RADIACIÓN SOLAR

UNIVERSIDAD NACIONAL MAYOR DE

SAN MARCOS Universidad del Perú, DECANA DE AMÉRICA E.A.P CIENCIAS BIOLÓGICAS

TEMA

: RADIACIÓN SOLAR

FECHA DE ENTREGA

: 2 de Mayo del 2013

DOCENTE

: DURAND CASTRO, David

ALUMNA

: GUTIÉRREZ DE LA CRUZ, Gerardo

CÓDIGO

: 11100008

LIMA – PERÚ 2013

1. INTRODUCCIÓN

La presente práctica consiste en determinar la variabilidad temporal y espacial de la radiación solar en el tope de la atmósfera y sobre la superficie terrestre. Estas evaluaciones son de gran importancia debido a que la radiación solar es una variable y al mismo tiempo es un factor climático que interviene en todos los procesos sobre el sistema tierra-atmósfera, tales como en los procesos de evaporación que genera el ciclo hidrológico, los movimientos de la atmósfera, los procesos biológicos, por ejemplo: la fotosíntesis de las plantas, el balance de energía, y en fin en todos los procesos del clima.

La variabilidad en el tope de la atmósfera se cuantificará haciendo uso de las ecuaciones correspondientes determinando la cantidad de energía que incide en el lapso de un día de cada mes durante el año. Mientras que la cantidad de energía incidente en la superficie son cuantificadas en las estaciones climatológicas mediante instrumentos.

2.

OBJETIVOS   

Cuantificar la variación temporal de la radiación solar incidente (Qs) en el tope de la atmósfera. Cuantificar la variación temporal y espacial de la radiación solar incidente en la superficie terrestre (Qi). Cuantificar la radiación absorbida, reflejada y dispersada por la atmósfera (Qard)

3. MATERIAL Y METODOS 3.1. MATERIALES: o Datos de temperatura máxima y mínima para el lugar de estudio o Ubicación geográfica del área correspondiente. o Microcomputadora o calculadora. o Equipo de dibujo. 3.2. METODOLOGIA: En este caso trabajaremos con los datos de la estación de Cañete: Estación Código Cuenca

CAÑETE

Latitud Sur

CO-616/DRE-04 Longitud Oeste : Río Cañete

Altitud

: 13°04´

Dpto.

Lima

: 76°20´

Prov.

Cañete

: 150 msnm

Dist. Nuevo Imperial

3.2.1. Tenemos que determinar en primer lugar la radiación solar (Qs) diaria siguiendo la siguiente fórmula: Qs = (1440 /) *S* (dm / d) 2 cos  cos k (sen H – H cos H) Ly / día Qs = 890*(dm / d) 2 (0.01745 H sen  sen k + cos  cos k sen H) Ly / día Donde: S = Constante solar d = distancia real entre sol-tierra dm = distancia media entre el sol-tierra.  = latitud k = declinación solar H = Angulo horario Para ello entonces tendremos que hallar los valores diarios del ángulo horario (H), declinación solar (k), (dm / d) 2 3.2.1.1. Determinamos la declinación solar (k) Siguiendo con la ecuación: k = 23.45° Cos (n.360 / 365)

Donde n es el número de días contabilizados a partir del 22 de diciembre(n= 0).durante el cual el sol se encuentra en el trópico de Capricornio o solsticio de verano del Hemisferio Sur, es decir el valor de n varía entre 0 y 365 días. O sea 0  n  365 y el 22 de diciembre n = 0 = 365 días. En nuestro caso estos valres se contabilizaran desde el 1 de enero del 2000. 3.2.1.2. Determinamos el ángulo horario (H) Para ello seguiremos con la siguiente fórmula: H = arcCos (Tg . cosk ) Para determinar esta ecuación, ya tenemos los datos de K (declinación solar) y ф que viene a ser la latitud que en nuestro caso es 13° 04´ 3.2.1.3. Determinamos las distancias (dm / d) 2 Para hallarlo se utilizó la siguiente fórmula: (dm/ d)2 = C1 + C2cos() + C3sen() +C4cos (2) C5sen (2) Donde: C1 = 1.00011, C2 = 0.033523, C3 = 0.00128, C4 = 0.000739, C5 = 0.000099) El valor de  está en función de los días del año (n) contabilizados a partir del primero de enero fecha en la cual n = 0 ó 365. Para años normales su valor está dado por:  = (2n 3.1416/ 365) radianes. Una vez obtenido todos estos valores recién podremos evaluarlas en la ecuación de la Radiación solar: Qs = 890*(dm / d) 2 (0.01745 H sen  sen k + cos  cos k sen H) Ly /día 3.2.2.

Ahora calcularemos LA RADIACIÓN INCIDENTE (Qi)

Para ello tenemos la siguiente fórmula: Qi = Qs ((a+b)x(Tma  Tmi)) / N Qs = radiación solar en el tope de la atamósfera N = Duración del día solar u horas de sol máximo. a = valor estimado empíricamente para cada caso b = valor estimado empíricamente para cada caso Tma = Temperatura máxima Tmi = Temperatura mínima T = Tma  Tmi Costa Central del Perú: Qi = Qs ((0.06 + 0.64) T / N ), esta ecuación será la que usaremos ya que Cañete se única en esta zona.

Costa Norte del Perú: Qi = Qs ((0.36 + 0.211) T / N ) Sierra Central del Perú: Qi = Qs ((0.457 + 0.207) T / N ) Sierra Norte del Perú: Qi = Qs ((0.284 + 0.205) T / N ) Sierra Sur del Perú: Qi = Qs ((0.23 + 0.38) T / N ) Para poder hallar Qi con esta fórmula lo único que nos falta el hallar el número de horas de sol (N). 3.2.2.1. Determinar el número de horas de sol (N) Usaremos para esto la ecuación siguiente empírica: N = 12h 00min + n(0.0762 + 0.04 (ΔL)) Donde: ΔL = L - 2 L = la latitud del lugar. n = es el número de días contabilizados a partir del 22 de setiembre (n =0) para otros días de primavera y otoño n>0 y en invierno y verano n<0. Además n se incrementa hasta el 22 de diciembre donde n adquiere su máximo valor y de esta fecha en adelante disminuye hasta el 22 de marzo y luego continúa disminuyendo hasta el 21 de junio fecha en la que n adquiere su valor más bajo para el hemisferio sur. Una vez que determinamos este valor podremos hallar la RADIACIÓN INCIDENTE. 3.2.3. Calculo de la Radiación de absorbida, dispersa y reflejada Qadr = Qs  Qi Ahora que sabemos lo pasos y han sido evaluados según cada ecuación se obtuvieron los siguientes resultados (RESULTADOS E INTERPRETACIÓN)

4. RESULTADOS E INTERPRETACIÓN 4.1. ANGULOS DE DECLINACIÓN POR DÍA DEL AÑO 2000

Determinando los ángulos de declinación por día del mes de Enero

A

-23.45

B

cos(

360 * ( N  10)) 365.25

  23.45 cos(

360 ( N  10) 365.25

Mes

Enero

FEBRERO

N° de Día Valor N ángulo en radianes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

0.189 0.207 0.224 0.241 0.258 0.275 0.293 0.31 0.327 0.344 0.361 0.379 0.396 0.413 0.43 0.448 0.465 0.482 0.499 0.516 0.534 0.551 0.568 0.585 0.602 0.62 0.637 0.654 0.671 0.689 0.706 0.723 0.74 0.757 0.775 0.792 0.809 0.826 0.843 0.861 0.878 0.895 0.912

B

δ = A*B

0.982 0.979 0.975 0.971 0.967 0.962 0.957 0.952 0.947 0.941 0.936 0.929 0.923 0.916 0.909 0.901 0.894 0.886 0.878 0.87 0.861 0.852 0.843 0.834 0.824 0.814 0.804 0.794 0.783 0.772 0.761 0.75 0.738 0.727 0.714 0.702 0.69 0.678 0.665 0.652 0.639 0.626 0.612

-23.028 -22.958 -22.864 -22.77 -22.676 -22.559 -22.442 -22.324 -22.207 -22.066 -21.949 -21.785 -21.644 -21.48 -21.316 -21.128 -20.964 -20.777 -20.589 -20.402 -20.19 -19.979 -19.768 -19.557 -19.323 -19.088 -18.854 -18.619 -18.361 -18.103 -17.845 -17.588 -17.306 -17.048 -16.743 -16.462 -16.181 -15.899 -15.594 -15.289 -14.985 -14.68 -14.351

MARZO

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88

0.93 0.947 0.964 0.981 0.998 1.016 1.033 1.05 1.067 1.084 1.102 1.119 1.136 1.153 1.171 1.188 1.205 1.222 1.239 1.257 1.274 1.291 1.308 1.325 1.343 1.36 1.377 1.394 1.412 1.429 1.446 1.463 1.48 1.498 1.515 1.532 1.549 1.566 1.584 1.601 1.618 1.635 1.653 1.67 1.687

0.598 0.584 0.57 0.556 0.542 0.527 0.512 0.498 0.483 0.468 0.452 0.437 0.421 0.406 0.389 0.374 0.358 0.342 0.326 0.309 0.292 0.276 0.26 0.243 0.226 0.209 0.193 0.176 0.158 0.141 0.124 0.108 0.091 0.073 0.056 0.039 0.022 0.005 -0.013 -0.03 -0.047 -0.064 -0.082 -0.099 -0.116

-14.023 -13.695 -13.367 -13.038 -12.71 -12.358 -12.006 -11.678 -11.326 -10.975 -10.599 -10.248 -9.872 -9.521 -9.122 -8.77 -8.395 -8.02 -7.645 -7.246 -6.847 -6.472 -6.097 -5.698 -5.3 -4.901 -4.526 -4.127 -3.705 -3.306 -2.908 -2.533 -2.134 -1.712 -1.313 -0.915 -0.516 -0.117 0.305 0.704 1.102 1.501 1.923 2.322 2.72

ABRIL

MAYO

30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13

89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

1.704 1.721 1.739 1.756 1.773 1.79 1.807 1.825 1.842 1.859 1.876 1.894 1.911 1.928 1.945 1.962 1.98 1.997 2.014 2.031 2.048 2.066 2.083 2.1 2.117 2.135 2.152 2.169 2.186 2.203 2.221 2.238 2.255 2.272 2.289 2.307 2.324 2.341 2.358 2.376 2.393 2.41 2.427 2.444 2.462

-0.133 -0.15 -0.167 -0.184 -0.201 -0.217 -0.234 -0.251 -0.268 -0.284 -0.3 -0.318 -0.334 -0.35 -0.366 -0.381 -0.398 -0.413 -0.429 -0.444 -0.459 -0.475 -0.49 -0.505 -0.519 -0.535 -0.549 -0.563 -0.577 -0.591 -0.605 -0.619 -0.632 -0.645 -0.658 -0.671 -0.684 -0.696 -0.708 -0.721 -0.733 -0.744 -0.755 -0.766 -0.778

3.119 3.518 3.916 4.315 4.713 5.089 5.487 5.886 6.285 6.66 7.035 7.457 7.832 8.208 8.583 8.934 9.333 9.685 10.06 10.412 10.764 11.139 11.491 11.842 12.171 12.546 12.874 13.202 13.531 13.859 14.187 14.516 14.82 15.125 15.43 15.735 16.04 16.321 16.603 16.907 17.189 17.447 17.705 17.963 18.244

JUNIO

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178

2.479 2.496 2.513 2.53 2.548 2.565 2.582 2.599 2.617 2.634 2.651 2.668 2.685 2.703 2.72 2.737 2.754 2.771 2.789 2.806 2.823 2.84 2.858 2.875 2.892 2.909 2.926 2.944 2.961 2.978 2.995 3.012 3.03 3.047 3.064 3.081 3.099 3.116 3.133 3.15 3.167 3.185 3.202 3.219 3.236

-0.788 -0.799 -0.809 -0.819 -0.829 -0.838 -0.847 -0.856 -0.866 -0.874 -0.882 -0.89 -0.898 -0.905 -0.912 -0.919 -0.926 -0.932 -0.938 -0.944 -0.95 -0.955 -0.96 -0.965 -0.969 -0.973 -0.977 -0.981 -0.984 -0.987 -0.989 -0.992 -0.994 -0.996 -0.997 -0.998 -0.999 -1 -1 -1 -1 -0.999 -0.998 -0.997 -0.996

18.479 18.737 18.971 19.206 19.44 19.651 19.862 20.073 20.308 20.495 20.683 20.871 21.058 21.222 21.386 21.551 21.715 21.855 21.996 22.137 22.278 22.395 22.512 22.629 22.723 22.817 22.911 23.004 23.075 23.145 23.192 23.262 23.309 23.356 23.38 23.403 23.427 23.45 23.45 23.45 23.45 23.427 23.403 23.38 23.356

JULIO

AGOSTO

28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11

179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223

3.253 3.271 3.288 3.305 3.322 3.34 3.357 3.374 3.391 3.408 3.426 3.443 3.46 3.477 3.494 3.512 3.529 3.546 3.563 3.581 3.598 3.615 3.632 3.649 3.667 3.684 3.701 3.718 3.735 3.753 3.77 3.787 3.804 3.822 3.839 3.856 3.873 3.89 3.908 3.925 3.942 3.959 3.976 3.994 4.011

-0.994 -0.992 -0.989 -0.987 -0.984 -0.98 -0.977 -0.973 -0.969 -0.965 -0.96 -0.955 -0.95 -0.944 -0.939 -0.932 -0.926 -0.919 -0.913 -0.905 -0.898 -0.89 -0.882 -0.874 -0.865 -0.856 -0.848 -0.838 -0.829 -0.819 -0.809 -0.799 -0.789 -0.777 -0.767 -0.755 -0.744 -0.733 -0.72 -0.709 -0.696 -0.684 -0.672 -0.658 -0.645

23.309 23.262 23.192 23.145 23.075 22.981 22.911 22.817 22.723 22.629 22.512 22.395 22.278 22.137 22.02 21.855 21.715 21.551 21.41 21.222 21.058 20.871 20.683 20.495 20.284 20.073 19.886 19.651 19.44 19.206 18.971 18.737 18.502 18.221 17.986 17.705 17.447 17.189 16.884 16.626 16.321 16.04 15.758 15.43 15.125

SETIEMBRE

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

4.028 4.045 4.063 4.08 4.097 4.114 4.131 4.149 4.166 4.183 4.2 4.217 4.235 4.252 4.269 4.286 4.304 4.321 4.338 4.355 4.372 4.39 4.407 4.424 4.441 4.458 4.476 4.493 4.51 4.527 4.545 4.562 4.579 4.596 4.613 4.631 4.648 4.665 4.682 4.699 4.717 4.734 4.751 4.768 4.786

-0.632 -0.619 -0.605 -0.591 -0.577 -0.563 -0.549 -0.534 -0.52 -0.505 -0.49 -0.475 -0.459 -0.444 -0.429 -0.414 -0.397 -0.381 -0.366 -0.35 -0.334 -0.317 -0.301 -0.284 -0.268 -0.252 -0.234 -0.218 -0.201 -0.184 -0.167 -0.15 -0.133 -0.116 -0.099 -0.081 -0.064 -0.047 -0.03 -0.013 0.005 0.022 0.039 0.056 0.074

14.82 14.516 14.187 13.859 13.531 13.202 12.874 12.522 12.194 11.842 11.491 11.139 10.764 10.412 10.06 9.708 9.31 8.934 8.583 8.208 7.832 7.434 7.058 6.66 6.285 5.909 5.487 5.112 4.713 4.315 3.916 3.518 3.119 2.72 2.322 1.899 1.501 1.102 0.704 0.305 -0.117 -0.516 -0.915 -1.313 -1.735

