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  1. #11
    Brian Tung's Avatar
    Brian Tung Guest

    Default Shadow of sundial a straight line on equinox day?



    Chris L Peterson wrote:

    Are we talking about the same question? At any latitude less than 90
    degrees, an "ideal" Sun (point source, no refraction) travels in a great
    circle across the sky. The gnomon's tip generates a plane with that
    great circle because they're coplanar. That plane should intersect with
    the plane of the sundial in a straight line, no matter the inclination
    of the two.

    At all other times, the gnomon's tip and the (less than great) circle
    travelled by the Sun should generate a cone. The intersection of that
    cone with the plane will be a hyperbola.

    --
    Brian Tung <brian@lunabase.org>
    The Astronomy Corner moved to http://www.astronomycorner.net/
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  2. #12
    Brian Tung's Avatar
    Brian Tung Guest

    Default Shadow of sundial a straight line on equinox day?

    Chris L Peterson wrote:

    Whaah? It sets in the west, yes, but the shadow is at infinity then,
    so no contradiction. The shadow could easily track (let's say) 100 m
    north of the east-west line at the gnomon, and still be exactly due
    east when the Sun sets. A hundred meters divided by infinity is still
    zero.

    --
    Brian Tung <brian@lunabase.org>
    The Astronomy Corner moved to http://www.astronomycorner.net/
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  3. #13
    William Hamblen's Avatar
    William Hamblen Guest

    Default Shadow of sundial a straight line on equinox day?

    On 2009-03-28, Brian Tung <brian@lunabase.org> wrote:

    It seems to me that the apparent daily path of the Sun is a small circle
    unless the declination of the Sun is zero.

    Bud


  4. #14
    OG's Avatar
    OG Guest

    Default Shadow of sundial a straight line on equinox day?


    "Peter Lewis" <kingkong88@gmail.com> wrote in message
    news:0fc51aa0-b263-4300-80e8-88b95946fc33@b7g2000pre.googlegroups.com...

    Web page refers to Kirskville MO
    40°11′37″N
    92°34′46″W


  5. #15
    Brian Tung's Avatar
    Brian Tung Guest

    Default Shadow of sundial a straight line on equinox day?

    William Hamblen wrote:

    Yes, OP is talking about equinox, where declination of the Sun is zero.

    --
    Brian Tung <brian@lunabase.org>
    The Astronomy Corner moved to http://www.astronomycorner.net/
    Unofficial C5+ Home Page at http://www.astronomycorner.net/c5plus/
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    My Own Personal FAQ (SAA) at http://www.astronomycorner.net/reference/faq.html

  6. #16
    canopus56@yahoo.com's Avatar
    canopus56@yahoo.com Guest

    Default Shadow of sundial a straight line on equinox day?

    On Mar 27, 9:04 pm, Peter Lewis <kingkon...@gmail.com> wrote:

    Yes, on the Earth at the equinoxes, a simple vertical gnomon sundial,
    regardless of latitude, traces a straight line within the limits of
    visual detection. There are a number of minor technical exceptions.

    This is because of the extreme distance of the Sun, all rays from the
    Sun appear to fall in parallel lines at all points in on the Earth's
    globe. At the equinoxes, the rays of the Sun aer parallel to the
    lines of latitude and the equator. Hence, the Sun's shadow traces a
    straight line. At other times of the year, the Sun's rays are at an
    angle to the lines of latitude, hence, the Sun's shadow from a gnomon
    does not trace a straight line - it traces a parabola.

    Here's an animation of images taken on the equinox at a public sundial
    in Salt Lake City:

    http://members.csolutions.net/fisher...43animated.gif

    A diagram showing northern hemisphere shadow traces for a vertical
    gnomon throughout the year can be found at:

    http://www.mysundial.ca/tsp/sundial_types.html

    According to Evans, the Greeks divided the latitudes of the earth into
    five major divisions based on the behavior of a simple gnomon
    sundial.

    The word "tropic" means "to turn" - refering to the point at the
    solistices at which the trace of the Sun's daily shadow turns back
    toward the gnonom. The Tropic of Capricorn defines the most southerly
    latitude in the northern hemisphere in which the Sun can pass directly
    overhead - that is the most southerly line on the sun dial traces
    depicted in http://www.mysundial.ca/tsp/sundial_types.html will cross
    directly over the gnonom. For sundials places at latitudes higher
    than the Tropic of Cancer, the most southernly shadow cast by the
    sundial will never reach the gnonom. For the equatorial region, the
    Sun will cast its most northernly and southerly traces on either side
    (north-south) of the gnomon. For the Tropic of Capricorn, the
    opposite shadow case of the Tropic of Cancer occurs.

    The two remaining regions are the arctic and anarctic, where the Sun
    can disappear below the horizon across multiple days and cast no
    shadow.

    For a citeable source, try:

    Evans, James. 1998. The History and Practice of Ancient Astronomy.
    Oxford Univ. Press. ISBN: 0195095391

    Waugh, Albert, Edmund. 1973. Sundials: Their Theory and Construction.
    Dover. ISBN: 0486229475

    Rohr, Rene R.J. 1996. Sundials: History, Theory, and Practice. Dover.
    ISBN: 0486291391

    You might find the following resources of interest:

    Franois Blateyron's Shadows sundial software Plots the dial for a
    variety of sundials particularlized for your observing point.
    http://pagesperso-orange.fr/blateyro...shadowspro/gb/

    The Shadows freeware version includes the ability to run simulations
    tracing the Sun's shadow on a dial throughout a year. Blayteron's
    software is really something. Check it out.

