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# Determination of Julian Day Numbers

The Julian day number of a given day can be determined from Tables 27-29. The date must be expressed in terms of the Gregorian calendar.

The procedure is as follows:

1. Enter the table of century years (Table 27) with the century year immediately preceding the date in question, and take out the tabular value. If the century year is marked with a , note this fact for use in step 2.
2. Enter the table of years of the century (Table 28) with the last two digits of the year in question, and take out the tabular value. If the century year used in step 1 was marked with a , diminish the tabular value by one day, unless the tabular value is zero. If the year in question is a leap year, marked with a , note this fact for use in step 3.

3. Enter the table of the days of the year (Table 29) with the day in question, and take out the tabular value. If the year in question is a leap year and the table entry falls after February 28, add one day to the tabular value. The sum of the values obtained in steps 1, 2, and 3 then gives the Julian day number of the date in question.

Example 1: June 10, 1992 CE:

 1. Century year 1900 2415020 2. Year of the century 92 33603 - 1 = 33602 3. Day of the year June 10 161+1 = 162 Julian day number 2448784

Observe that in step 2 the tabular value has been diminished by 1 because 1900 is a common year (marked with a in Table 27). In step 3, the tabular value has been increased by 1 because 1992 is a leap year (marked with a in Table 28), and the date falls after February 28.

Example 2: January 18, 1824 CE:

 1. Century year 1800 2378496 2. Year of the century 24 8766 - 1 = 8765 3. Day of the year January 18 18 = 18 Julian day number 2387279

Observe that in step 2 the tabular value has been diminished by 1 because 1800 is a common year (marked with a in Table 27). In step 3, the tabular value has not been increased by 1, despite the fact that 1824 is a leap year (marked with an in Table 28), because the date falls before February 28.

We can specify the time of day (in universal time), as well as the date, by means of fractional Julian day numbers. For instance, JD corresponds to 12:00 UT on June 10, 1992 CE, whereas JD corresponds to 24:00 UT later the same day.

Table 27: Julian Day Number: Century Years. Common years. All years are CE. From ``The History and Practice of Ancient Astronomy", J. Evans (Oxford University Press, Oxford UK, 1998).
 1800 2378496 1900 2415020 2000 2451544

Table 28: Julian Day Number: Years of the Century. Leap year. Leap year unless century is marked . In centuries marked , subtract one day from the tabulated values for the years 1 through 99. From ``The History and Practice of Ancient Astronomy", J. Evans (Oxford University Press, Oxford UK, 1998).
 0 0 20 7305 40 14610 60 21915 80 29220 1 336 21 7671 41 14976 61 22281 81 29586 2 731 22 8036 42 15341 62 22646 82 29951 3 1096 23 8401 43 15706 63 22011 83 30316 4 1461 24 8766 44 16071 64 23376 84 30681 5 1827 25 9132 45 16437 65 23742 85 31047 6 2192 26 9497 46 16802 66 24107 86 31412 7 2557 27 9862 47 17167 67 24472 87 31777 8 2922 28 10227 17532 24837 88 32142 9 3288 29 10593 49 17898 69 25203 89 32508 10 3653 30 10958 50 18263 70 25568 90 32873 11 4018 31 11323 51 18628 71 25933 91 33238 12 4383 32 11688 52 18993 72 26298 92 33603 13 4749 33 12054 53 19359 73 26664 93 33969 14 5114 34 12419 54 19724 74 27029 94 34334 15 5479 35 12784 55 20089 75 27394 95 34699 16 5844 36 13149 56 20454 76 27759 96 35064 17 6210 37 13515 57 20820 77 28125 97 35430 18 6575 38 13880 58 21185 78 28490 98 35795 19 6940 39 14245 59 21550 79 28855 99 36160

Table 29: Julian Day Number: Days of the Year. In leap year, after February 28, add 1 to the tabulated value. From ``The History and Practice of Ancient Astronomy", J. Evans (Oxford University Press, Oxford UK, 1998).
 Day Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 1 32 60 91 121 152 182 213 244 274 305 335 2 2 33 61 92 122 153 183 214 245 275 306 336 3 3 34 62 93 123 154 184 215 246 276 307 337 4 4 35 63 94 124 155 185 216 247 277 308 338 5 5 36 64 95 125 156 186 217 248 278 309 339 6 6 37 65 96 126 157 187 218 249 279 310 340 7 7 38 66 97 127 158 188 219 250 280 311 341 8 8 39 67 98 128 159 189 220 251 281 312 342 9 9 40 68 99 129 160 190 221 252 282 313 343 10 10 41 69 100 130 161 191 222 253 283 314 344 11 11 42 70 101 131 162 192 223 254 284 315 345 12 12 43 71 102 132 163 193 224 255 285 316 346 13 13 44 72 103 133 164 194 225 256 286 317 347 14 14 45 73 104 134 165 195 226 257 285 318 348 15 15 46 74 105 135 166 196 227 258 288 319 349 16 16 47 75 106 136 167 197 228 259 289 320 350 17 17 48 76 107 137 168 198 229 260 290 321 351 18 18 49 77 108 138 169 199 230 261 291 322 352 19 19 50 78 109 139 170 200 231 262 292 323 353 20 20 51 79 110 140 171 201 232 263 293 324 354 21 21 52 80 111 141 172 202 233 264 294 325 355 22 22 53 81 112 142 173 203 234 265 295 326 356 23 23 54 82 113 143 174 204 235 266 296 327 357 24 24 55 83 114 144 175 205 236 267 297 328 358 25 25 56 84 115 145 176 206 237 268 298 329 359 26 26 57 85 116 146 177 207 238 269 299 330 360 27 27 58 86 117 147 178 208 239 270 300 331 361 28 28 59 87 118 148 179 209 240 271 301 332 362 29 29 88 119 149 180 210 241 272 302 333 363 30 30 89 120 150 181 211 242 273 303 334 364 31 31 90 151 212 243 304 365

Next: Geometric Planetary Orbit Models Up: Dates Previous: Introduction
Richard Fitzpatrick 2010-07-21