OCTUBRE

NOVIEMBRE

26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9

269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313

4.803 4.82 4.837 4.854 4.872 4.889 4.906 4.923 4.94 4.958 4.975 4.992 5.009 5.027 5.044 5.061 5.078 5.095 5.113 5.13 5.147 5.164 5.181 5.199 5.216 5.233 5.25 5.268 5.285 5.302 5.319 5.336 5.354 5.371 5.388 5.405 5.422 5.44 5.457 5.474 5.491 5.509 5.526 5.543 5.56

0.09 0.107 0.124 0.141 0.159 0.176 0.192 0.209 0.226 0.243 0.26 0.276 0.292 0.309 0.326 0.342 0.358 0.373 0.39 0.406 0.421 0.436 0.452 0.468 0.483 0.497 0.512 0.527 0.542 0.556 0.57 0.584 0.598 0.612 0.625 0.639 0.652 0.665 0.678 0.69 0.702 0.715 0.727 0.738 0.75

-2.111 -2.509 -2.908 -3.306 -3.729 -4.127 -4.502 -4.901 -5.3 -5.698 -6.097 -6.472 -6.847 -7.246 -7.645 -8.02 -8.395 -8.747 -9.146 -9.521 -9.872 -10.224 -10.599 -10.975 -11.326 -11.655 -12.006 -12.358 -12.71 -13.038 -13.367 -13.695 -14.023 -14.351 -14.656 -14.985 -15.289 -15.594 -15.899 -16.181 -16.462 -16.767 -17.048 -17.306 -17.588

DICIEMBRE

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358

5.577 5.595 5.612 5.629 5.646 5.663 5.681 5.698 5.715 5.732 5.75 5.767 5.784 5.801 5.818 5.836 5.853 5.87 5.887 5.904 5.922 5.939 5.956 5.973 5.991 6.008 6.025 6.042 6.059 6.077 6.094 6.111 6.128 6.145 6.163 6.18 6.197 6.214 6.232 6.249 6.266 6.283 6.3 6.318 6.335

0.761 0.772 0.783 0.794 0.804 0.814 0.824 0.834 0.843 0.852 0.861 0.87 0.878 0.886 0.894 0.902 0.909 0.916 0.923 0.929 0.935 0.941 0.947 0.952 0.958 0.962 0.967 0.971 0.975 0.979 0.982 0.985 0.988 0.99 0.993 0.995 0.996 0.998 0.999 0.999 1 1 1 0.999 0.999

-17.845 -18.103 -18.361 -18.619 -18.854 -19.088 -19.323 -19.557 -19.768 -19.979 -20.19 -20.402 -20.589 -20.777 -20.964 -21.152 -21.316 -21.48 -21.644 -21.785 -21.926 -22.066 -22.207 -22.324 -22.465 -22.559 -22.676 -22.77 -22.864 -22.958 -23.028 -23.098 -23.169 -23.216 -23.286 -23.333 -23.356 -23.403 -23.427 -23.427 -23.45 -23.45 -23.45 -23.427 -23.427

25 26 27 28 29 30 31

359 360 361 362 363 364 365

6.352 6.369 6.386 6.404 6.421 6.438 6.455

0.998 0.996 0.995 0.993 0.991 0.988 0.985

-23.403 -23.356 -23.333 -23.286 -23.239 -23.169 -23.098

4.2. VALORES OBTENIDOS DE LOS ANGULOS HORARIOS (H) DETERMINAR EL ANGULO HORARIO tangente ANGULO HORARIO (H): grados radianes ф= Latitud 0.22806217 0.23210022 13°04´ δ= ángulo de declinación

arccos( tg( ) * cos( ))

Mes

Enero

N° deDia

δ = A*B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

-23.028 -22.958 -22.864 -22.77 -22.676 -22.559 -22.442 -22.324 -22.207 -22.066 -21.949 -21.785 -21.644 -21.48 -21.316 -21.128 -20.964 -20.777 -20.589 -20.402 -20.19 -19.979 -19.768 -19.557 -19.323 -19.088

δ en radianes -0.402 -0.401 -0.399 -0.397 -0.396 -0.394 -0.392 -0.39 -0.388 -0.385 -0.383 -0.38 -0.378 -0.375 -0.372 -0.369 -0.366 -0.363 -0.359 -0.356 -0.352 -0.349 -0.345 -0.341 -0.337 -0.333

cos(δ) 0.9203 0.9207 0.9214 0.9222 0.9226 0.9234 0.9241 0.9249 0.9257 0.9268 0.9275 0.9287 0.9294 0.9305 0.9316 0.9327 0.9338 0.9348 0.9362 0.9373 0.9387 0.9397 0.9411 0.9424 0.9438 0.9451

H 1.7861 1.7862 1.7863 1.7865 1.7866 1.7868 1.787 1.7871 1.7873 1.7876 1.7878 1.7881 1.7882 1.7885 1.7887 1.789 1.7893 1.7895 1.7898 1.7901 1.7904 1.7907 1.791 1.7913 1.7916 1.792

FEBRERO

MARZO

27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7 8 9 10 11 12

-18.854 -18.619 -18.361 -18.103 -17.845 -17.588 -17.306 -17.048 -16.743 -16.462 -16.181 -15.899 -15.594 -15.289 -14.985 -14.68 -14.351 -14.023 -13.695 -13.367 -13.038 -12.71 -12.358 -12.006 -11.678 -11.326 -10.975 -10.599 -10.248 -9.872 -9.521 -9.122 -8.77 -8.395 -8.02 -7.645 -7.246 -6.847 -6.472 -6.097 -5.698 -5.3 -4.901 -4.526 -4.127

-0.329 -0.325 -0.32 -0.316 -0.311 -0.307 -0.302 -0.298 -0.292 -0.287 -0.282 -0.277 -0.272 -0.267 -0.262 -0.256 -0.25 -0.245 -0.239 -0.233 -0.228 -0.222 -0.216 -0.21 -0.204 -0.198 -0.192 -0.185 -0.179 -0.172 -0.166 -0.159 -0.153 -0.147 -0.14 -0.133 -0.126 -0.12 -0.113 -0.106 -0.099 -0.093 -0.086 -0.079 -0.072

0.9464 0.9477 0.9492 0.9505 0.952 0.9532 0.9547 0.9559 0.9577 0.9591 0.9605 0.9619 0.9632 0.9646 0.9659 0.9674 0.9689 0.9701 0.9716 0.973 0.9741 0.9755 0.9768 0.978 0.9793 0.9805 0.9816 0.9829 0.984 0.9852 0.9863 0.9874 0.9883 0.9892 0.9902 0.9912 0.9921 0.9928 0.9936 0.9944 0.9951 0.9957 0.9963 0.9969 0.9974

1.7923 1.7926 1.7929 1.7932 1.7936 1.7939 1.7942 1.7945 1.795 1.7953 1.7956 1.796 1.7963 1.7966 1.7969 1.7973 1.7976 1.7979 1.7983 1.7986 1.7989 1.7992 1.7995 1.7998 1.8001 1.8004 1.8006 1.801 1.8012 1.8015 1.8018 1.802 1.8022 1.8025 1.8027 1.8029 1.8031 1.8033 1.8035 1.8037 1.8039 1.804 1.8041 1.8043 1.8044

ABRIL

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

-3.705 -3.306 -2.908 -2.533 -2.134 -1.712 -1.313 -0.915 -0.516 -0.117 0.305 0.704 1.102 1.501 1.923 2.322 2.72 3.119 3.518 3.916 4.315 4.713 5.089 5.487 5.886 6.285 6.66 7.035 7.457 7.832 8.208 8.583 8.934 9.333 9.685 10.06 10.412 10.764 11.139 11.491 11.842 12.171 12.546 12.874 13.202

-0.065 -0.058 -0.051 -0.044 -0.037 -0.03 -0.023 -0.016 -0.009 -0.002 0.005 0.012 0.019 0.026 0.034 0.041 0.047 0.054 0.061 0.068 0.075 0.082 0.089 0.096 0.103 0.11 0.116 0.123 0.13 0.137 0.143 0.15 0.156 0.163 0.169 0.176 0.182 0.188 0.194 0.201 0.207 0.212 0.219 0.225 0.23

0.9979 0.9983 0.9987 0.999 0.9993 0.9996 0.9997 0.9999 1 1 1 0.9999 0.9998 0.9997 0.9994 0.9992 0.9989 0.9985 0.9981 0.9977 0.9972 0.9966 0.996 0.9954 0.9947 0.994 0.9933 0.9924 0.9916 0.9906 0.9898 0.9888 0.9879 0.9867 0.9858 0.9846 0.9835 0.9824 0.9812 0.9799 0.9787 0.9776 0.9761 0.9748 0.9737

1.8045 1.8046 1.8047 1.8048 1.8049 1.8049 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.8049 1.8048 1.8048 1.8047 1.8046 1.8045 1.8044 1.8042 1.8041 1.8039 1.8038 1.8036 1.8034 1.8032 1.803 1.8028 1.8026 1.8024 1.8021 1.8019 1.8016 1.8014 1.8011 1.8008 1.8005 1.8002 1.8 1.7997 1.7993 1.799 1.7988

MAYO

JUNIO

27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10

13.531 13.859 14.187 14.516 14.82 15.125 15.43 15.735 16.04 16.321 16.603 16.907 17.189 17.447 17.705 17.963 18.244 18.479 18.737 18.971 19.206 19.44 19.651 19.862 20.073 20.308 20.495 20.683 20.871 21.058 21.222 21.386 21.551 21.715 21.855 21.996 22.137 22.278 22.395 22.512 22.629 22.723 22.817 22.911 23.004

0.236 0.242 0.248 0.253 0.259 0.264 0.269 0.275 0.28 0.285 0.29 0.295 0.3 0.305 0.309 0.314 0.318 0.323 0.327 0.331 0.335 0.339 0.343 0.347 0.35 0.354 0.358 0.361 0.364 0.368 0.37 0.373 0.376 0.379 0.381 0.384 0.386 0.389 0.391 0.393 0.395 0.397 0.398 0.4 0.401

0.9723 0.9709 0.9694 0.9682 0.9666 0.9654 0.964 0.9624 0.9611 0.9597 0.9582 0.9568 0.9553 0.9538 0.9526 0.9511 0.9499 0.9483 0.947 0.9457 0.9444 0.9431 0.9417 0.9404 0.9394 0.938 0.9366 0.9355 0.9345 0.933 0.9323 0.9312 0.9301 0.929 0.9283 0.9272 0.9264 0.9253 0.9245 0.9238 0.923 0.9222 0.9218 0.9211 0.9207

1.7984 1.7981 1.7977 1.7975 1.7971 1.7968 1.7965 1.7961 1.7958 1.7954 1.7951 1.7947 1.7944 1.794 1.7937 1.7934 1.7931 1.7927 1.7924 1.7921 1.7918 1.7915 1.7911 1.7908 1.7906 1.7903 1.7899 1.7897 1.7894 1.7891 1.7889 1.7886 1.7884 1.7881 1.788 1.7877 1.7875 1.7872 1.7871 1.7869 1.7867 1.7865 1.7864 1.7862 1.7862

JULIO

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

23.075 23.145 23.192 23.262 23.309 23.356 23.38 23.403 23.427 23.45 23.45 23.45 23.45 23.427 23.403 23.38 23.356 23.309 23.262 23.192 23.145 23.075 22.981 22.911 22.817 22.723 22.629 22.512 22.395 22.278 22.137 22.02 21.855 21.715 21.551 21.41 21.222 21.058 20.871 20.683 20.495 20.284 20.073 19.886 19.651

0.403 0.404 0.405 0.406 0.407 0.408 0.408 0.408 0.409 0.409 0.409 0.409 0.409 0.409 0.408 0.408 0.408 0.407 0.406 0.405 0.404 0.403 0.401 0.4 0.398 0.397 0.395 0.393 0.391 0.389 0.386 0.384 0.381 0.379 0.376 0.374 0.37 0.368 0.364 0.361 0.358 0.354 0.35 0.347 0.343

0.9199 0.9195 0.9191 0.9187 0.9183 0.9179 0.9179 0.9179 0.9175 0.9175 0.9175 0.9175 0.9175 0.9175 0.9179 0.9179 0.9179 0.9183 0.9187 0.9191 0.9195 0.9199 0.9207 0.9211 0.9218 0.9222 0.923 0.9238 0.9245 0.9253 0.9264 0.9272 0.9283 0.929 0.9301 0.9309 0.9323 0.933 0.9345 0.9355 0.9366 0.938 0.9394 0.9404 0.9417

1.786 1.7859 1.7858 1.7857 1.7856 1.7855 1.7855 1.7855 1.7854 1.7854 1.7854 1.7854 1.7854 1.7854 1.7855 1.7855 1.7855 1.7856 1.7857 1.7858 1.7859 1.786 1.7862 1.7862 1.7864 1.7865 1.7867 1.7869 1.7871 1.7872 1.7875 1.7877 1.788 1.7881 1.7884 1.7886 1.7889 1.7891 1.7894 1.7897 1.7899 1.7903 1.7906 1.7908 1.7911

AGOSTO

SETIEMBRE

26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8

19.44 19.206 18.971 18.737 18.502 18.221 17.986 17.705 17.447 17.189 16.884 16.626 16.321 16.04 15.758 15.43 15.125 14.82 14.516 14.187 13.859 13.531 13.202 12.874 12.522 12.194 11.842 11.491 11.139 10.764 10.412 10.06 9.708 9.31 8.934 8.583 8.208 7.832 7.434 7.058 6.66 6.285 5.909 5.487 5.112

0.339 0.335 0.331 0.327 0.323 0.318 0.314 0.309 0.305 0.3 0.295 0.29 0.285 0.28 0.275 0.269 0.264 0.259 0.253 0.248 0.242 0.236 0.23 0.225 0.219 0.213 0.207 0.201 0.194 0.188 0.182 0.176 0.169 0.162 0.156 0.15 0.143 0.137 0.13 0.123 0.116 0.11 0.103 0.096 0.089

0.9431 0.9444 0.9457 0.947 0.9483 0.9499 0.9511 0.9526 0.9538 0.9553 0.9568 0.9582 0.9597 0.9611 0.9624 0.964 0.9654 0.9666 0.9682 0.9694 0.9709 0.9723 0.9737 0.9748 0.9761 0.9774 0.9787 0.9799 0.9812 0.9824 0.9835 0.9846 0.9858 0.9869 0.9879 0.9888 0.9898 0.9906 0.9916 0.9924 0.9933 0.994 0.9947 0.9954 0.996

1.7915 1.7918 1.7921 1.7924 1.7927 1.7931 1.7934 1.7937 1.794 1.7944 1.7947 1.7951 1.7954 1.7958 1.7961 1.7965 1.7968 1.7971 1.7975 1.7977 1.7981 1.7984 1.7988 1.799 1.7993 1.7996 1.8 1.8002 1.8005 1.8008 1.8011 1.8014 1.8016 1.8019 1.8021 1.8024 1.8026 1.8028 1.803 1.8032 1.8034 1.8036 1.8038 1.8039 1.8041

OCTUBRE

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

4.713 4.315 3.916 3.518 3.119 2.72 2.322 1.899 1.501 1.102 0.704 0.305 -0.117 -0.516 -0.915 -1.313 -1.735 -2.111 -2.509 -2.908 -3.306 -3.729 -4.127 -4.502 -4.901 -5.3 -5.698 -6.097 -6.472 -6.847 -7.246 -7.645 -8.02 -8.395 -8.747 -9.146 -9.521 -9.872 -10.224 -10.599 -10.975 -11.326 -11.655 -12.006 -12.358

