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Full Version: (42S/DM42) Solar Declination, Zenith, and Sunrise
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Introduction

The program SUNS will calculate:

1. Approximation declination given month and day. A 365-year is assumed.

δ ≈ 23.45° sin(.9863 * (284 + n))

where n is the nth day of the year:

If month = 1 or month = 2, then:
n = IP(30.6 * month + 368.8) + day - 399

If month ≥ 3 then:
n = IP(30.6 * month + 1.6) + day - 34

2. Zenith angle θ:

θ ≈ acos(sin δ * sin ϕ + cos δ * cos ϕ * cos hour_angle)

where:
ϕ = latitude, north is positive
hour_angle = (12 - number of hours before noon) * 15

3. Approximate time of sunrise:

ω ≈ acos(-tan ϕ * tan δ)
Sunrise time ≈ (12 - ω/15) converted to HMS

The program was entered on a HP 42S, and should work for the Free42 and Swiss Micros DM42.

HP 42S/DM42 Program SUNS

Code:
```00 {206-Byte Prgm} 01 LBL "SUNS" 02 DEG 03 "MONTH?" 04 PROMPT 05 STO 01 06 "DAY?" 07 PROMPT  08 STO 02 09 "HRS BEFORE NOON" 10 PROMPT  11 STO 03 12 "LAT (N+)?" 13 PROMPT 14 →HR 15 STO 04 16 RCL 02     // calculate n 17 RCL 01 18 CF 00 19 3 20 X>Y? 21 SF 00 22 R↓ 23 30.6 24 * 25 1.6 26 + 27 FS? 00 28 367.2 29 FS? 00 30 + 31 IP 32 + 33 34 34 - 35 FS? 00 36 365 37 FS? 00 38 - 39 CF 00 40 STO 11 41 284     // calculate δ 42 + 43 0.9863 44 * 45 SIN 46 23.45 47 *  48 STO 12 49 "DEC=" 50 ARCL ST X 51 AVIEW  52 STOP 53 12 54 RCL- 03 55 15 56  * 57 STO 13 58 RCL 12   // calculate θ 59 SIN 60 RCL 04 61 SIN 62 * 63 RCL 12 64 COS 65 RCL 04 66 COS 67 * 68 RCL 13 69 COS  70 * 71 + 72 ACOS 73 STO 14 74 "ZENITH=" 75 ARCL ST X 76 AVIEW 77 STOP 78 RCL 04   // calculate ω 79 TAN 80 +/- 81 RCL 12 82 TAN 83 * 84 ACOS 85 15 86 ÷ 87 12 88 X<>Y 89 - 90 →HMS 91 STO 15 92 "SUNRISE=" 93 ARCL ST X 94 AVIEW 95 END```

Variables:
R01 = month
R02 = day
R03 = hours before moon
R04 = latitude

R11 = n, nth day of the year
R12 = δ, declination
R13 = hour_angle
R14 = θ, zenith
R15 = ω, approximate sunrise

Example

March 15, 8:00 AM (4 hours before noon), latitude is 40°

Results:
DEC = -2.8191 (-2.8191°)
ZENITH = 114.4672
SUNRISE = 6.0928 (around 6:09:28)

Remember, these results are approximate!

Source:
Hewlett Packard. "Solar-Beam Irradiation" Hewlett Packard User's Library Solution: Solar Engineering. HP 41C January 1984.
Reference URL's
• HP Forums: https://www.hpmuseum.org/forum/index.php
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