(11C) The Sun's Declination, Altitude, Azimuth

[Eddie W. Shore]

The following program calculates three positions for our Sun in our Solar System:

1. Declination of the Sun (δ = 0° at the Equinoxes)
2. Altitude of the Sun (height of the sun)
3. Azimuth of the Sun (degree from latitude ground-wise north)

Formulas Used:

Inputs:
D = days after the vernal equinox (usually March 20 or March 21)
L = latitude given in D.MMSS format (avoid ±90°)
T = time before solar noon (12 PM). Example: 9 AM, T= 3. 3 PM, T = -3.

Declination:
δ = 23.45 * sin(D * 0.9856)

Altitude:
H = asin(cos L * cos D * cos(15 * T)) + sin L * sin D)

Azimuth:
A = acos((sin H * sin L - sin D) / (cos L * cos H))

Before running the program, store D in R1, L in R2, and T in R3.

Code:

001 42, 21, 13  LBL C
002 43, 7  DEG
003 45, 1  RCL 1
004 48   .
005 9   9
006 8   8
007 5   5
008 6   6
009 20   ×
010 23   SIN
011 2   2
012 3   3
013 48   .
014 4   4
015 5   5
016 20   ×
017 44, 4  STO 4
018 31   R/S
019 24   COS
020 45, 2  RCL 2
021 43, 2  →H     
022 24   COS
023 20   ×
024 45, 3  RCL 3
025 1   1
026 5   5
027 20   ×
028 24   COS
029 20   ×
030 45, 2  RCL 2
031 43, 2  →H
032 23   SIN
033 45, 4  RCL 4
034 23   SIN
035 20   ×
036 40   +
037 43, 23  ASIN
038 44, 5  STO 5
039 31   R/S
040 23   SIN
041 45, 2  RCL 2
042 43, 2  →H
043 23   SIN
044 20   ×
045 45, 4  RCL 4
046 23   SIN
047 30   -
048 45, 2  RCL 2
049 43, 2  →H
050 24   COS
051 45, 5  RCL 5
052 24   COS
053 20   ×
054 10   ÷
055 43, 24  ACOS
056 44, 6  STO 6
057 43,32   RTN

Example:
Stored Data:
R0 = 184 (approximately September 21),
R1 = -14° 50' 12" (entered as -14.5012)
R2 = 0 (noon)

Output:
δ ≈ 13.1576°
H ≈ 62.0058°
A = 180.0000°


Link to blog entry: https://edspi31415.blogspot.com/2018/10/...imate.html