0.082 0.075 0.068 0.061 0.054 0.047 0.041 0.033 0.026 0.019 0.012 0.005 -0.002 -0.009 -0.016 -0.023 -0.03 -0.037 -0.044 -0.051 -0.058 -0.065 -0.072 -0.079 -0.086 -0.093 -0.099 -0.106 -0.113 -0.12 -0.126 -0.133 -0.14 -0.147 -0.153 -0.16 -0.166 -0.172 -0.178 -0.185 -0.192 -0.198 -0.203 -0.21 -0.216

0.9966 0.9972 0.9977 0.9981 0.9985 0.9989 0.9992 0.9995 0.9997 0.9998 0.9999 1 1 1 0.9999 0.9997 0.9996 0.9993 0.999 0.9987 0.9983 0.9979 0.9974 0.9969 0.9963 0.9957 0.9951 0.9944 0.9936 0.9928 0.9921 0.9912 0.9902 0.9892 0.9883 0.9872 0.9863 0.9852 0.9842 0.9829 0.9816 0.9805 0.9795 0.978 0.9768

1.8042 1.8044 1.8045 1.8046 1.8047 1.8048 1.8048 1.8049 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.8049 1.8049 1.8048 1.8047 1.8046 1.8045 1.8044 1.8043 1.8041 1.804 1.8039 1.8037 1.8035 1.8033 1.8031 1.8029 1.8027 1.8025 1.8022 1.802 1.8018 1.8015 1.8013 1.801 1.8006 1.8004 1.8001 1.7998 1.7995

NOVIEMBRE

DICIEMBRE

24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7

-12.71 -13.038 -13.367 -13.695 -14.023 -14.351 -14.656 -14.985 -15.289 -15.594 -15.899 -16.181 -16.462 -16.767 -17.048 -17.306 -17.588 -17.845 -18.103 -18.361 -18.619 -18.854 -19.088 -19.323 -19.557 -19.768 -19.979 -20.19 -20.402 -20.589 -20.777 -20.964 -21.152 -21.316 -21.48 -21.644 -21.785 -21.926 -22.066 -22.207 -22.324 -22.465 -22.559 -22.676 -22.77

-0.222 -0.228 -0.233 -0.239 -0.245 -0.25 -0.256 -0.262 -0.267 -0.272 -0.277 -0.282 -0.287 -0.293 -0.298 -0.302 -0.307 -0.311 -0.316 -0.32 -0.325 -0.329 -0.333 -0.337 -0.341 -0.345 -0.349 -0.352 -0.356 -0.359 -0.363 -0.366 -0.369 -0.372 -0.375 -0.378 -0.38 -0.383 -0.385 -0.388 -0.39 -0.392 -0.394 -0.396 -0.397

0.9755 0.9741 0.973 0.9716 0.9701 0.9689 0.9674 0.9659 0.9646 0.9632 0.9619 0.9605 0.9591 0.9574 0.9559 0.9547 0.9532 0.952 0.9505 0.9492 0.9477 0.9464 0.9451 0.9438 0.9424 0.9411 0.9397 0.9387 0.9373 0.9362 0.9348 0.9338 0.9327 0.9316 0.9305 0.9294 0.9287 0.9275 0.9268 0.9257 0.9249 0.9241 0.9234 0.9226 0.9222

1.7992 1.7989 1.7986 1.7983 1.7979 1.7976 1.7973 1.7969 1.7966 1.7963 1.796 1.7956 1.7953 1.7949 1.7945 1.7942 1.7939 1.7936 1.7932 1.7929 1.7926 1.7923 1.792 1.7916 1.7913 1.791 1.7907 1.7904 1.7901 1.7898 1.7895 1.7893 1.789 1.7887 1.7885 1.7882 1.7881 1.7878 1.7876 1.7873 1.7871 1.787 1.7868 1.7866 1.7865

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

-22.864 -22.958 -23.028 -23.098 -23.169 -23.216 -23.286 -23.333 -23.356 -23.403 -23.427 -23.427 -23.45 -23.45 -23.45 -23.427 -23.427 -23.403 -23.356 -23.333 -23.286 -23.239 -23.169 -23.098

-0.399 -0.401 -0.402 -0.403 -0.404 -0.405 -0.406 -0.407 -0.408 -0.408 -0.409 -0.409 -0.409 -0.409 -0.409 -0.409 -0.409 -0.408 -0.408 -0.407 -0.406 -0.406 -0.404 -0.403

0.9214 0.9207 0.9203 0.9199 0.9195 0.9191 0.9187 0.9183 0.9179 0.9179 0.9175 0.9175 0.9175 0.9175 0.9175 0.9175 0.9175 0.9179 0.9179 0.9183 0.9187 0.9187 0.9195 0.9199

1.7863 1.7862 1.7861 1.786 1.7859 1.7858 1.7857 1.7856 1.7855 1.7855 1.7854 1.7854 1.7854 1.7854 1.7854 1.7854 1.7854 1.7855 1.7855 1.7856 1.7857 1.7857 1.7859 1.786

4.3. Distancias diarias de la tierra al sol DETERMINANDO LAS DISTANCIAS (dm/d)^2 diario

(dm/ d)2 = C1 + C2cos() + C3sen() +C4cos (2) C5sen (2)

Mes

Enero

N° deDia Valor "n" 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12

c1 c2 c3 c4 c5 ф

1.00011 0.033523 0.00218 0.000739 0.000099 2nπ/365

n

número de días

ф 0.0172 0.0344 0.0516 0.0689 0.0861 0.1033 0.1205 0.1377 0.1549 0.1721 0.1894 0.2066

cos(ф) 0.9999 0.9994 0.9987 0.9976 0.9963 0.9947 0.9927 0.9905 0.988 0.9852 0.9821 0.9787

sen(ф) cos(2ф) sen(2ф) 0.0172 0.9994 0.0344 0.0344 0.9976 0.0687 0.0516 0.9947 0.103 0.0688 0.9905 0.1374 0.086 0.9852 0.1714 0.1031 0.9787 0.2051 0.1202 0.9711 0.2387 0.1373 0.9623 0.2719 0.1543 0.9524 0.3049 0.1713 0.9413 0.3374 0.1883 0.9291 0.3698 0.2051 0.9158 0.4015

(dm/d)^2 1.03441 1.03443 1.03445 1.03445 1.03444 1.03442 1.03439 1.03435 1.0343 1.03424 1.03417 1.03408

FEBRERO

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

0.2238 0.241 0.2582 0.2754 0.2926 0.3099 0.3271 0.3443 0.3615 0.3787 0.3959 0.4131 0.4304 0.4476 0.4648 0.482 0.4992 0.5164 0.5336 0.5509 0.5681 0.5853 0.6025 0.6197 0.6369 0.6541 0.6714

0.9751 0.9711 0.9669 0.9623 0.9575 0.9524 0.947 0.9413 0.9354 0.9291 0.9226 0.9159 0.9088 0.9015 0.8939 0.8861 0.878 0.8696 0.861 0.8521 0.8429 0.8335 0.8239 0.8141 0.8039 0.7936 0.783

0.2219 0.2387 0.2553 0.2719 0.2884 0.305 0.3213 0.3375 0.3537 0.3697 0.3856 0.4015 0.4172 0.4328 0.4482 0.4636 0.4787 0.4938 0.5086 0.5235 0.538 0.5524 0.5667 0.5808 0.5947 0.6084 0.6221

0.9015 0.8861 0.8696 0.8521 0.8336 0.814 0.7935 0.7721 0.7498 0.7266 0.7026 0.6777 0.6518 0.6254 0.5982 0.5702 0.5416 0.5124 0.4826 0.452 0.421 0.3896 0.3577 0.3254 0.2926 0.2596 0.226

0.4328 0.4636 0.4938 0.5234 0.5524 0.5809 0.6085 0.6355 0.6616 0.687 0.7116 0.7354 0.7584 0.7803 0.8014 0.8215 0.8406 0.8587 0.8759 0.892 0.907 0.921 0.9338 0.9456 0.9562 0.9657 0.9741

1.03399 1.03389 1.03377 1.03364 1.03351 1.03336 1.0332 1.03303 1.03286 1.03267 1.03247 1.03226 1.03204 1.03181 1.03157 1.03133 1.03107 1.0308 1.03053 1.03024 1.02994 1.02963 1.02932 1.029 1.02867 1.02833 1.02798

MARZO

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

0.6886 0.7058 0.723 0.7402 0.7574 0.7746 0.7919 0.8091 0.8263 0.8435 0.8607 0.8779 0.8951 0.9124 0.9296 0.9468 0.964 0.9812 0.9984 1.0156 1.0329 1.0501 1.0673 1.0845 1.1017 1.1189 1.1361

0.7721 0.7611 0.7498 0.7383 0.7266 0.7147 0.7025 0.6902 0.6776 0.6649 0.6519 0.6388 0.6254 0.6118 0.5982 0.5843 0.5702 0.556 0.5416 0.5271 0.5123 0.4975 0.4825 0.4674 0.4521 0.4367 0.4211

0.6355 0.6486 0.6616 0.6744 0.687 0.6994 0.7117 0.7237 0.7354 0.747 0.7583 0.7694 0.7803 0.791 0.8014 0.8115 0.8215 0.8312 0.8406 0.8498 0.8588 0.8675 0.8759 0.8841 0.892 0.8996 0.907

0.1924 0.1585 0.1245 0.0903 0.056 0.0216 -0.013 -0.0474 -0.0817 -0.1159 -0.15 -0.184 -0.2176 -0.2513 -0.2844 -0.3172 -0.3497 -0.3817 -0.4132 -0.4443 -0.475 -0.505 -0.5344 -0.5632 -0.5912 -0.6186 -0.6453

0.9813 0.9874 0.9922 0.9959 0.9984 0.9998 0.9999 0.9989 0.9967 0.9933 0.9887 0.9829 0.976 0.9679 0.9587 0.9483 0.9369 0.9243 0.9106 0.8959 0.88 0.8631 0.8452 0.8263 0.8065 0.7857 0.7639

1.02762 1.02725 1.02688 1.0265 1.02611 1.02571 1.0253 1.02489 1.02447 1.02404 1.0236 1.02316 1.02271 1.02225 1.0218 1.02133 1.02085 1.02037 1.01988 1.01939 1.01889 1.01839 1.01788 1.01737 1.01685 1.01633 1.0158

ABRIL

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93

1.1534 1.1706 1.1878 1.205 1.2222 1.2394 1.2566 1.2739 1.2911 1.3083 1.3255 1.3427 1.3599 1.3771 1.3944 1.4116 1.4288 1.446 1.4632 1.4804 1.4976 1.5149 1.5321 1.5493 1.5665 1.5837 1.6009

0.4054 0.3896 0.3737 0.3577 0.3416 0.3254 0.3091 0.2926 0.2761 0.2595 0.2428 0.2261 0.2093 0.1925 0.1755 0.1585 0.1415 0.1245 0.1074 0.0903 0.0731 0.0559 0.0387 0.0215 0.0043 -0.0129 -0.0301

0.9141 0.921 0.9275 0.9338 0.9399 0.9456 0.951 0.9562 0.9611 0.9657 0.9701 0.9741 0.9778 0.9813 0.9845 0.9874 0.9899 0.9922 0.9942 0.9959 0.9973 0.9984 0.9993 0.9998 1 0.9999 0.9995

-0.6713 -0.6964 -0.7207 -0.7441 -0.7666 -0.7883 -0.809 -0.8288 -0.8476 -0.8653 -0.8821 -0.8977 -0.9124 -0.9259 -0.9384 -0.9497 -0.9599 -0.969 -0.9769 -0.9837 -0.9893 -0.9938 -0.997 -0.9991 -1 -0.9997 -0.9982

0.7412 0.7176 0.6933 0.6681 0.6421 0.6153 0.5878 0.5595 0.5307 0.5012 0.4711 0.4405 0.4094 0.3778 0.3455 0.313 0.2802 0.247 0.2135 0.1798 0.1459 0.1116 0.0773 0.043 0.0086 -0.0258 -0.0602

1.01527 1.01473 1.0142 1.01365 1.01311 1.01256 1.01201 1.01145 1.01089 1.01032 1.00976 1.00919 1.00862 1.00806 1.00748 1.00691 1.00633 1.00575 1.00518 1.0046 1.00402 1.00344 1.00286 1.00228 1.0017 1.00112 1.00054

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

1.6181 1.6354 1.6526 1.6698 1.687 1.7042 1.7214 1.7386 1.7559 1.7731 1.7903 1.8075 1.8247 1.8419 1.8591 1.8764 1.8936 1.9108 1.928 1.9452 1.9624 1.9796 1.9969 2.0141 2.0313 2.0485 2.0657

-0.0473 -0.0646 -0.0817 -0.0988 -0.1159 -0.133 -0.15 -0.167 -0.184 -0.2009 -0.2177 -0.2345 -0.2512 -0.2678 -0.2843 -0.3009 -0.3172 -0.3335 -0.3497 -0.3657 -0.3817 -0.3975 -0.4133 -0.4289 -0.4444 -0.4597 -0.4749

0.9989 0.9979 0.9967 0.9951 0.9933 0.9911 0.9887 0.986 0.9829 0.9796 0.976 0.9721 0.9679 0.9635 0.9587 0.9537 0.9483 0.9428 0.9369 0.9307 0.9243 0.9176 0.9106 0.9033 0.8958 0.8881 0.88

-0.9955 -0.9917 -0.9866 -0.9805 -0.9731 -0.9646 -0.955 -0.9442 -0.9323 -0.9193 -0.9052 -0.89 -0.8738 -0.8566 -0.8383 -0.819 -0.7987 -0.7776 -0.7555 -0.7325 -0.7087 -0.684 -0.6583 -0.632 -0.605 -0.5773 -0.5489

-0.0945 -0.1288 -0.1629 -0.1967 -0.2303 -0.2637 -0.2967 -0.3293 -0.3618 -0.3937 -0.425 -0.4559 -0.4863 -0.516 -0.5452 -0.5739 -0.6017 -0.6288 -0.6552 -0.6808 -0.7056 -0.7295 -0.7527 -0.7749 -0.7962 -0.8165 -0.8359

0.99996 0.99937 0.9988 0.99822 0.99765 0.99707 0.9965 0.99593 0.99536 0.99479 0.99423 0.99367 0.99311 0.99255 0.992 0.99144 0.99089 0.99035 0.98981 0.98927 0.98874 0.98821 0.98768 0.98716 0.98664 0.98613 0.98562

MAYO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

2.0829 2.1001 2.1174 2.1346 2.1518 2.169 2.1862 2.2034 2.2206 2.2379 2.2551 2.2723 2.2895 2.3067 2.3239 2.3411 2.3584 2.3756 2.3928 2.41 2.4272 2.4444 2.4616 2.4789 2.4961 2.5133 2.5305

-0.49 -0.5049 -0.5198 -0.5344 -0.5489 -0.5632 -0.5773 -0.5912 -0.605 -0.6187 -0.6321 -0.6454 -0.6584 -0.6713 -0.6839 -0.6964 -0.7087 -0.7207 -0.7325 -0.7441 -0.7555 -0.7666 -0.7776 -0.7883 -0.7988 -0.809 -0.819

0.8717 0.8632 0.8543 0.8452 0.8359 0.8263 0.8165 0.8065 0.7962 0.7856 0.7749 0.7639 0.7527 0.7412 0.7296 0.7177 0.7055 0.6933 0.6808 0.6681 0.6552 0.6421 0.6288 0.6152 0.6016 0.5878 0.5738

-0.5198 -0.4901 -0.4596 -0.4288 -0.3975 -0.3657 -0.3335 -0.3009 -0.2679 -0.2344 -0.2008 -0.167 -0.133 -0.0988 -0.0645 -0.0302 0.0044 0.0388 0.0731 0.1074 0.1415 0.1755 0.2093 0.243 0.2762 0.3091 0.3416

