Sunday, October 21, 2018

HP 11C (and Emulators): Sun's Approximate Declination, Altitude, and Azimuth

HP 11C (and Emulators):  Sun's Approximate Declination, Altitude, and Azimuth

Introduction

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.

HP 11C Program: Sun Declination, Altitude, Azimuth

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 1:
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°

Example 2:
Stored Data:
R0 = 68
R1 = 46°
R2 = 4 (8 AM)

Output:
δ ≈ 21.5892°
H ≈ 35.9899°
A ≈ 84.4083°

Sources:

Hewlett Packard.  "Sun Altitude, Azimuth, Solar Pond Absorption", HP 67/97 Energy Conservation December 1978.
Shore, Edward.  "HP 35S: Sun Altitude, Azimuth, Solar Pond Absorption"  Eddie's Math and Calculator Blog:  http://edspi31415.blogspot.com/2013/06/hp-35s-sun-altitude-azimuth-solar-pond.html  June 7, 2013

Eddie

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