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1 | /* | |
2 | * (C)2012 Michael Duane Rice All rights reserved. | |
3 | * | |
4 | * Redistribution and use in source and binary forms, with or without | |
5 | * modification, are permitted provided that the following conditions are | |
6 | * met: | |
7 | * | |
8 | * Redistributions of source code must retain the above copyright notice, this | |
9 | * list of conditions and the following disclaimer. Redistributions in binary | |
10 | * form must reproduce the above copyright notice, this list of conditions | |
11 | * and the following disclaimer in the documentation and/or other materials | |
12 | * provided with the distribution. Neither the name of the copyright holders | |
13 | * nor the names of contributors may be used to endorse or promote products | |
14 | * derived from this software without specific prior written permission. | |
15 | * | |
16 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | |
17 | * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
18 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
19 | * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE | |
20 | * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR | |
21 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF | |
22 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS | |
23 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN | |
24 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
25 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | |
26 | * POSSIBILITY OF SUCH DAMAGE. | |
27 | */ | |
28 | ||
29 | /* $Id: equation_of_time.c 2369 2013-04-28 14:19:35Z swfltek $ */ | |
30 | ||
31 | /* | |
32 | The so called Equation of Time. | |
33 | ||
34 | The eccentricity of Earths orbit contributes about 7.7 minutes of variation to the result. It | |
35 | has a period of 1 anomalous year, with zeroes at perihelion and aphelion. | |
36 | ||
37 | The tilt of Earths rotational axis (obliquity) contributes about 9.9 minutes of variation. It | |
38 | has a period of 1/2 tropical year, with zeroes at solstices and equinoxes. The time of Earths | |
39 | arrival at these events is influenced by the eccentricity, which causes it to progress along its | |
40 | orbital path faster as it approaches perihelion, imposing a 'modulation' on the tropical phase. | |
41 | ||
42 | The algorithm employed computes the orbital position with respect to perihelion, deriving | |
43 | from that a 'velocity correction factor'. The orbital position with respect to the winter solstice | |
44 | is then computed, as modulated by that factor. The individual contributions of the obliquity and the | |
45 | eccentricity components are then summed, and returned as an integer value in seconds. | |
46 | ||
47 | */ | |
48 | ||
49 | #include <time.h> | |
50 | #include <math.h> | |
51 | #include "ephemera_common.h" | |
52 | ||
53 | int | |
54 | equation_of_time(const time_t * timer) | |
55 | { | |
56 | int32_t s, p; | |
57 | double pf, sf, dV; | |
58 | ||
59 | /* compute orbital position relative to perihelion */ | |
60 | p = *timer % ANOM_YEAR; | |
61 | p += PERIHELION; | |
62 | pf = p; | |
63 | pf /= ANOM_CYCLE; | |
64 | pf = sin(pf); | |
65 | ||
66 | /* Derive a velocity correction factor from the perihelion angle */ | |
67 | dV = pf * DELTA_V; | |
68 | ||
69 | /* compute approximate position relative to solstice */ | |
70 | s = *timer % TROP_YEAR; | |
71 | s += SOLSTICE; | |
72 | s *= 2; | |
73 | sf = s; | |
74 | sf /= TROP_CYCLE; | |
75 | ||
76 | /* modulate to derive actual position */ | |
77 | sf += dV; | |
78 | sf = sin(sf); | |
79 | ||
80 | /* compute contributions */ | |
81 | sf *= 592.2; | |
82 | pf *= 459.6; | |
83 | s = pf + sf; | |
84 | return -s; | |
85 | ||
86 | } |