-0.8543 -0.8717 -0.8881 -0.9034 -0.9176 -0.9307 -0.9428 -0.9537 -0.9635 -0.9721 -0.9796 -0.986 -0.9911 -0.9951 -0.9979 -0.9995 -1 -0.9992 -0.9973 -0.9942 -0.9899 -0.9845 -0.9779 -0.97 -0.9611 -0.951 -0.9398

0.98512 0.98462 0.98412 0.98363 0.98315 0.98267 0.9822 0.98173 0.98127 0.98081 0.98036 0.97992 0.97948 0.97905 0.97863 0.97821 0.97779 0.97739 0.97699 0.9766 0.97622 0.97584 0.97547 0.97511 0.97475 0.97441 0.97406

JUNIO

28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174

2.5477 2.5649 2.5821 2.5994 2.6166 2.6338 2.651 2.6682 2.6854 2.7026 2.7199 2.7371 2.7543 2.7715 2.7887 2.8059 2.8231 2.8404 2.8576 2.8748 2.892 2.9092 2.9264 2.9436 2.9609 2.9781 2.9953

-0.8288 -0.8383 -0.8475 -0.8566 -0.8653 -0.8738 -0.8821 -0.89 -0.8977 -0.9052 -0.9124 -0.9193 -0.9259 -0.9323 -0.9384 -0.9442 -0.9497 -0.955 -0.9599 -0.9646 -0.969 -0.9731 -0.9769 -0.9805 -0.9837 -0.9867 -0.9893

0.5596 0.5453 0.5308 0.516 0.5012 0.4862 0.4711 0.4559 0.4405 0.425 0.4093 0.3936 0.3777 0.3617 0.3456 0.3294 0.3131 0.2967 0.2802 0.2636 0.247 0.2303 0.2135 0.1967 0.1797 0.1628 0.1458

0.3737 0.4054 0.4366 0.4675 0.4976 0.5271 0.556 0.5843 0.6119 0.6387 0.6649 0.6902 0.7147 0.7383 0.7611 0.783 0.8039 0.824 0.843 0.861 0.878 0.8939 0.9088 0.9226 0.9354 0.947 0.9575

-0.9275 -0.9141 -0.8997 -0.884 -0.8674 -0.8498 -0.8312 -0.8115 -0.791 -0.7695 -0.7469 -0.7236 -0.6994 -0.6744 -0.6486 -0.6221 -0.5948 -0.5666 -0.5379 -0.5086 -0.4787 -0.4482 -0.4172 -0.3857 -0.3536 -0.3212 -0.2884

0.97373 0.97341 0.97309 0.97278 0.97248 0.97218 0.97189 0.97162 0.97135 0.97109 0.97083 0.97059 0.97035 0.97012 0.9699 0.96969 0.96949 0.9693 0.96911 0.96893 0.96877 0.96861 0.96846 0.96831 0.96818 0.96806 0.96794

JULIO

24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201

3.0125 3.0297 3.0469 3.0641 3.0814 3.0986 3.1158 3.133 3.1502 3.1674 3.1846 3.2018 3.2191 3.2363 3.2535 3.2707 3.2879 3.3051 3.3223 3.3396 3.3568 3.374 3.3912 3.4084 3.4256 3.4428 3.4601

-0.9917 -0.9937 -0.9955 -0.997 -0.9982 -0.9991 -0.9997 -1 -1 -0.9997 -0.9991 -0.9982 -0.997 -0.9955 -0.9937 -0.9917 -0.9893 -0.9867 -0.9837 -0.9805 -0.9769 -0.9731 -0.969 -0.9646 -0.9599 -0.955 -0.9497

0.1287 0.1117 0.0946 0.0774 0.0602 0.043 0.0258 0.0086 -0.0086 -0.0258 -0.043 -0.0602 -0.0774 -0.0946 -0.1117 -0.1287 -0.1458 -0.1628 -0.1797 -0.1967 -0.2135 -0.2303 -0.247 -0.2637 -0.2802 -0.2967 -0.3131

0.9669 0.9751 0.9821 0.988 0.9928 0.9963 0.9987 0.9999 0.9999 0.9987 0.9963 0.9928 0.988 0.9821 0.9751 0.9668 0.9575 0.947 0.9354 0.9226 0.9088 0.8939 0.878 0.861 0.843 0.824 0.8039

-0.2553 -0.2219 -0.1883 -0.1544 -0.1201 -0.0859 -0.0516 -0.0172 0.0172 0.0516 0.0859 0.1201 0.1544 0.1883 0.222 0.2554 0.2885 0.3212 0.3536 0.3857 0.4172 0.4483 0.4787 0.5086 0.538 0.5666 0.5948

0.96784 0.96774 0.96765 0.96757 0.9675 0.96744 0.96739 0.96734 0.96731 0.96728 0.96727 0.96726 0.96726 0.96728 0.9673 0.96732 0.96736 0.96741 0.96747 0.96753 0.96761 0.96769 0.96778 0.96789 0.968 0.96811 0.96824

AGOSTO

21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228

3.4773 3.4945 3.5117 3.5289 3.5461 3.5633 3.5806 3.5978 3.615 3.6322 3.6494 3.6666 3.6838 3.7011 3.7183 3.7355 3.7527 3.7699 3.7871 3.8043 3.8216 3.8388 3.856 3.8732 3.8904 3.9076 3.9248

-0.9442 -0.9384 -0.9323 -0.9259 -0.9193 -0.9124 -0.9052 -0.8977 -0.89 -0.882 -0.8738 -0.8653 -0.8566 -0.8475 -0.8383 -0.8288 -0.819 -0.809 -0.7988 -0.7883 -0.7776 -0.7666 -0.7555 -0.7441 -0.7325 -0.7207 -0.7087

-0.3294 -0.3456 -0.3617 -0.3777 -0.3936 -0.4093 -0.425 -0.4405 -0.4559 -0.4712 -0.4863 -0.5012 -0.516 -0.5308 -0.5453 -0.5596 -0.5738 -0.5878 -0.6016 -0.6153 -0.6288 -0.6421 -0.6552 -0.6681 -0.6808 -0.6933 -0.7056

0.7829 0.7611 0.7383 0.7147 0.6902 0.6649 0.6387 0.6118 0.5843 0.556 0.5271 0.4976 0.4674 0.4366 0.4054 0.3737 0.3416 0.309 0.2761 0.2429 0.2092 0.1755 0.1415 0.1074 0.0731 0.0388 0.0044

0.6221 0.6487 0.6744 0.6994 0.7236 0.7469 0.7695 0.791 0.8116 0.8312 0.8498 0.8674 0.884 0.8997 0.9142 0.9276 0.9399 0.951 0.9611 0.97 0.9779 0.9845 0.9899 0.9942 0.9973 0.9992 1

0.96838 0.96853 0.96868 0.96885 0.96902 0.9692 0.96939 0.96959 0.96979 0.97001 0.97023 0.97046 0.9707 0.97095 0.97121 0.97147 0.97175 0.97203 0.97232 0.97262 0.97292 0.97324 0.97356 0.97389 0.97422 0.97457 0.97492

SETIEMBRE

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12

229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

3.9421 3.9593 3.9765 3.9937 4.0109 4.0281 4.0453 4.0626 4.0798 4.097 4.1142 4.1314 4.1486 4.1658 4.1831 4.2003 4.2175 4.2347 4.2519 4.2691 4.2863 4.3036 4.3208 4.338 4.3552 4.3724 4.3896

-0.6963 -0.6839 -0.6712 -0.6584 -0.6454 -0.6321 -0.6187 -0.605 -0.5912 -0.5773 -0.5631 -0.5489 -0.5344 -0.5198 -0.5049 -0.49 -0.4749 -0.4597 -0.4444 -0.4289 -0.4133 -0.3975 -0.3817 -0.3657 -0.3496 -0.3335 -0.3172

-0.7177 -0.7296 -0.7412 -0.7527 -0.7639 -0.7749 -0.7856 -0.7962 -0.8065 -0.8165 -0.8264 -0.8359 -0.8452 -0.8543 -0.8632 -0.8717 -0.88 -0.8881 -0.8958 -0.9033 -0.9106 -0.9176 -0.9243 -0.9307 -0.9369 -0.9428 -0.9484

-0.0302 -0.0646 -0.0989 -0.133 -0.167 -0.2008 -0.2344 -0.2679 -0.3009 -0.3335 -0.3657 -0.3975 -0.4288 -0.4597 -0.4901 -0.5198 -0.5489 -0.5773 -0.605 -0.6321 -0.6583 -0.684 -0.7087 -0.7325 -0.7555 -0.7776 -0.7988

0.9995 0.9979 0.9951 0.9911 0.986 0.9796 0.9721 0.9634 0.9537 0.9427 0.9307 0.9176 0.9034 0.8881 0.8717 0.8543 0.8359 0.8165 0.7962 0.7749 0.7527 0.7295 0.7055 0.6807 0.6551 0.6288 0.6017

0.97528 0.97564 0.97602 0.9764 0.97678 0.97718 0.97758 0.97799 0.97841 0.97882 0.97925 0.97968 0.98013 0.98057 0.98103 0.98148 0.98195 0.98242 0.98289 0.98337 0.98386 0.98435 0.98485 0.98535 0.98585 0.98636 0.98688

OCTUBRE

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9

256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282

4.4068 4.4241 4.4413 4.4585 4.4757 4.4929 4.5101 4.5273 4.5446 4.5618 4.579 4.5962 4.6134 4.6306 4.6478 4.6651 4.6823 4.6995 4.7167 4.7339 4.7511 4.7683 4.7856 4.8028 4.82 4.8372 4.8544

-0.3009 -0.2843 -0.2678 -0.2512 -0.2345 -0.2177 -0.2009 -0.184 -0.167 -0.15 -0.133 -0.1159 -0.0988 -0.0817 -0.0645 -0.0473 -0.0301 -0.0129 0.0043 0.0215 0.0387 0.0559 0.0731 0.0903 0.1074 0.1245 0.1415

-0.9537 -0.9587 -0.9635 -0.9679 -0.9721 -0.976 -0.9796 -0.9829 -0.986 -0.9887 -0.9911 -0.9933 -0.9951 -0.9967 -0.9979 -0.9989 -0.9995 -0.9999 -1 -0.9998 -0.9993 -0.9984 -0.9973 -0.9959 -0.9942 -0.9922 -0.9899

-0.819 -0.8383 -0.8566 -0.8738 -0.89 -0.9052 -0.9193 -0.9323 -0.9442 -0.955 -0.9646 -0.9731 -0.9805 -0.9867 -0.9917 -0.9955 -0.9982 -0.9997 -1 -0.9991 -0.997 -0.9938 -0.9893 -0.9837 -0.9769 -0.969 -0.9599

0.5738 0.5452 0.516 0.4862 0.4559 0.425 0.3936 0.3618 0.3293 0.2966 0.2636 0.2303 0.1967 0.1628 0.1288 0.0944 0.0601 0.0258 -0.0086 -0.043 -0.0773 -0.1116 -0.1459 -0.1798 -0.2136 -0.247 -0.2802

0.9874 0.98792 0.98845 0.98898 0.98952 0.99006 0.9906 0.99115 0.9917 0.99225 0.9928 0.99336 0.99392 0.99449 0.99505 0.99562 0.99619 0.99676 0.99733 0.99791 0.99848 0.99906 0.99964 1.00022 1.0008 1.00138 1.00196

NOVIEMBRE

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5

283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309

4.8716 4.8888 4.9061 4.9233 4.9405 4.9577 4.9749 4.9921 5.0093 5.0266 5.0438 5.061 5.0782 5.0954 5.1126 5.1298 5.1471 5.1643 5.1815 5.1987 5.2159 5.2331 5.2503 5.2676 5.2848 5.302 5.3192

0.1585 0.1755 0.1925 0.2094 0.2261 0.2429 0.2595 0.2761 0.2926 0.3091 0.3254 0.3416 0.3577 0.3737 0.3896 0.4054 0.4211 0.4367 0.4521 0.4674 0.4825 0.4975 0.5123 0.5271 0.5417 0.556 0.5703

-0.9874 -0.9845 -0.9813 -0.9778 -0.9741 -0.9701 -0.9657 -0.9611 -0.9562 -0.951 -0.9456 -0.9398 -0.9338 -0.9275 -0.921 -0.9141 -0.907 -0.8996 -0.892 -0.8841 -0.8759 -0.8675 -0.8588 -0.8498 -0.8406 -0.8312 -0.8215

-0.9497 -0.9384 -0.9259 -0.9123 -0.8977 -0.882 -0.8653 -0.8476 -0.8288 -0.809 -0.7883 -0.7666 -0.7441 -0.7207 -0.6964 -0.6713 -0.6453 -0.6186 -0.5912 -0.5631 -0.5344 -0.505 -0.475 -0.4443 -0.4132 -0.3816 -0.3496

-0.3131 -0.3455 -0.3778 -0.4094 -0.4406 -0.4712 -0.5012 -0.5307 -0.5595 -0.5879 -0.6153 -0.6421 -0.6681 -0.6933 -0.7177 -0.7412 -0.764 -0.7857 -0.8065 -0.8264 -0.8452 -0.8631 -0.88 -0.8959 -0.9106 -0.9243 -0.9369

1.00254 1.00312 1.0037 1.00428 1.00486 1.00544 1.00601 1.00659 1.00717 1.00774 1.00831 1.00888 1.00945 1.01001 1.01058 1.01114 1.0117 1.01225 1.0128 1.01335 1.0139 1.01444 1.01497 1.01551 1.01604 1.01656 1.01709

DICIEMBRE

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2

310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336

5.3364 5.3536 5.3708 5.3881 5.4053 5.4225 5.4397 5.4569 5.4741 5.4913 5.5086 5.5258 5.543 5.5602 5.5774 5.5946 5.6118 5.6291 5.6463 5.6635 5.6807 5.6979 5.7151 5.7323 5.7496 5.7668 5.784

0.5843 0.5982 0.6119 0.6255 0.6388 0.6519 0.6649 0.6776 0.6902 0.7025 0.7147 0.7266 0.7383 0.7498 0.7611 0.7721 0.783 0.7936 0.804 0.8141 0.8239 0.8336 0.8429 0.8521 0.861 0.8696 0.878

-0.8115 -0.8014 -0.791 -0.7803 -0.7694 -0.7583 -0.747 -0.7354 -0.7237 -0.7117 -0.6994 -0.687 -0.6744 -0.6616 -0.6486 -0.6354 -0.6221 -0.6084 -0.5947 -0.5808 -0.5667 -0.5524 -0.538 -0.5234 -0.5086 -0.4937 -0.4787

-0.3172 -0.2844 -0.2513 -0.2176 -0.1839 -0.15 -0.1159 -0.0817 -0.0474 -0.013 0.0216 0.056 0.0903 0.1245 0.1586 0.1924 0.2261 0.2596 0.2927 0.3254 0.3577 0.3896 0.4211 0.452 0.4826 0.5124 0.5417

-0.9484 -0.9587 -0.9679 -0.976 -0.9829 -0.9887 -0.9933 -0.9967 -0.9989 -0.9999 -0.9998 -0.9984 -0.9959 -0.9922 -0.9874 -0.9813 -0.9741 -0.9657 -0.9562 -0.9456 -0.9338 -0.921 -0.907 -0.892 -0.8758 -0.8587 -0.8406

1.0176 1.01811 1.01862 1.01912 1.01961 1.0201 1.02059 1.02106 1.02154 1.022 1.02246 1.02291 1.02336 1.0238 1.02423 1.02465 1.02507 1.02548 1.02589 1.02628 1.02667 1.02705 1.02742 1.02778 1.02813 1.02848 1.02882

