Motion of Stars (both celestial poles)

Light body of a star over the equator

As we see in the pictures above, stars are lights in the firmament that represents a flat and solid layer dividing the 7th and the 8th heaven. Every star has a light body; the light bodies of stars south of the equator are deflected to the southern Foundation of Heaven, while the light bodies of stars north of the equator are deflected to the northern Foundation of Heaven; The light bodies of stars right above the equator are "equalized" between the northern and southern Foundations of Heaven.

All stars/lights in the Firmament move from east to west in a straight line, but the bent light bodies create the illusion of them encircling two celestial poles, one in the South and one in the North.

The lights in the firmament are projected by a celestial sphere, also referred to as "the Houses of the Stars" or "The Stars of God". Each of the abstract rings on the illustrated celestial sphere corresponds to a latitude on the firmament, meaning stars on one ring on the celestial sphere are projected onto the corresponding latitude in the firmament. Naturally, the amount of stars decreases towards the south and north....

We can see this distribution of stars in star trails - each ring on the star trail picture corresponds to one latitude in the firmament and each each ring corresponds to one physical cycle of 40 075 km. The rings closer to the pivot point have less stars on them then rings further away.

The light bodies of stars north of the equator are deflected to the northern foundation thus forming a continuous “light-wave” running along the northern foundation. The light bodies of stars south of the equator form continuous “light-waves” along the southern foundation. Notice that the range of the light body always stretches 90° away from the star. This means that a star over the latitude 25° North can be seen above the horizon as far as 65° South

An important detail to pay attention to is that the area covered by the light body is always 50% of the Earth's surface, while 50% remain uncovered. The ratio of 50/50 does not change at any latitude. Whether the  star is at latitude 25° North, 89° South, or at 0° over the equator, its light always covers 50% of the  Earth's total area.  A star is observed above the  horizon anywhere within the area covered by its light body. In the uncovered area the star is below the horizon line. The ratio 50/50 applies to the Sun, Moon, planets, and stars. 

We have moved the star from 25° North to 45° North. As we see, the light body still stretches 90° south from the star. Now the star can be seen above the horizon as far as the latitude 45° South. The ratio of 50/50 still remains. The covered area and the uncovered area are still equal. As we moved the star further north, the outline flattened as the star is now closer to the Foundation of Heaven. Let's move it further north

We moved the star further north, to latitude 62°N. Nothing really changes – the light body still stretches over 90° degrees south, making the star appear above the horizon all the way down to latitude 28° South,  the ratio 50/50 still remains, and  as we moved the star further north, the outline of its light body flattened out even more.

We moved the star to latitude 80°. The light body now stretches as far as 10° South. Question : What will happen if we place the star at latitude 90°N ? 

If you expected the sine-wave to straighten out completely, you were right. As we move our star to latitude 90°, the outline of the light body becomes a completely straight line which aligns with the equator line. Now we can see how the area north of the equator is completely covered, whereas the area south of the equator is completely untouched by the light body. This means that the star is visible at any point north of the equator, but cannot be seen south of the equator. Since it is over latitude 90°, the light body does not stretch beyond latitude 0°. This is why Polaris cannot be seen south of the latitude 0,5° South.

Next step : We let the star complete one full cycle from east to west. Picture above shows five vantage points. The vantage points 2 and 5 are within the light body and see the star above their horizon line. The star is below the horizon line for the points 1, 4 and 3 as they are outside of the light body.

We move the star due west. Now the light body withdraws from point 2, and is about to cover the point 1. This means that the star “sets” below the horizon line for VP2, and “rises” for VP1.

Apparent cycle of a star

Picture above  shows the physical cycle – from east to west in a straight line; and the apparent visual cycle – a circle. It also shows two vantage points situated on the same longitude. We are going to let the star complete  one full cycle from east to west.

The star has moved one quarter of the cycle. Its physical cycle is a straight line from east to west, but the apparent cycle is a circle. VP1 and VP2 observe the star revolving counter-clockwise around  the pivot point at 90° latitude.

