The zenith distance of a star at latitude 60° N is 25°. Calculate its declination
Answers
Answered by
4
To solve this question we must be familiar with some definitions.
Zenith - The point directly above the observer's head.
Declination - 90° minus the angle the star makes with the earth's axis.
Horizon plane - a plane tangent to the earth and passes through the observer.
The north star is also known as the polaris.
The reference point is the polaris.
We assume that the zenith, the polaris and the observed star lie on the same plane.
The zenith crosses at 90° with the horizon plane.
The altitude of the observed star equals : Altitude of polaris + angle of observed star from polaris.
The altitude of the observed star is compliment to to the zenith meaning if zenith equals to D the altitude of the observed star = 90° - D
The formulae connecting these three is :
Latitude = Altitude of the observed star + declination - 90°
Where latitude is the latitude of the observer.
Substituting this in the formulae we get:
Zenith = 25°
Altitude of observed star = 90 - 25 = 65°
latitude = 60°
CALCULATIONS:
60 = 65 + declination -90
Declination = 60 - 65 + 90 = 85°
The declination is thus 85°
Zenith - The point directly above the observer's head.
Declination - 90° minus the angle the star makes with the earth's axis.
Horizon plane - a plane tangent to the earth and passes through the observer.
The north star is also known as the polaris.
The reference point is the polaris.
We assume that the zenith, the polaris and the observed star lie on the same plane.
The zenith crosses at 90° with the horizon plane.
The altitude of the observed star equals : Altitude of polaris + angle of observed star from polaris.
The altitude of the observed star is compliment to to the zenith meaning if zenith equals to D the altitude of the observed star = 90° - D
The formulae connecting these three is :
Latitude = Altitude of the observed star + declination - 90°
Where latitude is the latitude of the observer.
Substituting this in the formulae we get:
Zenith = 25°
Altitude of observed star = 90 - 25 = 65°
latitude = 60°
CALCULATIONS:
60 = 65 + declination -90
Declination = 60 - 65 + 90 = 85°
The declination is thus 85°
Similar questions