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The sun


The sun Due to the earth s tilt and its orbit around the sun, the declination of the sun changes with time of year 23.45o at summer solstice (21 June) – PowerPoint PPT presentation

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Title: The sun

The sun
  • Due to the earths tilt and its orbit around the
    sun, the declination of the sun changes with time
    of year
  • 23.45o at summer solstice (21 June)
  • 0o at vernal and autumnal equniox (21 Mar, Sept)
  • -23.45o at winter solstice (21 Dec)
  • The sun looks like a star that changes
    declination, but also moves through the
    background of fixed stars over the course of the

In a given day
  • To a good approximation
  • The sun moves like a star with
  • A fixed declination
  • A fixed Sidereal Hour Angle

Over the course of a year
  • To a good approximation
  • The sun moves against the background of fixed
  • Declination changes like a sinusoid
  • SHA changes by approx. 1o per day

(No Transcript)
Declination as a function of date
Summer Solstice
Winter Solstice
Meridian height is related to latitude and
Meridian height
Latitude 90oDecl-Meridian height
Due South
Calculating declination on a desert island
d declination Day number of days after 21
What if you dont have a calculator or a table of
sines or MS Exel?
Graphically draw approximation to sine
curve and interpolate visually
Rule of 12ths changes are 123321 for sine
Draw a circle, and measure angles (Burch)
Could approximate angle as days after 21 March
Something you wont remember on a desert island
This varies from the other formula by as much as
2 degrees
Blame orbital parameters of the earth, leap year
differences, eccentricity of orbit..buyer
Who are you going to trust? - Declination
for Oct. 16th from various sources
Source Declination (degrees) Length of day (hours)
Simple form. -10.3302 10.7663
Complex form -9.5993 10.8588
Random website -8.6667 11.0666
NOAA online -9.25 10.9028
Another NOAA -9.02 11.000
NB if you tried to estimate latitude from
length of day, you would see variations of 360
nautical miles!! Also- changes most rapidly this
time of year.
The sun moves across the sky at 15o per
hour With a compass can be used to tell local
time With a shadow stick can be used to find
due South (shortest shadow) or latitude
Watch method for finding South
  • Not talked about much because we all have digital
    watches these days.
  • Point the hour hand at the sun.
  • Due south is halfway between the hour hand and 12
    on the watch
  • NB works only when the sun is below 45o in the
  • When sun is high, lines of azimuth converge -
  • See tables in Gattys book for more accurate
    numbers using a compass

Shadow stick method
Precision of altitude measurements
These are limited by 1.) height of sun and 2.)
measuring instrument With hands only if very
low in the sky (arctic) can one get a degree or
With shadow stick depends on the geometry
maybe 1o With quadrant maybe 1o Warning do
not look directly at noon-day sun use smoked
glass etc With sextant maybe 2-4
Steve Callahan from Adrift
Example Shadow stick work compared with GPS on
trip from Orlando to PA
The sun will look like a star that has a
declination that varies with time of year hence
rising/setting azimuth changes Rising and setting
angles are (90o-Latitude) at the equinox At any
latitude the maximum rising/setting angle north
or south of due east/wests called the suns
Winter Solstice rises S of E
Equinox, rises due east
Summer Solstice rises N of E
Due East
Viking sun compass Found in Greenland by the
archeologist C. L. Vebæk
Indicates 32 compass points. Hole in the center
is where the gnomon (or pointer for Sun-shadow)
goes. Markings on surface are Interpreted as
guides for sunrise and sunset angles.
Interpretation of the scratches are hyperbolae
that give the position of the gnomons shadow at
different times of the day
From the azimuth/declination/latitude
formula, you can get the amplitude for any
latitude (use Rz formula from last week)
Note it goes offscale at 66oN or S, at the artic
Terminator of earth sunset in the summer
over Europe and Africa
Direction of sunset is perpendicular to terminator
Length of day from latitude and declination
Side view
Top view
Length of day 24d/360o
Example Boston constant lat, different dates
16-Oct-2008, Decl. of sun -10.28o hours of
  • Need a watch typical wristwatches are pretty
  • Can calibrate NIST time service
  • http//
  • Keep track of gain/loss
  • Precision of a few seconds possible (less than a
    nautical mile)
  • Limiting factors become accuracy of sightings

Close up of daylight on Oct. 16 near latitude of
1o of Latitude 0.04 hours 2.4 min.
Comments on latitude from length of day
  • Angular diameter of the sun is 32.5 (2 minutes)
  • At horizon, must factor in refraction effects
  • Works best around the solstices
  • Almost impossible to use around equinox
  • Daylight the same at all latitudes
  • Accuracy of declination, other factors