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363

5.8012 5.8184 5.8356 5.8528 5.8701 5.8873 5.9045 5.9217 5.9389 5.9561 5.9733 5.9906 6.0078 6.025 6.0422 6.0594 6.0766 6.0938 6.1111 6.1283 6.1455 6.1627 6.1799 6.1971 6.2143 6.2316 6.2488

0.8861 0.8939 0.9015 0.9088 0.9159 0.9227 0.9292 0.9354 0.9413 0.947 0.9524 0.9575 0.9623 0.9669 0.9711 0.9751 0.9787 0.9821 0.9852 0.988 0.9905 0.9928 0.9947 0.9963 0.9976 0.9987 0.9994

-0.4635 -0.4482 -0.4328 -0.4172 -0.4014 -0.3856 -0.3697 -0.3537 -0.3375 -0.3213 -0.3049 -0.2884 -0.2719 -0.2553 -0.2387 -0.2219 -0.2051 -0.1883 -0.1712 -0.1543 -0.1373 -0.1202 -0.1031 -0.086 -0.0688 -0.0516 -0.0344

0.5703 0.5982 0.6254 0.6519 0.6777 0.7026 0.7266 0.7498 0.7722 0.7936 0.814 0.8336 0.8521 0.8696 0.8861 0.9015 0.9159 0.9291 0.9414 0.9524 0.9623 0.9711 0.9787 0.9852 0.9905 0.9947 0.9976

-0.8215 -0.8014 -0.7803 -0.7583 -0.7353 -0.7116 -0.687 -0.6616 -0.6354 -0.6085 -0.5808 -0.5523 -0.5233 -0.4937 -0.4635 -0.4328 -0.4015 -0.3698 -0.3374 -0.3048 -0.2719 -0.2386 -0.2051 -0.1713 -0.1373 -0.103 -0.0687

1.02914 1.02946 1.02977 1.03007 1.03037 1.03065 1.03092 1.03118 1.03144 1.03168 1.03192 1.03214 1.03235 1.03256 1.03275 1.03294 1.03311 1.03327 1.03343 1.03357 1.0337 1.03382 1.03393 1.03403 1.03412 1.0342 1.03427

30 31

364 365

6.266 6.2832

0.9999 1

-0.0172 0.9994 -0.0344 0 1 0

1.03433 1.03437

4.4. Radiación solar diaria

Determinando la radiación solar incidente

Qs = 458.37 S(dm / d)2 S

1.94

grados ф= Latitud

Mes

Enero

(0.01745H sen  sen δ + cos  cos δ sen H ) 13°04´

N° de Dia (dm/d)^2 H H en rad senH 1 1.03441 1.7861 0.03117333 0.03116828 2 1.03443 1.7862 0.03117507 0.03117002 3 1.03445 1.7863 0.03117682 0.03117177 4 1.03445 1.7865 0.03118031 0.03117526 5 1.03444 1.7866 0.03118205 0.031177 6 1.03442 1.7868 0.03118554 0.03118049 7 1.03439 1.787 0.03118903 0.03118398 8 1.03435 1.7871 0.03119078 0.03118572 9 1.0343 1.7873 0.03119427 0.03118921 10 1.03424 1.7876 0.03119951 0.03119444 11 1.03417 1.7878 0.031203 0.03119793 12 1.03408 1.7881 0.03120823 0.03120317 13 1.03399 1.7882 0.03120998 0.03120491

radianes 0.22806217

sen(ф) 0.2260903

cos(ф) 0.97410635

δ -23.028 -22.958 -22.864 -22.77 -22.676 -22.559 -22.442 -22.324 -22.207 -22.066 -21.949 -21.785 -21.644

δ en radianes -0.402 -0.401 -0.399 -0.397 -0.396 -0.394 -0.392 -0.39 -0.388 -0.385 -0.383 -0.38 -0.378

sen(δ) -0.3913 -0.3903 -0.3885 -0.3867 -0.3857 -0.3839 -0.382 -0.3802 -0.3783 -0.3756 -0.3737 -0.3709 -0.3691

cos(δ) 0.9203 0.9207 0.9214 0.9222 0.9226 0.9234 0.9241 0.9249 0.9257 0.9268 0.9275 0.9287 0.9294

QS 25.6572771 25.6704942 25.692183 25.71761 25.7300881 25.7550245 25.776933 25.799935 25.8241437 25.8580251 25.8789451 25.9148904 25.9338516

FEBRERO

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9

1.03389 1.03377 1.03364 1.03351 1.03336 1.0332 1.03303 1.03286 1.03267 1.03247 1.03226 1.03204 1.03181 1.03157 1.03133 1.03107 1.0308 1.03053 1.03024 1.02994 1.02963 1.02932 1.029 1.02867 1.02833 1.02798 1.02762

1.7885 1.7887 1.789 1.7893 1.7895 1.7898 1.7901 1.7904 1.7907 1.791 1.7913 1.7916 1.792 1.7923 1.7926 1.7929 1.7932 1.7936 1.7939 1.7942 1.7945 1.795 1.7953 1.7956 1.796 1.7963 1.7966

0.03121521 0.0312187 0.03122394 0.03122918 0.03123267 0.0312379 0.03124314 0.03124837 0.03125361 0.03125885 0.03126408 0.03126932 0.0312763 0.03128154 0.03128677 0.03129201 0.03129724 0.03130423 0.03130946 0.0313147 0.03131993 0.03132866 0.0313339 0.03133913 0.03134611 0.03135135 0.03135659

0.03121014 0.03121363 0.03121887 0.0312241 0.03122759 0.03123282 0.03123806 0.03124329 0.03124852 0.03125376 0.03125899 0.03126422 0.0312712 0.03127643 0.03128167 0.0312869 0.03129214 0.03129911 0.03130435 0.03130958 0.03131481 0.03132354 0.03132877 0.031334 0.03134098 0.03134621 0.03135145

-21.48 -21.316 -21.128 -20.964 -20.777 -20.589 -20.402 -20.19 -19.979 -19.768 -19.557 -19.323 -19.088 -18.854 -18.619 -18.361 -18.103 -17.845 -17.588 -17.306 -17.048 -16.743 -16.462 -16.181 -15.899 -15.594 -15.289

-0.375 -0.372 -0.369 -0.366 -0.363 -0.359 -0.356 -0.352 -0.349 -0.345 -0.341 -0.337 -0.333 -0.329 -0.325 -0.32 -0.316 -0.311 -0.307 -0.302 -0.298 -0.292 -0.287 -0.282 -0.277 -0.272 -0.267

-0.3663 -0.3635 -0.3607 -0.3579 -0.3551 -0.3513 -0.3485 -0.3448 -0.342 -0.3382 -0.3344 -0.3307 -0.3269 -0.3231 -0.3193 -0.3146 -0.3108 -0.306 -0.3022 -0.2974 -0.2936 -0.2879 -0.2831 -0.2783 -0.2735 -0.2687 -0.2638

0.9305 0.9316 0.9327 0.9338 0.9348 0.9362 0.9373 0.9387 0.9397 0.9411 0.9424 0.9438 0.9451 0.9464 0.9477 0.9492 0.9505 0.952 0.9532 0.9547 0.9559 0.9577 0.9591 0.9605 0.9619 0.9632 0.9646

25.9667554 25.9977068 26.0298599 26.0620146 26.0894129 26.1293087 26.1604518 26.2000814 26.2279188 26.2667932 26.3026139 26.3409585 26.3777301 26.4127698 26.4478026 26.4880053 26.5222513 26.5636693 26.5945879 26.6337307 26.6641095 26.7144221 26.750216 26.7857353 26.8224717 26.8546484 26.8893497

MARZO

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7 8

1.02725 1.02688 1.0265 1.02611 1.02571 1.0253 1.02489 1.02447 1.02404 1.0236 1.02316 1.02271 1.02225 1.0218 1.02133 1.02085 1.02037 1.01988 1.01939 1.01889 1.01839 1.01788 1.01737 1.01685 1.01633 1.0158 1.01527

1.7969 1.7973 1.7976 1.7979 1.7983 1.7986 1.7989 1.7992 1.7995 1.7998 1.8001 1.8004 1.8006 1.801 1.8012 1.8015 1.8018 1.802 1.8022 1.8025 1.8027 1.8029 1.8031 1.8033 1.8035 1.8037 1.8039

0.03136182 0.0313688 0.03137404 0.03137927 0.03138626 0.03139149 0.03139673 0.03140196 0.0314072 0.03141244 0.03141767 0.03142291 0.0314264 0.03143338 0.03143687 0.03144211 0.03144734 0.03145083 0.03145432 0.03145956 0.03146305 0.03146654 0.03147003 0.03147352 0.03147701 0.0314805 0.03148399

0.03135668 0.03136366 0.03136889 0.03137413 0.0313811 0.03138634 0.03139157 0.0313968 0.03140204 0.03140727 0.0314125 0.03141774 0.03142123 0.0314282 0.03143169 0.03143693 0.03144216 0.03144565 0.03144914 0.03145437 0.03145786 0.03146135 0.03146484 0.03146833 0.03147182 0.0314753 0.03147879

-14.985 -14.68 -14.351 -14.023 -13.695 -13.367 -13.038 -12.71 -12.358 -12.006 -11.678 -11.326 -10.975 -10.599 -10.248 -9.872 -9.521 -9.122 -8.77 -8.395 -8.02 -7.645 -7.246 -6.847 -6.472 -6.097 -5.698

-0.262 -0.256 -0.25 -0.245 -0.239 -0.233 -0.228 -0.222 -0.216 -0.21 -0.204 -0.198 -0.192 -0.185 -0.179 -0.172 -0.166 -0.159 -0.153 -0.147 -0.14 -0.133 -0.126 -0.12 -0.113 -0.106 -0.099

-0.259 -0.2532 -0.2474 -0.2426 -0.2367 -0.2309 -0.226 -0.2202 -0.2143 -0.2085 -0.2026 -0.1967 -0.1908 -0.1839 -0.178 -0.1712 -0.1652 -0.1583 -0.1524 -0.1465 -0.1395 -0.1326 -0.1257 -0.1197 -0.1128 -0.1058 -0.0988

0.9659 0.9674 0.9689 0.9701 0.9716 0.973 0.9741 0.9755 0.9768 0.978 0.9793 0.9805 0.9816 0.9829 0.984 0.9852 0.9863 0.9874 0.9883 0.9892 0.9902 0.9912 0.9921 0.9928 0.9936 0.9944 0.9951

26.9209697 26.959764 26.996778 27.025029 27.062991 27.0963648 27.1212543 27.1543207 27.1843245 27.2112439 27.2409367 27.2675563 27.2895888 27.320573 27.3422904 27.3681149 27.3910452 27.4122641 27.4277904 27.4445476 27.4626596 27.4804656 27.4954735 27.5045432 27.5164653 27.5281061 27.5369565

ABRIL

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4

1.01473 1.0142 1.01365 1.01311 1.01256 1.01201 1.01145 1.01089 1.01032 1.00976 1.00919 1.00862 1.00806 1.00748 1.00691 1.00633 1.00575 1.00518 1.0046 1.00402 1.00344 1.00286 1.00228 1.0017 1.00112 1.00054 0.99996

1.804 1.8041 1.8043 1.8044 1.8045 1.8046 1.8047 1.8048 1.8049 1.8049 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.8049 1.8048 1.8048 1.8047 1.8046 1.8045 1.8044 1.8042 1.8041

0.03148574 0.03148749 0.03149098 0.03149272 0.03149447 0.03149621 0.03149796 0.0314997 0.03150145 0.03150145 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150145 0.0314997 0.0314997 0.03149796 0.03149621 0.03149447 0.03149272 0.03148923 0.03148749

0.03148054 0.03148228 0.03148577 0.03148752 0.03148926 0.031491 0.03149275 0.03149449 0.03149624 0.03149624 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149624 0.03149449 0.03149449 0.03149275 0.031491 0.03148926 0.03148752 0.03148403 0.03148228

-5.3 -4.901 -4.526 -4.127 -3.705 -3.306 -2.908 -2.533 -2.134 -1.712 -1.313 -0.915 -0.516 -0.117 0.305 0.704 1.102 1.501 1.923 2.322 2.72 3.119 3.518 3.916 4.315 4.713 5.089

-0.093 -0.086 -0.079 -0.072 -0.065 -0.058 -0.051 -0.044 -0.037 -0.03 -0.023 -0.016 -0.009 -0.002 0.005 0.012 0.019 0.026 0.034 0.041 0.047 0.054 0.061 0.068 0.075 0.082 0.089

-0.0929 -0.0859 -0.0789 -0.0719 -0.065 -0.058 -0.051 -0.044 -0.037 -0.03 -0.023 -0.016 -0.009 -0.002 0.005 0.012 0.019 0.026 0.034 0.041 0.047 0.054 0.061 0.0679 0.0749 0.0819 0.0889

0.9957 0.9963 0.9969 0.9974 0.9979 0.9983 0.9987 0.999 0.9993 0.9996 0.9997 0.9999 1 1 1 0.9999 0.9998 0.9997 0.9994 0.9992 0.9989 0.9985 0.9981 0.9977 0.9972 0.9966 0.996

27.5410991 27.5456183 27.5511027 27.5525508 27.5537001 27.5520841 27.5501826 27.5455097 27.5405536 27.5343342 27.5238497 27.5145882 27.5028419 27.4877973 27.4730246 27.4552325 27.4374426 27.4199278 27.3952543 27.3732199 27.3498599 27.3223701 27.294895 27.2674234 27.237247 27.2028526 27.1699888

MAYO

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1

0.99937 0.9988 0.99822 0.99765 0.99707 0.9965 0.99593 0.99536 0.99479 0.99423 0.99367 0.99311 0.99255 0.992 0.99144 0.99089 0.99035 0.98981 0.98927 0.98874 0.98821 0.98768 0.98716 0.98664 0.98613 0.98562 0.98512

1.8039 1.8038 1.8036 1.8034 1.8032 1.803 1.8028 1.8026 1.8024 1.8021 1.8019 1.8016 1.8014 1.8011 1.8008 1.8005 1.8002 1.8 1.7997 1.7993 1.799 1.7988 1.7984 1.7981 1.7977 1.7975 1.7971

0.03148399 0.03148225 0.03147876 0.03147527 0.03147178 0.03146829 0.0314648 0.03146131 0.03145781 0.03145258 0.03144909 0.03144385 0.03144036 0.03143513 0.03142989 0.03142465 0.03141942 0.03141593 0.03141069 0.03140371 0.03139847 0.03139498 0.031388 0.03138277 0.03137578 0.03137229 0.03136531

0.03147879 0.03147705 0.03147356 0.03147007 0.03146658 0.03146309 0.0314596 0.03145612 0.03145263 0.03144739 0.0314439 0.03143867 0.03143518 0.03142995 0.03142471 0.03141948 0.03141425 0.03141076 0.03140553 0.03139855 0.03139331 0.03138983 0.03138285 0.03137761 0.03137064 0.03136715 0.03136017

5.487 5.886 6.285 6.66 7.035 7.457 7.832 8.208 8.583 8.934 9.333 9.685 10.06 10.412 10.764 11.139 11.491 11.842 12.171 12.546 12.874 13.202 13.531 13.859 14.187 14.516 14.82

0.096 0.103 0.11 0.116 0.123 0.13 0.137 0.143 0.15 0.156 0.163 0.169 0.176 0.182 0.188 0.194 0.201 0.207 0.212 0.219 0.225 0.23 0.236 0.242 0.248 0.253 0.259

