LONGITUDE workshop 20.April.2004 *DRAFT*
    Celestial Navigation - part of Astronomy and Cosmologies - Spring 2004
    Goals
    Equipment
    Homework
    Background
    Activities
    Learning
    Web-X
    Links
    Working the Waters
    Astro Home

    Most workshops will span 2 weeks.  Do workshops in teams of about 4. After starting the workshop, fill out a workshop feedback form and hand it in at the end of class.  After finishing the workshop (the second week), post a workshop report on WebX.
     
    GOALS

    • to use a gnomon to find the time and solar altitude at Local Apparent Noon (LAN)
    • to better understand how the position of the sun depends on latitude
    • to better understand how the time of sunrise (relative to GMT) depends on longitude
    Gnomon diagram courtesy of
    http://www.sweethome.de/giesen/SME/details/seDetails.html#shadow
    Latitude workshop
     finding longitude from LAN
    HW sheet:  calibrate your watch IN ADVANCE
    http://greenwichmeantime.com
    http://www.time.gov/timezone.cgi?Pacific/d/-8/java
     Declination tables
     sunrise tables from US Naval Observatory:
    Gnomon
    longitude = 0,  latitude = 47o35' N
    longitude = 0,  latitude = 47o36' N
    longitude = 0,  latitude = 47o37' N

    Illustration    Diagram time zone maps        sunrise calculator     time calculator
        Nova longitude game        Equation of time        sideral time       time zones workshop solutions

    EQUIPMENT

    Gnomon, meter stick, sunrise-sunset tables, calculator
    BACKGROUND

    You have learned how to find your Latitude from the altitude of either the Sun or Polaris.

    You have calibrated your watch so it is a chronometer.

    You have learned how to find longitude from LAN.

    Homework to do before you come to class:

      * Re-read Burch Ch. 6, 11, 12
      * Finish the Latitude workshop from a week or two ago
      * Fill in the homework sheet for calibrating your watch WELL IN ADVANCE
      * Bring your sextant measurements from the boats, or make sure you have classmates who can provide this
      * Fill in the homework section (0.) below and turn it in.
      * Print out this workshop and bring a copy

    ACTIVITIES

    0.  Homework worksheet 2.  Find latitude from solar altitude at LAN
    1.  Take Gnomon measurements 3.  Find longitude from time at LAN

    Recommendations for finishing in limited time:

    • make sure a couple of people on your team did the longitude from LAN workshop on the boats
    • half the class could do Latitude (part 2) and half do Longitude (part 3), then share your results

     

    (0.)  Homework worksheet
    What is the difference between your watch time and Greenwich Mean Time?  It should be about 8 hours, but not exactly.  ______

    How much time does your watch gain or lose each day?  _____

    How far off could your answers above be?  ______

    Is your watch a chronometer?  How sure are you?

    Briefly describe Greenwich Mean Time (GMT) in your own words:

     

     

    Burch Ch.6:  Briefly describe Local Apparent Noon (LAN) in your own words:

     

     

    Burch Ch.11:  Briefly describe the relation between solar altitude and latitude on Earth, in your own words:

     

     


    Burch Ch.12:  Briefly describe the relation between the time of LAN and longitude on Earth, in your own words:

     

     

     
    (1.)  Take Gnomon measurements:
    Take turns marking the tip of the shadow as often as feasible.
    Write the time of each observation by the shadow tip, to the best precision possible.
    Use the same watch for all time measurements!
    How much uncertainty is in the measurements?  How much time can elapse before the shadow noticably moves?

    Then analyze your measurements:

    ANGLE:
    How long is the stick?  H = ______    (what units?  ____)

    How long is the shadow at LAN? D = ______  (what units?  ____)

    If H/D = tan q, what is the altitude of the sun at LAN?  q = ______     (what units?  ________)

    How uncertain is your solar altitude at LAN?

    TIME:

    What is the time of  LAN (here, in Olympia, today?) ___________
    Interpolate between shadow measurements, if necessary.

    What is GMT for your LAN?  __________

    How uncertain is your measured GMT at LAN?

    (2.)  Find latitude from solar altitude at LAN.  Use the techniques of the fall workshop, Latitude at Sea, to find your latitude from the solar altitude at noon.  KEEP ALL YOUR ANGLES IN DEGREES.  Solar semi-diameter = r = 16'

    Apparent altitude of the sun at LAN = q  = _________ = Hs (from part 1)

    Dip = correction if your eye is not lying on the ground = 1' Sqrt[ Height of Eye (in feet)] = ________

    Refraction correction for light bent up by thick atmosphere at the horizon (for Hs > 6 degrees):
        RC = 60' / Hs  = _________

    Ho = actual Solar altitude = Hs - dip - RC  + r = ________

    Your latitude = sun's declination - sun's zenith distance = declination - altitude + 90 degrees = _______

    How far off could this be in degrees, from the uncertainties in measurements? _______

    How far off could this be in nautical miles?  _______

    In your own words, explain if or why you have to make all those corrections to get Ho from Hs.

     


    In your own words, explain whether/why the equation for your latitude makes sense.  Give a couple examples to illustrate your explanation.

     

     

     
    (3.)  Find longitude from time of LAN. Use the techniques of Tuesday's workshop to find your longitude from the time of local apparent noon.

    (a)  measured GMT at LAN (at your latitude and longitude) = __________  from part (1) above

    sunrise time at 0 degrees longitude (at your latitude) = _________  (from sunrise-sunset tables - interpolate if necessary)
    sunset time at 0 degrees longitude (at your latitude) = _________  (from sunrise-sunset tables)

    (b) calculated GMT at LAN at 0o longitude (at your latitude) = _________  (average sunrise and sunset above)

    dT = (b) - (a) = time difference between  calculated GMT at LAN (at 0 degrees longitude) and measured GMT at LAN (at your longitude)  = ________

    Convert the time difference (dT in hours:minutes:seconds)  to a space difference (in degrees : minutes of arc' : seconds of arc"), knowing that the Earth rotates through a spatial angle of 360 degrees in a time of 24 hours.  There are 60 seconds in a minute and 60 minutes in a degree.

    _____ hours * |15 degree /hr| = ______ degrees

    _____ minutes * |1degree / 4 minutes| = ________ degrees of arc
     

    _____ seconds * |1' / 4 seconds| = ________ minutes of arc

    That is your longitude!  _____ degrees  ____ minutes  _____  seconds of arc

    Are you that far east or west of Greenwich? _____

    How far off could this be in degrees, from the uncertainties in measurements? _______

     

    How far off could this be in nautical miles?  _______

     

    LEARNING

    Think about the key points you have learned. What surprised you? Is anything still unclear? Is there anything you need help with before you can meet your learning goals? What would you like to learn, beyond this workshop?

    Please fill out workshop feedback before you leave, the first week we start this workshop.  You can post this on WebX now. Everyone on your team should contribute to the feedback. After finishing the workshop (the second week), you will post a complete workshop report on WebX.
    Maintained by: E.J. Zita