# Circumpolar star declination problem

• trina1990
In summary, the problem discusses the minimum declination for a star to be seen marginally circumpolar for an observer standing on the Damavand mountaintop in Iran. The calculations involve finding the angle of dip, declination, and verifying the correct method for calculating the minimum declination. The answer is 56 degrees 27 minutes 9.06 seconds.
trina1990
hi, heres' problem from an international olympiad

"The Damavand Mountain is located at the North part of Iran, in south coast of
Caspian Sea. Consider an observer standing on the Damavand mountaintop (latitude =
35° 57′ N; longitude = 52° 6' E; altitude 5.6 x 10^3m from the mean sea level) and looking at
the sky over the Caspian Sea. What is the minimum declination for a star, to be seen
marginally circumpolar for this observer. Geodetic radius of the Earth at this latitude
is 6370.8 km. Surface level of the Caspian Sea is approximately equal to the mean sea level."

i tried to walk through this problem this way...
the " angle of dip" or the angle subtended by the altitude to the horizon is
A= 57.3(root over) (2H/R) degree
where H=height of the mountain

i calculated A to be 2 degrees 24 minutes 9.06 seconds of arcs...

then i calculated the declination of the circumpolar star at this latitude from this formula,
declination>= ( 90 - latitude), so, dec=54 degrees 3minutes..

now to get the marginal declination for that altitude on the mountain top, should i add the "angle of dip" to this calculated declination? like declination=56 degrees 27 minutes 9.06 seconds...?

No, you subtract. On top of the mountain, you can see farther from Polaris, which means a lower minimum declination.

oki. . Got it. . Many many thanks

## 1. What is the circumpolar star declination problem?

The circumpolar star declination problem refers to the phenomenon in which stars located near the North or South celestial poles do not rise or set, but instead appear to rotate around the pole in a circular motion. This is due to the Earth's rotation and its tilted axis, which causes the positions of stars to appear to shift in the sky as they are observed from different latitudes on Earth.

## 2. How does the circumpolar star declination problem affect navigation and astronomy?

The circumpolar star declination problem can complicate navigation and astronomy, as it makes it difficult to accurately determine one's location and the positions of celestial objects. This is especially true near the poles, where the stars appear to rotate in a tight circle and can make it challenging to pinpoint one's exact position.

## 3. Are there any ways to overcome the circumpolar star declination problem?

There are several methods that can be used to overcome the circumpolar star declination problem. One approach is to use a tool called a sextant, which allows for more precise measurements of celestial objects and can help determine one's location. Additionally, using a combination of different stars and constellations can also help in navigation and astronomy.

## 4. How has the circumpolar star declination problem been studied and researched?

The circumpolar star declination problem has been studied and researched through various methods, including observations, mathematical calculations, and computer simulations. Astronomers and scientists also use tools such as telescopes and satellite imagery to study the movements and positions of stars near the celestial poles.

## 5. Does the circumpolar star declination problem have any cultural or historical significance?

Yes, the circumpolar star declination problem has cultural and historical significance in many societies. For example, ancient civilizations used the circumpolar stars as a reference point for navigation and timekeeping. The movements of these stars were also often tied to myths and legends in different cultures, and some societies used them to mark important events such as the changing of seasons or the beginning of a new year.

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