not effected by low visibility from bad weather. You need a map of the region with AM transmitters as landmarks.


[1].  tonytran2015, Using GPS in off-grid situations.,, posted December 6, 2016

[2]. tonytran2015, Selecting and using magnetic compasses,,, posted 09/7/2016.

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

[4]. tonytran2015, Finding North and time by stars in the tropics,,, posted on May 25, 2016

[5]. tonytran2015, Using polarized light to locate the Sun when it is hidden from view,, posted on May 9, 2015

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

[7]. tonytran2015, Finding directions and time using the Sun and a divider,,, posted on May 6, 2015.

[8]. Navigating with an AM MW radio receiver.



Using polarized light to locate the Sun when it is hidden from view. . Posted on May 9, 2015. This is a useful technique.

Using GPS in off-grid situations., posted December 6, 2016

Adding longitude and latitude lines to a map, posted August 23, 2017

Navigating with an AM MW radio receiver, posted January 17, 2017

radio sony

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Do not click on any unknown link external to your trusted sites

by tonytran2015 (Melbourne, Australia).
#cyber attack, #net security, #computer security, #malware, #worm,

Do not click on any unknown link external to your trusted sites

That is the obvious conclusion after reading the blog by johnip:

“In Hong Kong, Gazeley said his team had found a new version of the worm that didn’t use e-mail to lure victims.
Instead, it loaded scripts onto hacked websites where users who clicked on a malicious link would be infected directly. He said it was too early to tell how many websites had been affected.”
See the original blog: some-businesses-in-asia-disrupted-by-cyber-attack-on-monday-authorities-brace-for-more

Explore new unknown sites only when you know how to deal with worms and hijacking of your computer.


[1]. some-businesses-in-asia-disrupted-by-cyber-attack-on-monday-authorities-brace-for-more


Added after 2017 Dec 26:


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The Parasites of Western Economy, Part 2: Shifty Lenders.

by tonytran2015 (Melbourne, Australia)

#shifty lender, #parasite, #shark lender, #captive borrower, #inexperienced borrower, #private equity, 

The Parasites of Western Economy, Part 2: Shifty Lenders

Because of the requirements in life we do have take loans during some phases of our lives: A worker has to buy a car to go working far from home and later he has to buy his house using long term loans. We certainly have to borrow to buy houses if we neither use gold to store our saving  nor want to lose much of the saving in hand to the vicious inflation ([2]).

1. The shark lenders in car finance preying on new borrowers.

The lendings by banks to the starting up car buyers have to be appreciated. 

However, there are often more numerous greedy “shark lenders”, who are usually located next door to the car show rooms, and are associated with the car dealers to prey on the hot headed emotion of unseasoned young buyers to mislead them into disadvantageous loan contracts. Those contracts places very high interests on the young buyers and rob them of their savings or may even bankrupt them (see also [3,4]). 

2. The manipulators of captive borrowers on long term loans.

They are the  loan makers who initiated loans only to have their conditions changed during the life of the loans. Even housing loans may become financial traps to unwary borrowers.

There are many types of traps (see also [5,6].:

2a. Shifty lenders have a condition that any borrower who wants an earlier end to the loan has to pay an outrageous exit fee (about nearly one year of interest) which is many times the actual cost to the lenders for organizing the early termination of that loan. This stops their borrowers from switching to obviously cheaper loans.

Fortunately for Australians, exit fees have been banned in Australia for contract signed after 01 July 2011. I am not aware of any similar laws protecting Americans.

2b. Shifty lenders may impose a condition that lender can recall the loan at any time before the expiration of the loan contract. This is an outrageous condition and is used by shark lenders to send unwary borrowers into higher interest loans.

2d. In a typical loan contract offered by a shark lender, the initial interest rate is very low, but if there is any single late payment (which may even be caused by the failure of the computer of the lender!), the low interest rate will forever disappear and a high interest rate replaces it for the remaining life of the loan.

2e. If there is any second late payment, the shark lender will take possession of the mortgaged house and sell it at a low price to their associates.

2f. Shifty lenders may also impose conditions in the loan contract that the initial lender may resell the loan to a new lender who can set new loan conditions.

This trap can lead to unreasonable high interest rates to unwary borrowers.

