Circumpolar star declination problem

[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
R= radius of earth

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...?

i need a verification to my calculation & if ther's any error please suggest me the right way to solve...please help...

 

[ideasrule]

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

 

[trina1990]

oki. . Got it. . Many many thanks