0.0959 0.1028 0.1098 0.1157 0.1227 0.1296 0.1366 0.1425 0.1494 0.1554 0.1623 0.1682 0.1751 0.181 0.1869 0.1928 0.1996 0.2055 0.2104 0.2173 0.2231 0.228 0.2338 0.2396 0.2455 0.2503 0.2561

0.9954 0.9947 0.994 0.9933 0.9924 0.9916 0.9906 0.9898 0.9888 0.9879 0.9867 0.9858 0.9846 0.9835 0.9824 0.9812 0.9799 0.9787 0.9776 0.9761 0.9748 0.9737 0.9723 0.9709 0.9694 0.9682 0.9666

27.1353712 27.1000894 27.0630722 27.0262334 26.9838381 26.9444544 26.8996858 26.86026 26.8155556 26.7722845 26.7225153 26.6793162 26.6296365 26.5813869 26.5329164 26.482064 26.4289325 26.3799144 26.3320608 26.2725203 26.2197575 26.1737751 26.1172409 26.0622172 26.003398 25.955444 25.894318

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

0.98462 0.98412 0.98363 0.98315 0.98267 0.9822 0.98173 0.98127 0.98081 0.98036 0.97992 0.97948 0.97905 0.97863 0.97821 0.97779 0.97739 0.97699 0.9766 0.97622 0.97584 0.97547 0.97511 0.97475 0.97441 0.97406 0.97373

1.7968 1.7965 1.7961 1.7958 1.7954 1.7951 1.7947 1.7944 1.794 1.7937 1.7934 1.7931 1.7927 1.7924 1.7921 1.7918 1.7915 1.7911 1.7908 1.7906 1.7903 1.7899 1.7897 1.7894 1.7891 1.7889 1.7886

0.03136008 0.03135484 0.03134786 0.03134262 0.03133564 0.03133041 0.03132342 0.03131819 0.03131121 0.03130597 0.03130073 0.0312955 0.03128852 0.03128328 0.03127805 0.03127281 0.03126757 0.03126059 0.03125536 0.03125187 0.03124663 0.03123965 0.03123616 0.03123092 0.03122569 0.03122219 0.03121696

0.03135494 0.0313497 0.03134272 0.03133749 0.03133051 0.03132528 0.0313183 0.03131307 0.03130609 0.03130086 0.03129562 0.03129039 0.03128341 0.03127818 0.03127295 0.03126771 0.03126248 0.0312555 0.03125027 0.03124678 0.03124155 0.03123457 0.03123108 0.03122584 0.03122061 0.03121712 0.03121189

15.125 15.43 15.735 16.04 16.321 16.603 16.907 17.189 17.447 17.705 17.963 18.244 18.479 18.737 18.971 19.206 19.44 19.651 19.862 20.073 20.308 20.495 20.683 20.871 21.058 21.222 21.386

0.264 0.269 0.275 0.28 0.285 0.29 0.295 0.3 0.305 0.309 0.314 0.318 0.323 0.327 0.331 0.335 0.339 0.343 0.347 0.35 0.354 0.358 0.361 0.364 0.368 0.37 0.373

0.2609 0.2658 0.2715 0.2764 0.2812 0.286 0.2907 0.2955 0.3003 0.3041 0.3089 0.3127 0.3174 0.3212 0.325 0.3288 0.3325 0.3363 0.3401 0.3429 0.3467 0.3504 0.3532 0.356 0.3598 0.3616 0.3644

0.9654 0.964 0.9624 0.9611 0.9597 0.9582 0.9568 0.9553 0.9538 0.9526 0.9511 0.9499 0.9483 0.947 0.9457 0.9444 0.9431 0.9417 0.9404 0.9394 0.938 0.9366 0.9355 0.9345 0.933 0.9323 0.9312

25.8452854 25.7909658 25.7302751 25.6792608 25.6241909 25.5681981 25.5134919 25.4578698 25.4008863 25.3535003 25.2985542 25.2515172 25.1928594 25.1437784 25.0947418 25.0457493 24.9973019 24.9448703 24.8967778 24.8581888 24.8077861 24.7562878 24.715669 24.6763379 24.6244745 24.5946333 24.5535193

JUNIO

29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.97341 0.97309 0.97278 0.97248 0.97218 0.97189 0.97162 0.97135 0.97109 0.97083 0.97059 0.97035 0.97012 0.9699 0.96969 0.96949 0.9693 0.96911 0.96893 0.96877 0.96861 0.96846 0.96831 0.96818 0.96806 0.96794 0.96784

1.7884 1.7881 1.788 1.7877 1.7875 1.7872 1.7871 1.7869 1.7867 1.7865 1.7864 1.7862 1.7862 1.786 1.7859 1.7858 1.7857 1.7856 1.7855 1.7855 1.7855 1.7854 1.7854 1.7854 1.7854 1.7854 1.7854

0.03121347 0.03120823 0.03120649 0.03120125 0.03119776 0.03119252 0.03119078 0.03118729 0.0311838 0.03118031 0.03117856 0.03117507 0.03117507 0.03117158 0.03116984 0.03116809 0.03116634 0.0311646 0.03116285 0.03116285 0.03116285 0.03116111 0.03116111 0.03116111 0.03116111 0.03116111 0.03116111

0.0312084 0.03120317 0.03120142 0.03119619 0.0311927 0.03118747 0.03118572 0.03118223 0.03117874 0.03117526 0.03117351 0.03117002 0.03117002 0.03116653 0.03116479 0.03116304 0.0311613 0.03115955 0.03115781 0.03115781 0.03115781 0.03115607 0.03115607 0.03115607 0.03115607 0.03115607 0.03115607

21.551 21.715 21.855 21.996 22.137 22.278 22.395 22.512 22.629 22.723 22.817 22.911 23.004 23.075 23.145 23.192 23.262 23.309 23.356 23.38 23.403 23.427 23.45 23.45 23.45 23.45 23.427

0.376 0.379 0.381 0.384 0.386 0.389 0.391 0.393 0.395 0.397 0.398 0.4 0.401 0.403 0.404 0.405 0.406 0.407 0.408 0.408 0.408 0.409 0.409 0.409 0.409 0.409 0.409

0.3672 0.37 0.3718 0.3746 0.3765 0.3793 0.3811 0.383 0.3848 0.3867 0.3876 0.3894 0.3903 0.3922 0.3931 0.394 0.3949 0.3959 0.3968 0.3968 0.3968 0.3977 0.3977 0.3977 0.3977 0.3977 0.3977

0.9301 0.929 0.9283 0.9272 0.9264 0.9253 0.9245 0.9238 0.923 0.9222 0.9218 0.9211 0.9207 0.9199 0.9195 0.9191 0.9187 0.9183 0.9179 0.9179 0.9179 0.9175 0.9175 0.9175 0.9175 0.9175 0.9175

24.5140592 24.4732579 24.4458813 24.4056346 24.3745649 24.3346224 24.3056952 24.2780588 24.2480545 24.2180781 24.2003483 24.1735079 24.1573964 24.1284688 24.1115189 24.0948238 24.0783831 24.0619588 24.0457777 24.0418071 24.0378364 24.0224089 24.0186881 24.0154635 24.012487 24.0095104 24.0070299

JULIO

25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0.96774 0.96765 0.96757 0.9675 0.96744 0.96739 0.96734 0.96731 0.96728 0.96727 0.96726 0.96726 0.96728 0.9673 0.96732 0.96736 0.96741 0.96747 0.96753 0.96761 0.96769 0.96778 0.96789 0.968 0.96811 0.96824 0.96838

1.7855 1.7855 1.7855 1.7856 1.7857 1.7858 1.7859 1.786 1.7862 1.7862 1.7864 1.7865 1.7867 1.7869 1.7871 1.7872 1.7875 1.7877 1.788 1.7881 1.7884 1.7886 1.7889 1.7891 1.7894 1.7897 1.7899

0.03116285 0.03116285 0.03116285 0.0311646 0.03116634 0.03116809 0.03116984 0.03117158 0.03117507 0.03117507 0.03117856 0.03118031 0.0311838 0.03118729 0.03119078 0.03119252 0.03119776 0.03120125 0.03120649 0.03120823 0.03121347 0.03121696 0.03122219 0.03122569 0.03123092 0.03123616 0.03123965

0.03115781 0.03115781 0.03115781 0.03115955 0.0311613 0.03116304 0.03116479 0.03116653 0.03117002 0.03117002 0.03117351 0.03117526 0.03117874 0.03118223 0.03118572 0.03118747 0.0311927 0.03119619 0.03120142 0.03120317 0.0312084 0.03121189 0.03121712 0.03122061 0.03122584 0.03123108 0.03123457

23.403 23.38 23.356 23.309 23.262 23.192 23.145 23.075 22.981 22.911 22.817 22.723 22.629 22.512 22.395 22.278 22.137 22.02 21.855 21.715 21.551 21.41 21.222 21.058 20.871 20.683 20.495

0.408 0.408 0.408 0.407 0.406 0.405 0.404 0.403 0.401 0.4 0.398 0.397 0.395 0.393 0.391 0.389 0.386 0.384 0.381 0.379 0.376 0.374 0.37 0.368 0.364 0.361 0.358

0.3968 0.3968 0.3968 0.3959 0.3949 0.394 0.3931 0.3922 0.3903 0.3894 0.3876 0.3867 0.3848 0.383 0.3811 0.3793 0.3765 0.3746 0.3718 0.37 0.3672 0.3653 0.3616 0.3598 0.356 0.3532 0.3504

0.9179 0.9179 0.9179 0.9183 0.9187 0.9191 0.9195 0.9199 0.9207 0.9211 0.9218 0.9222 0.923 0.9238 0.9245 0.9253 0.9264 0.9272 0.9283 0.929 0.9301 0.9309 0.9323 0.933 0.9345 0.9355 0.9366

24.0162457 24.0140122 24.0120268 24.0219842 24.0321789 24.0426323 24.0530857 24.0640367 24.0866763 24.0967785 24.1173193 24.1290218 24.1529191 24.1768325 24.1981279 24.2211982 24.2549712 24.2799022 24.3139492 24.3354356 24.3700085 24.3957303 24.4388433 24.4624863 24.5082426 24.5415382 24.5763519

AGOSTO

22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.96853 0.96868 0.96885 0.96902 0.9692 0.96939 0.96959 0.96979 0.97001 0.97023 0.97046 0.9707 0.97095 0.97121 0.97147 0.97175 0.97203 0.97232 0.97262 0.97292 0.97324 0.97356 0.97389 0.97422 0.97457 0.97492 0.97528

1.7903 1.7906 1.7908 1.7911 1.7915 1.7918 1.7921 1.7924 1.7927 1.7931 1.7934 1.7937 1.794 1.7944 1.7947 1.7951 1.7954 1.7958 1.7961 1.7965 1.7968 1.7971 1.7975 1.7977 1.7981 1.7984 1.7988

0.03124663 0.03125187 0.03125536 0.03126059 0.03126757 0.03127281 0.03127805 0.03128328 0.03128852 0.0312955 0.03130073 0.03130597 0.03131121 0.03131819 0.03132342 0.03133041 0.03133564 0.03134262 0.03134786 0.03135484 0.03136008 0.03136531 0.03137229 0.03137578 0.03138277 0.031388 0.03139498

0.03124155 0.03124678 0.03125027 0.0312555 0.03126248 0.03126771 0.03127295 0.03127818 0.03128341 0.03129039 0.03129562 0.03130086 0.03130609 0.03131307 0.0313183 0.03132528 0.03133051 0.03133749 0.03134272 0.0313497 0.03135494 0.03136017 0.03136715 0.03137064 0.03137761 0.03138285 0.03138983

20.284 20.073 19.886 19.651 19.44 19.206 18.971 18.737 18.502 18.221 17.986 17.705 17.447 17.189 16.884 16.626 16.321 16.04 15.758 15.43 15.125 14.82 14.516 14.187 13.859 13.531 13.202

0.354 0.35 0.347 0.343 0.339 0.335 0.331 0.327 0.323 0.318 0.314 0.309 0.305 0.3 0.295 0.29 0.285 0.28 0.275 0.269 0.264 0.259 0.253 0.248 0.242 0.236 0.23

0.3467 0.3429 0.3401 0.3363 0.3325 0.3288 0.325 0.3212 0.3174 0.3127 0.3089 0.3041 0.3003 0.2955 0.2907 0.286 0.2812 0.2764 0.2715 0.2658 0.2609 0.2561 0.2503 0.2455 0.2396 0.2338 0.228

0.938 0.9394 0.9404 0.9417 0.9431 0.9444 0.9457 0.947 0.9483 0.9499 0.9511 0.9526 0.9538 0.9553 0.9568 0.9582 0.9597 0.9611 0.9624 0.964 0.9654 0.9666 0.9682 0.9694 0.9709 0.9723 0.9737

24.6219514 24.6661924 24.6992045 24.7413773 24.787838 24.8305863 24.8736066 24.9166538 24.9602426 25.0130473 25.0543258 25.103679 25.1455334 25.1968752 25.2468519 25.2961683 25.3467413 25.396388 25.4422702 25.4974459 25.5465719 25.5904583 25.6465447 25.6893415 25.7433866 25.7934079 25.8451719

SETIEMBRE

18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13

0.97564 0.97602 0.9764 0.97678 0.97718 0.97758 0.97799 0.97841 0.97882 0.97925 0.97968 0.98013 0.98057 0.98103 0.98148 0.98195 0.98242 0.98289 0.98337 0.98386 0.98435 0.98485 0.98535 0.98585 0.98636 0.98688 0.9874

1.799 1.7993 1.7996 1.8 1.8002 1.8005 1.8008 1.8011 1.8014 1.8016 1.8019 1.8021 1.8024 1.8026 1.8028 1.803 1.8032 1.8034 1.8036 1.8038 1.8039 1.8041 1.8042 1.8044 1.8045 1.8046 1.8047

0.03139847 0.03140371 0.03140895 0.03141593 0.03141942 0.03142465 0.03142989 0.03143513 0.03144036 0.03144385 0.03144909 0.03145258 0.03145781 0.03146131 0.0314648 0.03146829 0.03147178 0.03147527 0.03147876 0.03148225 0.03148399 0.03148749 0.03148923 0.03149272 0.03149447 0.03149621 0.03149796

0.03139331 0.03139855 0.03140378 0.03141076 0.03141425 0.03141948 0.03142471 0.03142995 0.03143518 0.03143867 0.0314439 0.03144739 0.03145263 0.03145612 0.0314596 0.03146309 0.03146658 0.03147007 0.03147356 0.03147705 0.03147879 0.03148228 0.03148403 0.03148752 0.03148926 0.031491 0.03149275

12.874 12.522 12.194 11.842 11.491 11.139 10.764 10.412 10.06 9.708 9.31 8.934 8.583 8.208 7.832 7.434 7.058 6.66 6.285 5.909 5.487 5.112 4.713 4.315 3.916 3.518 3.119

0.225 0.219 0.213 0.207 0.201 0.194 0.188 0.182 0.176 0.169 0.162 0.156 0.15 0.143 0.137 0.13 0.123 0.116 0.11 0.103 0.096 0.089 0.082 0.075 0.068 0.061 0.054

0.2231 0.2173 0.2114 0.2055 0.1996 0.1928 0.1869 0.181 0.1751 0.1682 0.1613 0.1554 0.1494 0.1425 0.1366 0.1296 0.1227 0.1157 0.1098 0.1028 0.0959 0.0889 0.0819 0.0749 0.0679 0.061 0.054

0.9748 0.9761 0.9774 0.9787 0.9799 0.9812 0.9824 0.9835 0.9846 0.9858 0.9869 0.9879 0.9888 0.9898 0.9906 0.9916 0.9924 0.9933 0.994 0.9947 0.9954 0.996 0.9966 0.9972 0.9977 0.9981 0.9985

