Horizontal Coordinate System

In math, we can see different types of coordinate system. The horizontal coordinate system is defined as celestial coordinate system in fundamental plane. It is used in earth sphere and another name of horizontal coordinate system is Alt/Az coordinate system. Now we are going to see about horizontal coordinate system.
Explanation for Horizontal Coordinate System

Horizontal coordinate system:

The horizontal coordinate system is combined with some coordinates. The name of coordinates are altitude and azimuth. The altitude is elevation or angle of object and observer’s local horizon. The azimuth is an angle in around the horizon.

The horizontal system is suitable for earth but not to stars. The altitude and azimuth are directly proportional that is if altitude increase means the azimuth also increases. We can convert the equatorial coordinate system to horizontal coordinate system and the horizontal coordinate system to equatorial coordinate system.

We can convert the equatorial to horizontal as follows:

sin a = sin Φ . sin δ + cos Φ . cos δ . cos H

cos A . cos a = cos Φ . sin δ - sin Φ . cos δ . cos H

sin A . cos a = - cos δ . sin H

We can convert horizontal to equatorial as follows:

sin δ = sin Φ . sin a - cos Φ . cos a . cos A

cos δ . cos H = cos Φ . sin a + sin Φ . cos a . cos A

cos δ . sin H = - sin A . cos a

We can find out the sun declination of the corresponding day of the year by following formula.

δ = -23.45o . cos`(360/365 .(N + 10))` .

Example problems for horizontal coordinate system:

Problem 1: Find out the corresponding day of the year for sun declination.

The number of days spent since January 1 = 150.

Solution:

Given number of days is 150.

Corresponding day of the year of sun declination is -23.45o . cos`(360/365 .(N + 10))`

δ = -23.45o . cos`(360/365 .(150 + 10))`

= -23.45 . cos (157.80)

= 22.53

Therefore, the sun declination is 22.53.

Problem 2: Find out the corresponding day of the year for sun declination.

The number of days spent since January 1 = 220.

Solution:

Given number of days is 220.

Corresponding day of the year of sun declination is -23.45o . cos`(360/365 .(N + 10))`

δ = -23.45o . cos`(360/365 .(220 + 10))`

= -23.45 . cos (226.84)

= 22.76

Therefore, the sun declination is 22.76.

Exercise problems for horizontal coordinate system:

1. Find out the sun declination from N = 170.

Solution: The sun declination is δ = 22.45.

2. Find out the sun declination from N = 250.

Solution: The sun declination is δ = 23.21.