Overview
-This program calculates the local solar time defined by: LST
= 12 h. + the hour angle of the Sun.
-12h are added because it's more convenient to regard the solar day
as commencing at midnight rather than at noon.
-The equation of time ( i-e the difference between apparent and mean
time ) is obtained by the following formula:
E = y.sin 2L - 2e.sin M + 4ey.sin M cos 2L - (y2/2).sin 4L - (5e2/4).sin 2M ( in radians )
where
y = tan2(obl/2)
obl = obliquity of the ecliptic
L = Sun's mean longitude
e = eccentricity of the Earth's orbit
M = Sun's mean anomaly
-A second routine has been added to get a similar accuracy over a longer
time-span.
Program Listing1
Data Registers: R00 thru R05
Flag: /
Subroutine: "J0" or "J1" or "J2" (
cf "Julian & Gregorian Calendars for the HP-41" )
none if you have a Time Module
-If you have a Time module, lines 09-10 may be replaced by
1.012 RCL Z DDAYS
-If you want, add 24 MOD after line 61
| 01 LBL "LST"
02 DEG 03 STO 00 04 RDN 05 HR 06 STO 01 07 24 08 / 09 X<>Y 10 XEQ "J0" 11 + 12 STO 02 13 .9856 |
14 *
15 2.964 16 - 17 X<> 02 18 1.971295 19 * 20 199.947 21 + 22 540 23 1/X 24 SQRT 25 P-R 26 STO 03 |
27 RCL 02
28 SIN 29 STO 04 30 4 31 * 32 * 33 3582 34 STO 05 35 SQRT 36 ST/ 04 37 / 38 + 39 X<>Y |
40 RCL 03
41 * 42 - 43 RCL 04 44 ST+ X 45 - 46 RCL 02 47 ST+ X 48 SIN 49 .8 50 / 51 RCL 05 52 / |
53 -
54 R-D 55 RCL 00 56 HR 57 + 58 15 59 / 60 RCL 01 61 + 62 HMS 63 END |
( 106 bytes / SIZE 006 )
| STACK | INPUTS | OUTPUTS |
| Z | YYYY.MNDD | / |
| Y | HH.MNSS (UT) | / |
| X | Longitude ( ° . ' " ) | LST = HH.MNSS |
Examples: Calculate the solar time on 2004/12/31 12h25mn41s (UT) in the U.S. Naval Observatory at Washington ( D.C.) ( Longitude = 77°03'56"W )
2004.1231 ENTER^
12.2541
ENTER^
-77.0356 XEQ
"LST" >>>> LST = 7h14mn13s4
Likewise,
2100.1231 ENTER^
12.2541
ENTER^
-77.0356 XEQ
"LST" >>>> LST = 7h14mn35s1
Notes:
-The longitudes are measured positively eastwards from the meridian
of Greenwich.
-The accuracy is of the order of 1 second between 1900 and 2100.
Program Listing2
-As usual, we must take into account more secular terms to get the same
accuracy a few millenia around J2000
Data Registers: R00 thru R05
Flag: /
Subroutine: "J0" or "J1" or "J2" (
cf "Julian & Gregorian Calendars for the HP-41" )
-If you want, add 24 MOD after line 83
| 01 LBL "LST"
02 DEG 03 STO 00 04 RDN 05 HR 06 STO 01 07 24 08 / 09 X<>Y 10 XEQ "J0" 11 + 12 365250 13 / 14 359990.503 15 RCL Y 16 65 17 / |
18 -
19 * 20 2.964 21 - 22 STO 02 23 RDN 24 42 25 + 26 * 27 CHS 28 1671 29 + 30 E5 31 / 32 STO 03 33 CLX 34 15 |
35 /
36 720015.397 37 + 38 * 39 199.947 40 + 41 X<>Y 42 .065 43 * 44 11.7196 45 - 46 TAN 47 X^2 48 P-R 49 STO 04 50 RCL 02 51 SIN |
52 STO 05
53 4 54 * 55 * 56 RCL 03 57 ST* 05 58 * 59 + 60 X<>Y 61 RCL 04 62 * 63 - 64 RCL 05 65 ST+ X 66 - 67 RCL 02 68 ST+ X |
69 SIN
70 .8 71 / 72 RCL 03 73 X^2 74 * 75 - 76 R-D 77 RCL 00 78 HR 79 + 80 15 81 / 82 RCL 01 83 + 84 HMS 85 END |
( 151 bytes / SIZE 006 )
| STACK | INPUTS | OUTPUTS |
| Z | YYYY.MNDD | / |
| Y | HH.MNSS (UT) | / |
| X | Longitude ( ° . ' " ) | LST = HH.MNSS |
Example:
4000.0716 ENTER^
16.2441
ENTER^
-77.0356 XEQ
"LST" >>>> LST = 11h05mn54s6
References:
[1] Jean Meeus , "Astronomical Algorithms" - Willmann-Bell
- ISBN 0-943396-61-1
[2] Robin M. Green - "Spherical Astronomy" - Cambridge University
Press - ISBN 0-521-31779-7