25.886243 25.934528 25.9828433 26.0326455 26.0774718 26.1263471 26.1729676 26.2172326 26.2612672 26.3069755 26.3515144 26.3926045 26.4322413 26.4735581 26.5093968 26.5510356 26.5873632 26.6263865 26.6604689 26.6947277 26.727541 26.7594338 26.7898643 26.8217995 26.849851 26.8755098 26.9011709

OCTUBRE

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10

0.98792 0.98845 0.98898 0.98952 0.99006 0.9906 0.99115 0.9917 0.99225 0.9928 0.99336 0.99392 0.99449 0.99505 0.99562 0.99619 0.99676 0.99733 0.99791 0.99848 0.99906 0.99964 1.00022 1.0008 1.00138 1.00196 1.00254

1.8048 1.8048 1.8049 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.805 1.8049 1.8049 1.8048 1.8047 1.8046 1.8045 1.8044 1.8043 1.8041 1.804 1.8039 1.8037 1.8035 1.8033 1.8031 1.8029

0.0314997 0.0314997 0.03150145 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150319 0.03150145 0.03150145 0.0314997 0.03149796 0.03149621 0.03149447 0.03149272 0.03149098 0.03148749 0.03148574 0.03148399 0.0314805 0.03147701 0.03147352 0.03147003 0.03146654

0.03149449 0.03149449 0.03149624 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149798 0.03149624 0.03149624 0.03149449 0.03149275 0.031491 0.03148926 0.03148752 0.03148577 0.03148228 0.03148054 0.03147879 0.0314753 0.03147182 0.03146833 0.03146484 0.03146135

2.72 2.322 1.899 1.501 1.102 0.704 0.305 -0.117 -0.516 -0.915 -1.313 -1.735 -2.111 -2.509 -2.908 -3.306 -3.729 -4.127 -4.502 -4.901 -5.3 -5.698 -6.097 -6.472 -6.847 -7.246 -7.645

0.047 0.041 0.033 0.026 0.019 0.012 0.005 -0.002 -0.009 -0.016 -0.023 -0.03 -0.037 -0.044 -0.051 -0.058 -0.065 -0.072 -0.079 -0.086 -0.093 -0.099 -0.106 -0.113 -0.12 -0.126 -0.133

0.047 0.041 0.033 0.026 0.019 0.012 0.005 -0.002 -0.009 -0.016 -0.023 -0.03 -0.037 -0.044 -0.051 -0.058 -0.065 -0.0719 -0.0789 -0.0859 -0.0929 -0.0988 -0.1058 -0.1128 -0.1197 -0.1257 -0.1326

0.9989 0.9992 0.9995 0.9997 0.9998 0.9999 1 1 1 0.9999 0.9997 0.9996 0.9993 0.999 0.9987 0.9983 0.9979 0.9974 0.9969 0.9963 0.9957 0.9951 0.9944 0.9936 0.9928 0.9921 0.9912

26.9268453 26.9487254 26.9718887 26.9927446 27.0094103 27.0260782 27.043021 27.0572603 27.0714986 27.0830274 27.0921148 27.102406 27.1090399 27.1138892 27.1190002 27.1213829 27.1237518 27.1233978 27.123288 27.118664 27.1157948 27.1130273 27.1058893 27.0960008 27.0860987 27.0790024 27.0663202

NOVIEMBRE

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6

1.00312 1.0037 1.00428 1.00486 1.00544 1.00601 1.00659 1.00717 1.00774 1.00831 1.00888 1.00945 1.01001 1.01058 1.01114 1.0117 1.01225 1.0128 1.01335 1.0139 1.01444 1.01497 1.01551 1.01604 1.01656 1.01709 1.0176

1.8027 1.8025 1.8022 1.802 1.8018 1.8015 1.8013 1.801 1.8006 1.8004 1.8001 1.7998 1.7995 1.7992 1.7989 1.7986 1.7983 1.7979 1.7976 1.7973 1.7969 1.7966 1.7963 1.796 1.7956 1.7953 1.7949

0.03146305 0.03145956 0.03145432 0.03145083 0.03144734 0.03144211 0.03143862 0.03143338 0.0314264 0.03142291 0.03141767 0.03141244 0.0314072 0.03140196 0.03139673 0.03139149 0.03138626 0.03137927 0.03137404 0.0313688 0.03136182 0.03135659 0.03135135 0.03134611 0.03133913 0.0313339 0.03132691

0.03145786 0.03145437 0.03144914 0.03144565 0.03144216 0.03143693 0.03143344 0.0314282 0.03142123 0.03141774 0.0314125 0.03140727 0.03140204 0.0313968 0.03139157 0.03138634 0.0313811 0.03137413 0.03136889 0.03136366 0.03135668 0.03135145 0.03134621 0.03134098 0.031334 0.03132877 0.03132179

-8.02 -8.395 -8.747 -9.146 -9.521 -9.872 -10.224 -10.599 -10.975 -11.326 -11.655 -12.006 -12.358 -12.71 -13.038 -13.367 -13.695 -14.023 -14.351 -14.656 -14.985 -15.289 -15.594 -15.899 -16.181 -16.462 -16.767

-0.14 -0.147 -0.153 -0.16 -0.166 -0.172 -0.178 -0.185 -0.192 -0.198 -0.203 -0.21 -0.216 -0.222 -0.228 -0.233 -0.239 -0.245 -0.25 -0.256 -0.262 -0.267 -0.272 -0.277 -0.282 -0.287 -0.293

-0.1395 -0.1465 -0.1524 -0.1593 -0.1652 -0.1712 -0.1771 -0.1839 -0.1908 -0.1967 -0.2016 -0.2085 -0.2143 -0.2202 -0.226 -0.2309 -0.2367 -0.2426 -0.2474 -0.2532 -0.259 -0.2638 -0.2687 -0.2735 -0.2783 -0.2831 -0.2888

0.9902 0.9892 0.9883 0.9872 0.9863 0.9852 0.9842 0.9829 0.9816 0.9805 0.9795 0.978 0.9768 0.9755 0.9741 0.973 0.9716 0.9701 0.9689 0.9674 0.9659 0.9646 0.9632 0.9619 0.9605 0.9591 0.9574

27.0508774 27.0353938 27.0212395 27.0029725 26.9902609 26.9702672 26.954759 26.9294006 26.9022355 26.8836227 26.866343 26.8350822 26.8118819 26.7861562 26.7573935 26.7369475 26.7078537 26.6744787 26.6509352 26.6189864 26.5852602 26.5583418 26.5288858 26.5019052 26.4704007 26.4405998 26.4003933

DICIEMBRE

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3

1.01811 1.01862 1.01912 1.01961 1.0201 1.02059 1.02106 1.02154 1.022 1.02246 1.02291 1.02336 1.0238 1.02423 1.02465 1.02507 1.02548 1.02589 1.02628 1.02667 1.02705 1.02742 1.02778 1.02813 1.02848 1.02882 1.02914

1.7945 1.7942 1.7939 1.7936 1.7932 1.7929 1.7926 1.7923 1.792 1.7916 1.7913 1.791 1.7907 1.7904 1.7901 1.7898 1.7895 1.7893 1.789 1.7887 1.7885 1.7882 1.7881 1.7878 1.7876 1.7873 1.7871

0.03131993 0.0313147 0.03130946 0.03130423 0.03129724 0.03129201 0.03128677 0.03128154 0.0312763 0.03126932 0.03126408 0.03125885 0.03125361 0.03124837 0.03124314 0.0312379 0.03123267 0.03122918 0.03122394 0.0312187 0.03121521 0.03120998 0.03120823 0.031203 0.03119951 0.03119427 0.03119078

0.03131481 0.03130958 0.03130435 0.03129911 0.03129214 0.0312869 0.03128167 0.03127643 0.0312712 0.03126422 0.03125899 0.03125376 0.03124852 0.03124329 0.03123806 0.03123282 0.03122759 0.0312241 0.03121887 0.03121363 0.03121014 0.03120491 0.03120317 0.03119793 0.03119444 0.03118921 0.03118572

-17.048 -17.306 -17.588 -17.845 -18.103 -18.361 -18.619 -18.854 -19.088 -19.323 -19.557 -19.768 -19.979 -20.19 -20.402 -20.589 -20.777 -20.964 -21.152 -21.316 -21.48 -21.644 -21.785 -21.926 -22.066 -22.207 -22.324

-0.298 -0.302 -0.307 -0.311 -0.316 -0.32 -0.325 -0.329 -0.333 -0.337 -0.341 -0.345 -0.349 -0.352 -0.356 -0.359 -0.363 -0.366 -0.369 -0.372 -0.375 -0.378 -0.38 -0.383 -0.385 -0.388 -0.39

-0.2936 -0.2974 -0.3022 -0.306 -0.3108 -0.3146 -0.3193 -0.3231 -0.3269 -0.3307 -0.3344 -0.3382 -0.342 -0.3448 -0.3485 -0.3513 -0.3551 -0.3579 -0.3607 -0.3635 -0.3663 -0.3691 -0.3709 -0.3737 -0.3756 -0.3783 -0.3802

0.9559 0.9547 0.9532 0.952 0.9505 0.9492 0.9477 0.9464 0.9451 0.9438 0.9424 0.9411 0.9397 0.9387 0.9373 0.9362 0.9348 0.9338 0.9327 0.9316 0.9305 0.9294 0.9287 0.9275 0.9268 0.9257 0.9249

26.3657785 26.3410012 26.3075365 26.2821877 26.2469428 26.218776 26.1844349 26.1559572 26.1269421 26.0964463 26.0643702 26.0350281 26.0026371 25.9811682 25.9482367 25.9237035 25.8904652 25.8698611 25.8445152 25.8191528 25.7949648 25.7690672 25.7570073 25.7278009 25.7140138 25.6873204 25.6699812

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1.02946 1.02977 1.03007 1.03037 1.03065 1.03092 1.03118 1.03144 1.03168 1.03192 1.03214 1.03235 1.03256 1.03275 1.03294 1.03311 1.03327 1.03343 1.03357 1.0337 1.03382 1.03393 1.03403 1.03412 1.0342 1.03427 1.03433

1.787 1.7868 1.7866 1.7865 1.7863 1.7862 1.7861 1.786 1.7859 1.7858 1.7857 1.7856 1.7855 1.7855 1.7854 1.7854 1.7854 1.7854 1.7854 1.7854 1.7854 1.7855 1.7855 1.7856 1.7857 1.7857 1.7859

0.03118903 0.03118554 0.03118205 0.03118031 0.03117682 0.03117507 0.03117333 0.03117158 0.03116984 0.03116809 0.03116634 0.0311646 0.03116285 0.03116285 0.03116111 0.03116111 0.03116111 0.03116111 0.03116111 0.03116111 0.03116111 0.03116285 0.03116285 0.0311646 0.03116634 0.03116634 0.03116984

0.03118398 0.03118049 0.031177 0.03117526 0.03117177 0.03117002 0.03116828 0.03116653 0.03116479 0.03116304 0.0311613 0.03115955 0.03115781 0.03115781 0.03115607 0.03115607 0.03115607 0.03115607 0.03115607 0.03115607 0.03115607 0.03115781 0.03115781 0.03115955 0.0311613 0.0311613 0.03116479

-22.465 -22.559 -22.676 -22.77 -22.864 -22.958 -23.028 -23.098 -23.169 -23.216 -23.286 -23.333 -23.356 -23.403 -23.427 -23.427 -23.45 -23.45 -23.45 -23.427 -23.427 -23.403 -23.356 -23.333 -23.286 -23.239 -23.169

-0.392 -0.394 -0.396 -0.397 -0.399 -0.401 -0.402 -0.403 -0.404 -0.405 -0.406 -0.407 -0.408 -0.408 -0.409 -0.409 -0.409 -0.409 -0.409 -0.409 -0.409 -0.408 -0.408 -0.407 -0.406 -0.406 -0.404

-0.382 -0.3839 -0.3857 -0.3867 -0.3885 -0.3903 -0.3913 -0.3922 -0.3931 -0.394 -0.3949 -0.3959 -0.3968 -0.3968 -0.3977 -0.3977 -0.3977 -0.3977 -0.3977 -0.3977 -0.3977 -0.3968 -0.3968 -0.3959 -0.3949 -0.3949 -0.3931

0.9241 0.9234 0.9226 0.9222 0.9214 0.9207 0.9203 0.9199 0.9195 0.9191 0.9187 0.9183 0.9179 0.9179 0.9175 0.9175 0.9175 0.9175 0.9175 0.9175 0.9175 0.9179 0.9179 0.9183 0.9187 0.9187 0.9195

25.6540777 25.6392487 25.6213911 25.6161766 25.597804 25.5833897 25.5771609 25.5709382 25.5642148 25.5574868 25.550259 25.5427684 25.5352852 25.5399839 25.532 25.5362021 25.5401569 25.5441118 25.5475723 25.5507856 25.5537517 25.5691654 25.5716384 25.5865624 25.6012536 25.6029864 25.6298797

31

1.03437

1.786 0.03117158 0.03116653

4.5. Radiación solar mensual PROMEDIO MENSUAL Qs MES Qs ENERO 26.05791952 FEBRERO 27.05365968 MARZO 27.48342763 ABRIL 26.66838175 MAYO 25.12078993 JUNIO 24.11737346 JULIO 24.44787598 AGOSTO 25.78160006 SEPTIEMBRE 26.90888779 OCTUBRE 26.9290268 NOVIEMBRE 26.12181694 DICIEMBRE 25.58810142

-23.098

-0.403

-0.3922

0.9199 25.6435773

4.6. Horas Solares Diarias HORAS DEL DÍA SOLAR Mes

Enero

FEBRERO

N° deDia Hora de salida Horade puesta N (horas) 1 05:41 18:35 12.9 2 05:42 18:35 12.883 05:43 3 18:36 12.883 05:43 4 18:36 12.883 5 05:44 18:36 12.867 6 05:44 18:37 12.883 7 05:45 18:37 12.867 8 05:45 18:37 12.867 9 05:46 18:37 12.85 10 05:47 18:38 12.85 11 05:47 18:38 12.85 12 05:48 18:38 12.833 13 05:48 18:38 12.833 14 05:49 18:39 12.833 15 05:49 18:39 12.833 16 05:50 18:39 12.817 17 05:51 18:39 12.8 18 05:51 18:39 12.8 19 05:52 18:39 12.783 20 05:52 18:40 12.8 21 05:53 18:40 12.783 22 05:54 18:40 12.767 23 05:54 18:40 12.767 24 05:54 18:40 12.767 25 05:55 18:40 12.75 26 05:55 18:40 12.75 27 05:56 18:40 12.73 28 05:56 18:40 12.73 29 05:57 18:40 12.717 30 05:57 18:39 12.7 31 05:58 18:39 12.683 1 05:58 18:39 12.683 2 05:59 18:39 12.667 3 05:59 18:39 12.667 4 05:59 18:39 12.667 5 06:00 18:39 12.65 6 06:00 18:38 12.633 7 06:01 18:38 12.617 8 06:01 18:38 12.617 9 06:01 18:38 12.617

MARZO

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

06:02 06:02 06:03 06:03 06:03 06:04 06:04 06:04 06:04 06:05 06:05 06:05 06:05 06:06 06:06 06:06 06:06 06:07 06:07 06:07 06:07 06:07 06:08 06:08 06:08 06:08 06:08 06:08 06:08 06:09 06:09 06:09 06:09 06:09 06:09 06:09 06:09 06:09 06:09 06:09 06:09 06:10 06:10 06:10 06:10