    Shadows sundial gallery
    http://pagesperso-orange.fr/blateyro...ersundials.htm

    North American Sundial Society. 2006. Registry of North American
    Sundials. Website. << http://sundials.org/registry/ >> accessed
    6/2006

    British Sundial Society. 2006. Dials of Distinction. In The British
    Sundial Society Homepage. Website. (Photographs of English sundials).
    << http://www.sundialsoc.org.uk/ >> accessed 6/2006

    British Sundial Society. 2006. Sundials on the Internet. Website.
    (Links to pictures of sundials around the world) << http://www.sundials.co.uk/
    accessed 6/2006

    Get Hooked on Gnomonics http://www.mysundial.ca/tsp/tsp_index.html

    Basic bibliography on sundials
    http://members.csolutions.net/fisher...ml/Biblio.html





  7. #17
    Brian Tung's Avatar
    Brian Tung Guest

    Default Shadow of sundial a straight line on equinox day?

    Kurt <canopus56@yahoo.com> wrote:

    It's only a parabola if the surface of the sundial is coplanar with the
    north celestial pole, since this is the axis of the cone generated by
    the gnomon's tip and the path of the Sun (to first order, ignoring the
    variation in declination of the Sun over the course of a day). Some
    sundials are in fact mounted this way. In all other cases, the path is
    a hyperbola. The asymptotes of the hyperbola are the lines drawn from
    the gnomon to the rising and setting Sun. At the equinoxes, these
    asymptotes are both identical to the east-west line, and the hyperbola
    degenerates into a straight line.

    --
    Brian Tung <brian@lunabase.org>
    The Astronomy Corner moved to http://www.astronomycorner.net/
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  8. #18
    Brian Tung's Avatar
    Brian Tung Guest

    Default Shadow of sundial a straight line on equinox day?

    Peter Lewis wrote:

    Heh, you've started a lively little discussion.

    Assuming

    * I've understood you correctly.
    * The Sun is a point source.
    * Atmospheric refraction is negligible.
    * Variation in the Sun's declination during the day is negligible.
    * The sundial is planar. (Some have cylindrical or other curved
    surfaces, for reasons we can ignore here.)

    Then the answer to your question is yes, the Sun's shadow does traverse
    a straight line at the equinoxes.

    Reasoning: The Sun's path during the course of a day is an arc of a
    circle on the celestial sphere. At the equinoxes, this circle is a
    great circle, like the equator on the Earth; at all other times, it's
    less than great, like the 10 degree north latitude circle.

    The Sun causes the gnomon's tip to cast a shadow. We see this shadow as
    a point on the surface of the sundial, but it's really a line extended
    from the gnomon's tip out to infinity, extending away from the Sun (just
    as the Earth casts a shadow out into outer space, which occasionally
    strikes the Moon, during a lunar eclipse).

    On most days, because the Sun's path is less than great, this shadow
    line traces out a cone (just as a line drawn from the center of the
    Earth to points on the 10 degree suoth latitude circle would describe a
    cone). What we see over the course of the day is the intersection of
    this cone with the plane of the sundial. From conics, the intersection
    of a cone with a plane is a conic section: a circle, an ellipse, a
    parabola, or a hyperbola. If the sundial is level, the path is a
    hyperbola.

    However, at the equinoxes, the cone degenerates to a plane (just as a
    line drawn from the center of the Earth to points on the equator would
    also describe a plane). The intersection of this plane with the plane
    of the sundial is necessarily a straight line, unless the two planes
    are parallel, as they would be for a level sundial at the poles. As
    you correctly said, there is *no* shadow for such a sundial at all on
    that day.

    I'm afraid there I can't think of a much simpler way to explain this
    in text. With graphics it would be much easier, so see the Web sites
    cited by others.

    --
    Brian Tung <brian@lunabase.org>
    The Astronomy Corner moved to http://www.astronomycorner.net/
    Unofficial C5+ Home Page at http://www.astronomycorner.net/c5plus/
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  9. #19
    Peter Lewis's Avatar
    Peter Lewis Guest

    Default Shadow of sundial a straight line on equinox day?

    On Mar 31, 5:00 am, Quadibloc <jsav...@ecn.ab.ca> wrote:

    Really appreciate all the effort to explain further. But I feel the
    discussion is deviating slightly from what I am seeking.

    I am not trying to explain the seasons. I think I have got that, at
    least I think so.

    What I am trying to do is to easily explain that the tip of a gnomon
    will trace a straight line around equinox. (As the equinox is
    strictly just a moment in time, I assume plus or minus a few hours
    around that moment would still be valid.)

    Purpose of this exercise? By collecting sun dial data, using the
    lines on different days to demonstrate that the earth is tilted and
    revolving round the sun.

    The equinox opportunity was two Saturdays ago, and it was cloudy, but
    I got some good data on Mar 19.

  10. #20
    Brian Tung's Avatar
    Brian Tung Guest

    Default Shadow of sundial a straight line on equinox day?

    Peter Lewis wrote:

    Gerald and John like to go rounds at each other. Not sure why.

    --
    Brian Tung <brian@lunabase.org>
    The Astronomy Corner moved to http://www.astronomycorner.net/
    Unofficial C5+ Home Page at http://www.astronomycorner.net/c5plus/
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    My Own Personal FAQ (SAA) at http://www.astronomycorner.net/reference/faq.html

 

 
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