12.215 Homework #2                                                       Due Monday, November 4, 2009

 

Latitude and Longitude determination.

 

The data needed for this homework are given below.

 

(a)  Find the time and the value of the maximum angle between the sun and its reflection using the data given below. On the web version, the data is this link  (26 points). (The file in the link has no headers so that load can be used in Matlab.  The columns are those shown below).

(b)  Find the mean index error of the sextant (data below) (5 points)

(c)   Using the mean index error for distance objects, compute the elevation angle to the Sun at its maximum (5 points)

(d)  Compute the approximate atmospheric bending contribution to this measured elevation to the sun (15 points)

(e)  Given the declination of the Sun and the in vacuum estimate of the elevation angle to the Sun, compute the latitude of the Green building. (25 points)

(f)   Given Greenwich hour angle at the Greenwich meridian crossing, compute the longitude of the Green building (25 points)

 

Data for Homework:

 

Index errors (minutes of arc): Measured values -10.0, -7.2, -5.0, -4.0

 

Measured sextant data (date Oct 14, 2009)

 

Hrs (EDT)

Min

Sec

Sun Deg

Sun Min

 

 14

 50

 26

 68

 54.8

 15

 13

 54

 72

 39.0

 15

 26

  8

 74

 18.6

 15

 29

 13

 74

 50.8

 15

 35

 39

 75

 29.2

 15

 39

 43

 75

 56.0

 15

 44

  9

 76

 23.4

 15

 55

 51

 77

 19.0

 16

  6

 17

 77

 47.6

 16

  5

 10

 77

 54.0

 16

 12

 15

 78

 17.6

 16

 18

 21

 78

 37.2

 16

 20

 28

 78

 31.8

 16

 24

 26

 78

 24.2

 16

 25

 47

 78

 31.8

 16

 29

  9

 78

 31.6

 16

 30

 24

 78

 37.8

 16

 32

  8

 78

 30.0

 16

 35

 19

 78

 31.6

 16

 36

 36

 78

 34.2

 16

 37

 49

 78

 36.0

 16

 39

 11

 78

 30.0

 16

 43

 98

 78

 18.0

 16

 44

 24

 78

 20.8

 16

 48

 38

 78

 10.0

 16

 50

 27

 78

 5.0

 

 

 

Almanac from:

http://www.tecepe.com.br/scripts/AlmanacPagesISAPI.isa/pages?date=10%2F14%2F2009

 

2009 OCT. 14 (WED)

------+-------------------+

      |   SUN             |

------+-------------------+

G.M.T |   GHA      Dec    |

 d  h |      '       '  |

14  0 | 183 28.7 S 8 06.8 |

    1 | 198 28.8 S 8 07.7 |

    2 | 213 29.0 S 8 08.7 |

    3 | 228 29.1 S 8 09.6 |

    4 | 243 29.3 S 8 10.5 |

 W  5 | 258 29.4 S 8 11.5 |

 E    |                   |

 D  6 | 273 29.6 S 8 12.4 |

 N  7 | 288 29.7 S 8 13.3 |

 E  8 | 303 29.8 S 8 14.2 |

 S  9 | 318 30.0 S 8 15.2 |

 D 10 | 333 30.1 S 8 16.1 |

 A 11 | 348 30.3 S 8 17.0 |

 Y    |                   |

   12 |   3 30.4 S 8 18.0 |

   13 |  18 30.6 S 8 18.9 |

   14 |  33 30.7 S 8 19.8 |

   15 |  48 30.8 S 8 20.7 |

   16 |  63 31.0 S 8 21.7 |

   17 |  78 31.1 S 8 22.6 |

      |                   |

   18 |  93 31.3 S 8 23.5 |

   19 | 108 31.4 S 8 24.5 |

   20 | 123 31.5 S 8 25.4 |

   21 | 138 31.7 S 8 26.3 |

   22 | 153 31.8 S 8 27.2 |

   23 | 168 32.0 S 8 28.2 |

------+-------------------+