18:37 18:37 18:37 18:36 18:36 18:36 18:35 18:35 18:35 18:34 18:34 18:33 18:33 18:32 18:32 18:31 18:31 18:30 18:30 18:29 18:28 18:28 18:27 18:26 18:26 18:25 18:25 18:24 18:23 18:23 18:22 18:22 18:21 18:20 18:20 18:19 18:18 18:18 18:17 18:16 18:16 18:15 18:14 18:14 18:13

12.583 12.583 12.567 12.55 12.55 12.533 12.517 12.517 12.517 12.483 12.483 12.467 12.467 12.433 12.433 12.417 12.417 12.383 12.383 12.367 12.35 12.35 12.317 12.3 12.3 12.283 12.283 12.267 12.25 12.233 12.217 12.217 12.2 12.183 12.183 12.167 12.15 12.15 12.133 12.117 12.117 12.083 12.067 12.067 12.05

ABRIL

MAYO

27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10

06:10 06:10 06:10 06:10 06:10 06:10 06:10 06:10 06:10 06:10 06:10 06:10 06:11 06:11 06:11 06:11 06:11 06:11 06:11 06:11 06:11 06:11 06:11 06:11 06:12 06:12 06:12 06:12 06:12 06:12 06:12 06:12 06:13 06:13 06:13 06:13 06:13 06:13 06:14 06:14 06:14 06:14 06:14 06:15 06:15

18:12 18:12 18:11 18:10 18:10 18:09 18:08 18:08 18:07 18:06 18:06 18:05 18:04 18:04 18:03 18:03 18:02 18:01 18:01 18:00 18:00 17:59 17:58 17:58 17:57 17:57 17:56 17:56 17:55 17:55 17:54 17:54 17:53 17:53 17:52 17:52 17:52 17:51 17:51 17:50 17:50 17:50 17:49 17:49 17:49

12.033 12.033 12.017 12 12 11.983 11.967 11.967 11.95 11.933 11.933 11.917 11.883 11.883 11.867 11.867 11.85 11.833 11.833 11.817 11.817 11.8 11.783 11.783 11.75 11.75 11.733 11.733 11.717 11.717 11.7 11.7 11.667 11.667 11.65 11.65 11.65 11.633 11.617 11.6 11.6 11.6 11.583 11.567 11.567

JUNIO

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

06:15 06:15 06:16 06:16 06:16 06:16 06:17 06:17 06:17 06:17 06:18 06:18 06:18 06:18 06:19 06:19 06:19 06:20 06:20 06:20 06:20 06:21 06:21 06:21 06:22 06:22 06:22 06:22 06:23 06:23 06:23 06:24 06:24 06:24 06:24 06:25 06:25 06:25 06:25 06:26 06:26 06:26 06:26 06:27 06:27

17:48 17:48 17:48 17:48 17:47 17:47 17:47 17:47 17:46 17:46 17:46 17:46 17:46 17:46 17:46 17:46 17:45 17:45 17:45 17:45 17:45 17:45 17:45 17:45 17:45 17:45 17:45 17:45 17:46 17:46 17:46 17:46 17:46 17:46 17:46 17:46 17:47 17:47 17:47 17:47 17:47 17:48 17:48 17:48 17:48

11.55 11.55 11.533 11.533 11.517 11.517 11.5 11.5 11.483 11.483 11.467 11.467 11.467 11.467 11.45 11.45 11.433 11.417 11.417 11.417 11.417 11.4 11.4 11.4 11.383 11.383 11.383 11.383 11.383 11.383 11.383 11.367 11.367 11.367 11.367 11.35 11.367 11.367 11.367 11.35 11.35 11.367 11.367 11.35 11.35

JULIO

AGOSTO

25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8

06:27 06:27 06:27 06:28 06:28 06:28 06:28 06:28 06:28 06:28 06:28 06:29 06:29 06:29 06:29 06:29 06:29 06:29 06:29 06:29 06:29 06:29 06:29 06:28 06:28 06:28 06:28 06:28 06:28 06:28 06:27 06:27 06:27 06:27 06:27 06:26 06:26 06:26 06:25 06:25 06:25 06:24 06:24 06:24 06:23

17:48 17:49 17:49 17:49 17:49 17:50 17:50 17:50 17:51 17:51 17:51 17:51 17:52 17:52 17:52 17:52 17:53 17:53 17:53 17:54 17:54 17:54 17:54 15:55 15:55 15:55 15:55 17:56 17:56 17:56 17:56 17:57 17:57 17:57 17:57 17:57 17:58 17:58 17:58 17:58 17:58 17:59 17:59 17:59 17:59

11.35 11.367 11.367 11.35 11.35 11.367 11.367 11.367 11.383 11.383 11.383 11.367 11.383 11.383 11.383 11.383 11.4 11.4 11.4 11.417 11.417 11.417 11.417 11.45 11.45 11.45 11.45 11.467 11.467 11.467 11.483 11.5 11.5 11.5 11.5 11.517 11.533 11.533 11.55 11.55 11.55 11.583 11.583 11.583 11.6

SETIEMBRE

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

06:23 06:22 06:22 06:22 06:21 06:21 06:20 06:20 06:19 06:19 06:18 06:18 06:17 06:17 06:16 06:15 06:15 06:14 06:14 06:13 06:12 06:12 06:11 06:10 06:10 06:09 06:08 06:07 06:07 06:06 06:06 06:05 06:04 06:04 06:03 06:02 06:02 06:01 06:00 05:59 05:59 05:58 05:57 05:57 05:56

17:59 17:59 18:00 18:00 18:00 18:00 18:00 18:00 18:00 18:00 18:00 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01

11.6 11.617 11.633 11.633 11.65 11.65 11.667 11.667 11.683 11.683 11.7 11.717 11.733 11.733 11.75 11.767 11.767 11.783 11.783 11.8 11.817 11.817 11.833 11.85 11.85 11.867 11.883 11.9 11.9 11.917 11.917 11.933 11.95 11.95 11.967 11.983 11.983 12 12.017 12.033 12.033 12.05 12.067 12.067 12.083

OCTUBRE

NOVIEMBRE

23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6

05:55 05:54 05:54 05:53 05:53 05:52 05:51 05:50 05:49 05:49 05:48 05:47 05:47 05:46 05:45 05:45 05:44 05:43 05:43 05:42 05:42 05:41 05:40 05:40 05:39 05:39 05:38 05:38 05:37 05:37 05:36 05:36 05:35 05:35 05:34 05:34 05:33 05:33 05:33 05:32 05:32 05:31 05:31 05:31 05:31

18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:01 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:02 18:03 18:03 18:03 18:03 18:03 18:03 18:03 18:04 18:04 18:04 18:04 18:05 18:05 18:05 18:05 18:06 18:06 18:06 18:06 18:07 18:07 18:07 18:08

12.1 12.117 12.117 12.133 12.133 12.15 12.167 12.183 12.2 12.217 12.233 12.25 12.25 12.267 12.283 12.283 12.3 12.317 12.317 12.333 12.333 12.35 12.383 12.383 12.4 12.4 12.417 12.417 12.433 12.45 12.467 12.467 12.483 12.5 12.517 12.517 12.533 12.55 12.55 12.567 12.567 12.6 12.6 12.6 12.617

DICIEMBRE

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

05:30 05:30 05:30 05:30 05:29 05:29 05:29 05:29 05:29 05:29 05:28 05:28 05:28 05:28 05:28 05:28 05:28 05:28 05:28 05:28 05:29 05:29 05:29 05:29 05:29 05:29 05:30 05:30 05:30 05:30 05:31 05:31 05:31 05:31 05:32 05:32 05:33 05:33 05:33 05:34 05:34 05:35 05:35 05:36 05:36

18:08 18:08 18:09 18:09 18:09 18:10 18:10 18:11 18:11 18:12 18:12 18:12 18:13 18:13 18:14 18:14 18:15 18:15 18:16 18:16 18:17 18:17 18:18 18:19 18:19 18:20 18:20 18:21 18:21 18:22 18:22 18:23 18:23 18:24 18:25 18:25 18:26 18:26 18:27 18:27 18:28 18:28 18:29 18:29 18:30

12.633 12.633 12.65 12.65 12.667 12.683 12.683 12.7 12.7 12.717 12.733 12.733 12.75 12.75 12.767 12.767 12.783 12.783 12.8 12.8 12.8 12.8 12.817 12.833 12.833 12.85 12.833 12.85 12.85 12.867 12.85 12.867 12.867 12.883 12.883 12.883 12.883 12.883 12.9 12.883 12.9 12.883 12.9 12.883 12.9

22 23 24 25 26 27 28 29 30 31

05:37 05:37 05:38 05:38 05:39 05:39 05:40 05:40 05:41 05:41

18:30 18:31 18:31 18:32 18:32 18:33 18:33 18:34 18:34 18:35

12.833 12.9 12.883 12.9 12.883 12.9 12.833 12.9 12.883 12.9

4.7. Horas solares mensuales PROMEDIO mensual de HORA SOLAR (N) MES N ENERO 12.8084 FEBRERO 12.5393 MARZO 12.1769 ABRIL 11.815 MAYO 11.5194 JUNIO 11.3695 JULIO 11.4317 AGOSTO 11.6779 SEPTIEMBRE 12.01 OCTUBRE 12.3806 NOVIEMBRE 12.7061 DICIEMBRE 12.8757

4.8. Radiación incidente (Qi) y radiación de absorción, dispersada y reflejada (Qadr)

DETERMINANDO LA RADIACIÓN INCIDENTE Qs PARA EL CASO DE LA ESTACIÓN METEOROLOGICA DE CAÑETE

Qi = Qs ((a+b)x(Tma  Tmi)) / N Qadr = Qs  Qi

PROMEDIO DE N Y Qs MES

N

Qs

Temperaturas en el 2000 T máx

T min

Radiación de incidente

Radiación absorb., disper. y reflej.

Qi

Qadr

ENERO FEBRERO MARZO ABRIL MAYO JUNIO JULIO AGOSTO SEPTIEMBRE OCTUBRE NOVIEMBRE DICIEMBRE

12.8084 12.5393 12.1769 11.815 11.5194 11.3695 11.4317 11.6779 12.01 12.3806 12.7061 12.8757

26.0579195 27.0536597 27.4834276 26.6683817 25.1207899 24.1173735 24.447876 25.7816001 26.9088878 26.9290268 26.1218169 25.5881014

27.2 28.7 28.3 27.6 23.9 20.4 19.2 19.2 20.6 22.2 23.5 25.7

23.4 24.1 23.4 22.8 19.9 17.6 16.8 16.9 16.9 18.5 19.05 22

4.9. Variabilidad temporal de las Qs Qi y Qadr

MES ENERO FEBRERO MARZO ABRIL MAYO JUNIO JULIO AGOSTO SEPTIEMBRE OCTUBRE NOVIEMBRE DICIEMBRE

Qs 26.05791952 27.05365968 27.48342763 26.66838175 25.12078993 24.11737346 24.44787598 25.78160006 26.90888779 26.9290268 26.12181694 25.58810142

Qs &Tiempo 28 27 26 25 24 23 22

5.412 6.947 7.742 7.584 6.106 4.158 3.593 3.554 5.803 5.634 6.404 5.147

20.646 20.107 19.741 19.084 19.015 19.959 20.855 22.228 21.106 21.295 19.718 20.441

INTERPRETACIÓN: La radiación solar incidente también, sufre una caída por junio a julio por que la Tierra está más alejada, mientras que entre Marzo- Abril y Setiembre- Octubre recibe una incidencia mayor que son casi similares debido a que se encuentra a una distancia similar de la tierra y las incidencias coinciden un poco.

MES

Qi

ENERO FEBRERO MARZO ABRIL MAYO JUNIO JULIO AGOSTO SEPTIEMBRE OCTUBRE NOVIEMBRE DICIEMBRE

5.412 6.947 7.742 7.584 6.106 4.158 3.593 3.554 5.803 5.634 6.404 5.147

Qi & Tiempo 9 8 7 6 5 4 3 2 1 0

INTERPRETACIÓN: En cuanto a la radiación incidente tiene una crecida durante el verano, esto se debe a que los rayos caen perpendicularmente sobre la superficie terrestre produciendo la mayor incidencia además que en esta estación la tierra está más cerca del sol, mientras que en el invierno de Junio hasta los inicios de Setiembre, la radiación es menor, ya que la tierra se encuentra más lejos.

MES ENERO FEBRERO MARZO ABRIL MAYO JUNIO JULIO AGOSTO SEPTIEMBRE OCTUBRE NOVIEMBRE DICIEMBRE

Qadr 20.646 20.107 19.741 19.084 19.015 19.959 20.855 22.228 21.106 21.295 19.718 20.441

Qard & Tiempo 23 22 21 20 19 18 17

INTERPRETACIÓN: En este tipo de radiación observamos que entre Julio a agosto, se encuentra los valores más altos de radiación de absorción, dispersión y reflejada, ya que en este periodo al encontrarnos en invierno se necesita una mayor absorción para mantener la temperatura de la superficie de la tierra, mientras que en Abril y Mayo tenemos radiaciones más bajas, porque al estar cerca el sol a la tierra (equinoccio) hay mas dispersión de los rayos, es más reflejada para mantener una temperatura homogénea en la superficie terrestre.

MESES ENERO FEBRERO MARZO ABRIL MAYO JUNIO JULIO AGOSTO SEPTIEMBRE OCTUBRE NOVIEMBRE DICIEMBRE

Suma de Qs Suma de Qi Suma de Qadr 25.22036517 5.238 19.982 26.38822272 6.776 19.612 27.19075159 7.659 19.532 26.8419985 7.633 19.209 25.67217356 6.24 19.432 24.87991795 4.289 20.591 25.25212645 3.711 21.541 26.43575966 3.645 22.791 27.21172782 5.868 21.344 26.77076141 5.6 21.171 25.56109699 6.267 19.294 24.79108601 4.987 19.804

Tiempo en relación de Qs, Qi y Qadr 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

26.8419985

26.38822272 27.19075159 25.22036517

19.532

19.209

7.659 5.238

7.633

6.776

21.541

20.591

FEBRERO

MARZO

ABRIL

6.24

Suma de Qs

JULIO

Suma de Qi

3.645

24.79108601 19.804

19.294

6.267

5.868

4.289

JUNIO

21.171 21.344

19.432

MAYO

26.77076141 25.56109699

22.791

3.711 ENERO

27.21172782

25.25212645

24.87991795

19.612 19.982

26.43575966

25.67217356

5.6

4.987

AGOSTO SEPTIEMBRE OCTUBRE NOVIEMBRE DICIEMBRE Suma de Qadr

INTERPRETACIÓN: Al ver la gráfica se observa que entre los meses de Junio a Setiembre, que es el periodo de invierno, la radiación solar tiene sus valores más bajos, y esta es inversamente a la radiación de absorción, dispersada y reflejada que durante este mismo tiempo sus valores son más altos. ¿Cuál es su opinión respecto a la ecuación utilizada para cuantificar la radiación al tope de la atmósfera (Qs) y la radiación incidente (Qi) con solo el rango diurno de la temperatura? La radiación se basa principalmente en la incidencia de los rayos del sol sobre la superficie de la tierra, por lo que trabajar en las ecuaciones durante el periodo diurno es lo más eficiente, teniendo en cuenta cuanto es la duración de las horas de sol. Además las ecuaciones son adecuadas ya que la radiación dependen tanto de la distancia de la tierra al sol en cada día y de la constante solar. También es correcto usar la latitud porque la incidencia de rayos solares es diferente en cada lugar, por lo tanto evaluar tanto la latitud como longitud en la ecuación dará una precisión mas cercada de los valores reales de radiación. Además sabemos que en cada día, las temperaturas mínimas y máximas son diferentes esto por el movimiento rotacional de la tierra así como la traslaciones que hace que cambie la duración de horas de sol, por ello la ecuación de radiación incidente depende mucha de esta variable.