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Re: Bennett's '...Celestial Navigator' --An improved Zn calculation

From: d walden (no email)
Date: Mon Dec 05 2005 - 23:31:23 EST

  • Next message: Mike Hannibal: "Re: Lunar reference"

      A coin flip decided which latitude to use. My example was in fact the mean of George’s two examples. Doing both of his examples, for both possible latitudes, again both ‘frontward’ and then ‘backward’. Frontward demonstrates that the latitude, calculated as George showed, does indeed yield the desired altitude.

      Example 1:

                              deg min
      13 LHA 54 31 -> 8838
      14 DR Lat 60 26 -> 3997
      15 Dec 55 29 -> 3214
      16 (theta) 28 2 <- SUM 16049 -> RES 11730
      17 Lat~Dec 4 57 -> 373
      18 Comp Alt 61 31 <- ALT 12103

      18 Dec 55 29 -> ALT 17604
      17 Lat~Alt 1 5 -> 18
      16 (theta) 34 30 <- SUM 13758 <- RES 17586
      15 Alt 61 31 -> 4190
      14 DR Lat 60 26 -> 3997
      13 Z 75 22 <- 5570
                  Zn 284 38

                              deg min
      13 LHA 54 31 -> 8838
      14 DR Lat 76 3 -> 8051
      15 Dec 55 29 -> 3214
      16 (theta) 19 30 <- SUM 20103 -> RES 5731
      17 Lat~Dec 20 34 -> 6374
      18 Comp Alt 61 31 <- ALT 12105

      18 Dec 55 29 -> ALT 17604
      17 Lat~Alt 14 32 -> 3200
      16 (theta) 31 8 <- SUM 14887 <- RES 14404
      15 Alt 61 31 -> 4190
      14 DR Lat 76 3 -> 8051
      13 Z 104 39 <- 2647
                  Zn 255 21

      Example 2:

                              deg min
      13 LHA 54 29 -> 8844
      14 DR Lat 60 10 -> 3951
      15 Dec 55 31 -> 3219
      16 (theta) 28 7 <- SUM 16014 -> RES 11803
      17 Lat~Dec 4 39 -> 329
      18 Comp Alt 61 29 <- ALT 12132

      18 Dec 55 31 -> ALT 17571
      17 Lat~Alt 1 19 -> 26
      16 (theta) 34 27 <- SUM 13771 <- RES 17545
      15 Alt 61 29 -> 4184
      14 DR Lat 60 10 -> 3951
      13 Z 74 51 <- 5636
                  Zn 285 9

                              deg min
      13 LHA 54 29 -> 8844
      14 DR Lat 76 20 -> 8164
      15 Dec 55 31 -> 3219
      16 (theta) 19 17 <- SUM 20228 -> RES 5606
      17 Lat~Dec 20 49 -> 6528
      18 Comp Alt 61 29 <- ALT 12134

      18 Dec 55 31 -> ALT 17571
      17 Lat~Alt 14 51 -> 3341
      16 (theta) 30 56 <- SUM 14956 <- RES 14230
      15 Alt 61 29 -> 4184
      14 DR Lat 76 20 -> 8164
      13 Z 105 9 <- 2608
                  Zn 254 51

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