The Firmamentum is a unique measurement and navigation instrument. Fully in the tradition of the historic watches used for observation, it not only shows the Earth’s rotation through the classic measurement of time, but with the aid of the hour angle it measures the Earth’s rotation
around its own axis and the visible movement of the sun, planets and stars in the heavens.
The hour angle defines a full rotation of the Earth on its own axis as being 360 degrees of angular movement. It therefore measures the movement of the Earth not in the classic sense as a unit of time, but rather it defines it in degrees. The hour angle expresses 4 minutes of our time as one
degree and 60 minutes as 15 degrees. Due to this division into degrees, navigators can determine their own position on Earth with the help of the hour angle and the visible movement of the sun, planets and stars in the sky.
In order to directly display the speed of the stars - the so-called sidereal time - which is slightly different from the bodies in our solar system, Firmamentum has integrated into it a special mechanism for the direct and exact display of one’s own position with the aid of a heavenly body
outside our solar system. It therefore not only shows the solar hour angle, but also the sidereal hour angle in a second display designed to be variable. This second display of sidereal time thus permits Firmamentum to be used for the observation of a heavenly body within our solar system at the same time as the observation of a star outside our solar system. Due to a unique mechanism with a variable-speed gear train, this second display has been designed so that it can switch to the measurement of the regular solar time by means of a pushbutton at the two o’clock position. In this measurement variant, the solar hour angle and the solar time are also directly displayed, therefore making possible the simultaneous observation of two heavenly bodies within our solar system. At the same time, the solar time shown on this variable display can also be set to read regular time and therefore makes Firmamentum, which has been designed to be a true measuring instrument, into a completely normal watch with hour and minute hands if so desired.
Both displays have been designed such that they not only show angular degrees, but also the solar or sidereal hours and minutes used by astronomers. In parallel, the fixed solar time display has been conceived such that it can be additionally used as an adjustable second time zone with a 24-hour display accurate to the minute.
The Firmamentum also has an integrated function that, via a second pushbutton at four o’clock, synchronizes the time in accordance with a time signal. For this purpose it is equipped with a stopwatch mechanism accurate to a second that is activated by pulling the crown into the hands
adjustment position. This mechanism can also be independently activated by the pushbutton in the four o’clock position without needing to go into the hands adjustment position. As soon as the pushbutton is released, the watch recommences operation. Both pushbuttons are protected
against accidental operation by means of a screw-down protector.
The Firmamentum also incorporates a power reserve indicator that brings the underlying data of the watch to the fore. A stop lever halts operation of the watch movement after a running time of 56 hours - the traditional power reserve of naval chronometers.
With its restrained and discreet design, the dial of Firmamentum directly shows the different values in degrees according to the various navigation methods that are possible with this watch.
Anchored in the traditions of navigation, these permit determination of position according to azimuth, the equatorial method and the ecliptic system.
The second method of measurement, the so-called equatorial method, is the measurement of latitude. The latitude corresponds to the circle upon which can be found the visible horizon of the observer, the true horizon. One speaks of a parallel of latitude when referring to a circle parallel to the Equator. When one approaches the North Pole or the South Pole ever more closely, the diameter of the parallel of latitude becomes smaller. It is split into 360 degrees. All meridians leading from the North Pole to the South Pole are equally long. The zero point is the line from the North to the South Pole that by definition passes through the Greenwich Observatory.
It is known as the Prime Meridian and all other meridians, including the one passing from North to South through the observer’s own location, are removed from this by up to + 180 degrees in a westerly direction and – 180 degrees in an easterly direction. In the equatorial method, the meridians are projected outwards from the centre of the Earth onto an imaginary heavenly circle and the first coordinate is provided by the degrees measured. In this method, the meridians are called declination or hour circles. These lines start from the Equator and go up to +90 degrees in a northerly direction and up to – 90 degrees in a southerly direction as if they were marked on a
globe. The spatial depth, i.e. the differing distances from the stars to the earth, does not play a role here. The second coordinate is given by the Equator with its 360-degree divisions. This coordinate
is known as right ascension and is given from the North to the West, South and East from 0 degrees to 360 degrees.
The third system, that of the ecliptic, has the same coordinate system as the second system, the equatorial. However both coordinate axes are shifted by the value of the ecliptic. The ecliptic is the difference (the angle) between the orbit of the Earth around the Sun and the Sun’s equator.
The right ascension then gives the longitude, the declination the latitude.
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Every hour angle, independently of its frame of reference and numerical system, consists of a 360-degree circle. Each degree is divided into 60 units, the so-called arcminutes. These arcminutes are identified by a single quote (60') and in their turn these are subdivided into 60 arcseconds (60"). These units can however very, for example in nautical systems. 360 degrees times 60' gives 21 600', and this result is taken to divide the circumference of the Earth at the Equator. This gives a value of 1 852 metres per arc minute.
A nautical sea mile is therefore 1/21 600th of the Earth’s circumference at the Equator. This sea mile is subdivided into 10 cable lengths, each of 185 metres. This means that when a ship on the Equator has travelled one sea mile, it has also travelled one arcminute (1').
DIFFERENCE BETWEEN SOLAR AND SIDEREAL TIME
Due to the rotation of the Earth on its own axis and the same direction of rotation around the sun, this gives the effect that within our solar system a year consists of 365 sun- and planet-rises.
However outside our solar system, 366 sun- and planet-rises are measured in the same period.
The system of time that splits the year into 365 days is thus called solar time, and that which splits a year into 366 days is known as the sidereal time. This results in a daily difference of approximately 4 minutes between both time systems. Accordingly, the length of one sidereal day is 23 hours, 56 minutes and 4.0905 seconds. The special Firmamentum gear train that measures the difference between solar and sidereal time is so precise that the difference per day is only 0.0005 seconds.
METHODS OF DETERMINING POSITION
There are different ways of measuring one’s position on the Earth’s surface. The first, and the most natural way of observing this, is that of the azimuth. The basis for this is given by the location of the observer. He observes the horizon and, with the help of a device that measures degrees — a sextant — he determines the height of a heavenly body above the horizon as he sees it in front of him. When determining terrestrial locations, things that stand out in
the landscape or buildings can be used as the starting point. This gives the first coordinate. For the North direction it is given from 0 to + 90 degrees, and from the South direction from 0 to – 90 degrees.