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  1. #1
    Peter Lewis's Avatar
    Peter Lewis Guest

    Default Shadow of sundial a straight line on equinox day?



    Hi, I couldn't derive or visualize this using simple geometry.

    Does the shadow of a simple sundial form a straight line plus/minus a
    few hours around equinox (at all latitudes)? And a curve at all other
    times?

    Thanks.

  2. #2
    Sam Wormley's Avatar
    Sam Wormley Guest

    Default Shadow of sundial a straight line on equinox day?


  3. #3
    Chris L Peterson's Avatar
    Chris L Peterson Guest

    Default Shadow of sundial a straight line on equinox day?

    On Fri, 27 Mar 2009 20:04:41 -0700 (PDT), Peter Lewis
    <kingkong88@gmail.com> wrote:


    Only if your sundial is at the equator. While the Sun rises in the east
    and sets in the west everywhere on Earth (on the equinox), it only
    crosses the zenith at the equator. Consider an extreme example of a
    sundial at one of the poles. The Sun makes a complete circle around the
    horizon. That's going to produce a sundial shadow that's nearly a
    perfect circle.
    _________________________________________________

    Chris L Peterson
    Cloudbait Observatory
    http://www.cloudbait.com

  4. #4
    Sam Wormley's Avatar
    Sam Wormley Guest

    Default Shadow of sundial a straight line on equinox day?


  5. #5
    Sam Wormley's Avatar
    Sam Wormley Guest

    Default Shadow of sundial a straight line on equinox day?

    Sam Wormley wrote:

    Here is the original reference: http://solarclockgarden.truman.edu/sundial.htm


  6. #6
    Peter Lewis's Avatar
    Peter Lewis Guest

    Default Shadow of sundial a straight line on equinox day?

    On Mar 28, 12:10 pm, Sam Wormley <sworml...@mchsi.com> wrote:

    Thanks for anticipating my next question, and beating me to it.

  7. #7
    Peter Lewis's Avatar
    Peter Lewis Guest

    Default Shadow of sundial a straight line on equinox day?

    Mmm..., the puzzle deepens.

    The example at http://solarclockgarden.truman.edu/sundial.htm is
    clearly not at the equator. Seems to be in conflict with Chris'
    explanation.

    After thinking about it for a bit more, Chris, your polar example
    would produce no shadow as the sun rays at the gnomon would be
    parallel to the ground at the pole. Am I correct?

  8. #8
    Sam Wormley's Avatar
    Sam Wormley Guest

    Default Shadow of sundial a straight line on equinox day?

    Peter Lewis wrote:

    Flat horizontal surface - Equinox Shadow tip follows a straight line.
    http://www-groups.dcs.st-and.ac.uk/~.../Sundials.html

    Other dates hyperbolic paths (between Arctic and Antarctic circles).

  9. #9
    Chris L Peterson's Avatar
    Chris L Peterson Guest

    Default Shadow of sundial a straight line on equinox day?

    On Fri, 27 Mar 2009 21:33:08 -0700 (PDT), Peter Lewis
    <kingkong88@gmail.com> wrote:


    Well, that's not a very typical sundial. It has a vertical gnomon, not
    one pointing towards the pole. I don't see how the equinox shadow could
    be as indicated (since on that day the Sun rises and sets very near
    cardinal east and west), unless it has something to do with the shape of
    the surface below the gnomon. The report says it is on some sort of
    slope.


    Well, it depends. Refraction actually brings the Sun higher, so it
    circles a little above the horizon. And even if there were no
    atmosphere, the Sun is an extended object, so there is a penumbral
    shadow that is closer that the horizon.

    The pole is a sort of singularity, and it might be confusing. But you
    can imagine that you are just a little below the pole, where the Sun
    will rise in the east, travel across the sky crossing the meridian just
    a little above the southern horizon (for the north pole), and set in the
    west. It seems pretty clear that the gnomon's shadow isn't going to
    trace a straight line under those circumstances.
    _________________________________________________

    Chris L Peterson
    Cloudbait Observatory
    http://www.cloudbait.com

  10. #10
    Sam Wormley's Avatar
    Sam Wormley Guest

    Default Shadow of sundial a straight line on equinox day?


 

 
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