3. The lenders who discloses only the advantages but not the disavantages of the loans.

The lender may offer his client low interest loans from Switzland [7] but failed to say that the declining exchange rate of US dollars versus Swiss franc may require more than the low interest to repay the loan (see [8]).

Many business owners have lost their businesses due to those lenders.

4. The lenders who want exclusive rights to all banking of the borrowers.

The lenders who want exclusive banking rights are really ready to take over the business of the borrowing companies. The lenders are usually owned by some private equities. Any such lender actually wants to take over some target company without paying the price of a normal take over! Such a lender will do it by causing financial distress in a target company and to trigger its default. A typical example is reported by BBC (ref. [9]):

Judge Martin Beddoe said Scourfield “sold his soul” to Mills in exchange for “sex”, “bling” and “for swag”.….

Scourfield, 54, a former HBOS manager, told customers to use a turnaround firm called Quayside Corporate Services… Mills, 60, who ran Quayside…, bribed Scourfield … “…What Scourfield gave Mills in addition to fees was the opportunity to take control of the various businesses and, in some cases, to acquire ownership of them,” prosecutor Brian O’Neill QC told the court. “

Any such targeted or collapsed company will be acquired for cheap price and restructured by some private equity associated with the lender and on sold to new buyers at huge profit as a healthy restructured company (see [10,11]). 

See also ([14],[15]), added after Mar 2017.

The shifty lender provides all finance and  banking services at very low costs to the  “healthy restructured”  company. But as soon as the sale has been completed. those services will be withdrawn, leaving the company to seek the services at much higher costs from other provider companies in the market.

The  “healthy restructured”  company is bound to collapse. The following comment ([12]) from the original founder of a company illustrates the problem:

“It was bought by a type of merchant bank who paid a hundred million [dollars] for it and 18 months later floated it for $500 million,” Dick Smith said.

“Now you don’t have to be very bright to know that’s absolute greed, it’s impossible and unfortunately that’s caused this terrible problem at the moment.”

Even multimillion dollars pension funds have been tricked into buying those “healthy restructured” companies loaded with heavy debts. 

5. Outright loan scam makers.

Carried out by faked lenders. They asked people to pay huge application fees for a cheap loans but they only took the fees and disappeared (see [13]).

6. Conclusions

All lenders are not the same and all loans are not the same. Borrowers need to be financial competent as the traps become more and more elaborate. Even multimillion dollars have been trapped.


[1]. The Parasites of Western Economy, Part 1: Motorvehicle Insurance Scams., posted April 17, 2017.

[2]. gold-for-storing-wealth, posted April 28, 2017.

[3]. warning-on-unfair-car-loans, date

[4]. car-loans, date

[5]. home-loans fees, date

[6]. prepaymentpenalty, access date 05MAY2017

[7]. countries with the lowest interest rates for loans mortgages,

[8]. Luigi Zingales, Guy Rolnik, Amit Seru, Putting the Client Last: former-investment-banker-explains-clients-sucker-punched, posted

[9]. Ex-HBOS banker ‘sold his soul for swag’, bbc new,, 2 February 2017.

[10]. the-private-equity-giants-the-greek-target-and-a-trojan-horseOctober 28, 2015

[11]. report-says-big-buyouts-are-likelier-to-default, date 05Nov2009

[12]. dick smith blames-private-equity-owners-greed-for-collapse,

[13]. loan-scams, date

[14]. dick-smith-class-action-ready-to-launch,

[15]. brick and mortar retail meltdown fueled by asset stripping details emerge in bankruptcy courts by wolf-richter,,


Added after 2017 Dec. 20:




 , posted on 17 April 2017 ,

, posted on 07 May 2017 ,

, posted on 10 Jun 2017 ,


The Parasites of Western Economy, Part 5: Company Asset Strippers and Conspirators posted on 13 August 2017 ,

, Cashless bartering for survival, Federal Reserve Bank charges undeserved fees to Americans., A satirical guide to signs of an impending crash for small investorsYour fiat money (Part 2)Your fiat moneyBankers given outrageous incomes by their boardsSigns pointing to an impending crash for small investors,Bankers earn more than interest margin on secured loansCan most pension funds last?, … all 

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