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Polaris Clock
Philip G Ney 20/3/09
© 2009
Need. Every navigator needs accurate time. Even the best chronometer may gain of lose. It is possible to check the accuracy of any timepiece with a radio signal but that may not be available.
Observation. The march of stars around Polaris every 24 hrs must be accurate. If Polaris were the hub of the clocks arms, the angle from any star in the northern hemisphere to Polaris and the earth’s horizon will provide accurate time, once the clock is set.
Setting the Polaris clock.
For any known longitude at sunrise or sunset, a) Measure the altitude of Polaris (+ or – 0 to 1 degree depending on the angle to Ruchbah) which is your latitude. (Hoi) b) Measure the altitude of Dubhe. (Star on the upper outer lip of the Big Dipper). (Hoii) Note time from an accurate watch. This is best when Dubhe is lower than Polaris. c) Subtract Hoii from Hoi to give side x of a right angle triangle. d) Measure the angular distance between Polaris and Dubhe to give you side y for this triangle. e) Solve for angle alpha at Polaris between the vertical and Dubhe. ( cos alpha = y/x ) That is now the angle for that time. Your clock is set. You can now check your clock by calculating angle alpha using the altitude of Dubhe or any other convenient star with a government calculated factor accounting for any error introduced by the earth’s revolving around the sun on an elliptical orbit.
Longitude
This local Polaris clock time compared the GMT of your chronometer gives the basis for calculating your longitude.
Side Looking Sextant (SLS)
A normal sextant modified with additional mirrors to view stars looking sideways plus an accurate bubble for level would make it possible to measure the angle beta at Dubhe between the artificial horizon and Polaris directly.
Other stars
Using GMT and the Polaris clock and the side looking sextant, it is possible to establish an artificial horizon at different heights above the horizon for any convenient star. Making star sights can then be done at almost any time of the night.
Southern Hemisphere
The 2 arms of the Southern Pole Clock are a line connecting Acrux and Achernar that passes thru the southern pole. That clock can be set by obtaining the angles above the horizon of both stars and calculating the angle at one of them for a given time. Then it is possible to use the Side-Looking Sextant (SLS) to measure the angles from one star or the other passing thru the southern pole and know the time.
Lost in the woods
Part of the disorientation causing panic of those lost in the woods, is not knowing the time at night. A brief almanac for different longitudes could be carried in the woods-person’s backpack. It would give times for various easy to identify angles for major stars swinging around Polaris, eg. Dubhe level with Polaris, Arcturus level with Polaris.
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