 The star has set for VP1. VP2, on the other hand, observes the entire circle as it remains covered by the light body over the entire cycle of the star.

The star has completed its cycle. VP2 sees the entire apparent circle, and VP1 sees the star rising and setting in a circular, counter-clockwise motion. 

We want to focus on the correlation between the radius of the apparent circle and the distance of the star to the Foundation of Heaven.

 We moved the star closer to the Foundation of Heaven. Notice that its apparent circle is now smaller.
 

 The star is only 10° degrees south of the foundation. It has a small apparent circle. VP1, VP2 and VP3 see the entire circle above the horizon line. VP4 sees the star rising and setting.

The star has completed one half of its cycle. It is still visible for VP1, VP2, VP3 , but it has set for VP4. Question : How will the apparent cycle of the star look like if we place it right on right on latitude 90°?

We moved the star to latitude 90°. As we can see, the outline of its light body has become a flat line running along the equator, and the star does no longer describe a circle. Instead, it revolves around its own axis as the distance to the pivot point at 90° has been reduced to zero.

The star has moved one quarter of its cycle. Notice that the star has rotated by 90°, since 360° : 4 = 90°. ( Red arrows mark its rotation)

The star is about to complete its cycle. Both, the apparent cycle and the physical return to their starting point. The vantage points 1 – 3 have observed the star rotate around its own axis, while the physical path of the star described a straight path of 40 075 km from east to west. 

The celestial poles are not geographic

The next question is, how and where does each vantage point observe the apparent circular cycle of the star.

The observed celestial equator is not geographic. All three vantage points see the celestial pole in the exact geographic North. In fact, the observed direction of the celestial poles, be it in the North or in the South, is in a precise alignment with the longitude of the observer. There is but one difference – all vantage points observe a different cycle of the star.  Another example...

All three observers see the star rotate around the observed celestial axis; all three see a different cycle. The star is in the zenith for VP2. At this point, the observed star aligns with the observed celestial axis and with the longitude. As for VP1 - the star rises and commences its observable circuit until it eventually aligns with the longitude of VP1.

The star is now in the zenith for VP1, and aligns with the longitude of VP1. The observed cycle for VP2 has moved on and the star revolves away from the observer and approaches the horizon line (..sets). The observed star will align with the longitude of VP3 and later return to the starting point at the longitude of VP2. 

The southern celestial pole

Everything we have learned about the motion of stars in the North works in the exact same manner in the South, with the exception that the stars rotate in the opposite direction. Stars south of the equator appear to be rotating clockwise (when seen from below), stars north of the equator appear to be rotating counter-clockwise.

Picture above shows four stars in the North running along the latitudes 45°, 60°, 75°, and 90°, and four stars in the South on equivalent latitudes. The circles represent their apparent cycles. As we see, the principle is identical in the North and in the South. In the South, stars appear to be rotating clockwise, in the North counter-clockwise. The further a star in the firmament is from the Foundation of Heaven, the smaller the radius of the apparent cycle. A star running along latitude 90° appears to be rotating around its own axis. The example in picture above is made for the three depicted longitudes only. Every point on Earth and every longitude has its own apparent cycle which is in correlation with the physical cycle. 

Straight and fixed celestial equator

The light body of a star over the equator  is neither  bent to the northern foundation nor to the southern, but is equalized between the two. A star at latitude 0° does not form a continuous  “wave”, but covers an area which represents a nearly perfect square (pic.above). As a result, the celestial equator appears as a straight and fixed line from any location on Earth, dividing the northern star spin from the southern. The celestial equator is not subjected to the laws of  perspective for  a rotating sphere, which dictates that every location on Earth would have an individual celestial equator. 

The celestail equator appears as a straight and fixed line from any point on Earth. If the Earth were a spinning sphere, the celestail equator would vary from latitude to latitude