Distortion of sunset from refraction
Comparison naïve approach (mine) to
NOAA calculation at solstice and Oct 16th
Oct 16th 1o 2.4 minutes of daylight Solstice
1o 15 minutes of daylight Oct 16th 1o
error in declination Solstice no error in
declination Oct 16th 28 minutes difference in
daylight Solstice 8.4 minutes difference in
daylight Oct 16th difference in latitude 6o
Solstice difference in latitude 0.56o Huge
Special considerations for areas near the North
or South Pole
Midnight above the arctic circle perfect
for determining latitude from horizon grazing!!
Mean Solar Time
  • The common meaning of time (how we set our
    watches) is mean solar time.
  • Places the highest point of the sun in the sky
    (solar meridian) roughly at noon.
  • Achieved by shifting time zones for every 15o of
  • Greenwich Mean Time (GMT) is used as prime
  • Variations caused by
  • Axial tilt of earth
  • Eccentricity of earths orbit (speeds up and
    slows down)
  • Position within time zone
  • Leap year effects one year is not precisely
    365.25 days (minor for the primitive navigator)
  • Tidal forces from moon slows down the earths
    rotation ever so slightly (VERY minor)

Time zones are approx. 15o wide in
longitude centered on local noon (modulo
political boundaries)
Equation of time describes deviations of the
suns true position at noon from mean solar
time (negative means the sun is late relative to
mean solar time)
Memorization trick for E.o.T. 14 minutes late
on Feb. 14th (Valentines day), 4 days early
three months later (May 15th), 16 minutes early
on Halloween, 6 minutes late 3 months earlier
(June 26th) Approximate this 2 weeks either
side of points are flat, use trapezoids to connect
Longitude from local noon
  • Variation of height of sun at meridian crossing
    is very slow not accurate
  • Mid-point between a time of sunrise and sunset is
    most accurate
  • With a watch measure identical height above
    horizon at sunrise and sunset using hands or
    kamal for accuracy

The kamal used by ancient Arab sea
traders Based on same principle as use of hands
to measure angles Knotted string allows for
range of angles Board at end is calibrated in
degrees Hold knot in teeth and read off
elevation from horizon
Local Area Noon
Correction from equation of time Then knowing
watch time zone (from GMT) caclulate time
difference from of LAN from GMT, and convert to
degrees from prime meridian Accuracy of sighting
of sunrise and sunset with a kamal should be
fairly accurate much better than 1
degree. Fraction of the suns diameter (10 10
nautical miles)
The analema
A photo of the sun at the same time every day for
a year
A simultaneous plot of solar declination and time
of the sun (relative to mean solar time) produces
a figure 8 called an analema
An analemmatic sundial corrects for the
equation of time with different locations of
the gnomon (shadow stick) depending on date.
Why the sky is blue and polarized?
The light reaching your eyes from the sky is the
result of a single scatter off of air molecules.
This scattering is called Rayleigh scattering.
It is larger at higher Frequencies (shorter
wavelengths) so blue scatters best. Also, light
is polarized when scattered at 90o
Scattered light is polarized at 90o scattering
At sunset, light has all the blue scattered out
of it, and is red.
Polarization of the sky depends on the location
of the sun
Sun at zenith
Sun at horizon
Photo of the sky with a polarization filter
Polarization filter
The Viking sun stone
  • From Harafns Saga
  • the weather was thick and stormyThe king looked
    about and saw no blue skythen the king took out
    the sunstone and held it up, and then he saw
    where the Sun beamed from the stone.
  • Modern speculation is that the sun stone was
    Icelandic spar (calcite) that was used to get
    polarization information from the sky for the
    direction of the sun.

Calcite is birefringent meaning that two
different polarization states of light have two
different refractive indices
Speculation on the sun stone
  • The sun was often low on the horizon during the
    voyaging season
  • A lot of fog also was low in the sky and could
    obscure the sun
  • Sky polarization would be observable overhead,
    and could have been used
  • Large sources of calcite on east coast of

The moon
  • Although the moon can be used for celestial
    navigation, it cant really be used for
    primitive navigation, except for rough
    direction finding (i.e. not latitude and
    longitude need sextant, clock and tables)
  • Tidal forces from the earth slowed down the
    moons rotation until it shows the same face to
  • The moon moves to the east in rotation by 12o per
    day (half a degree per hour).
  • Moves west like the sun, at 15o per hour
  • The lit side of the moon always faces the sun
  • Full moon rises opposite the setting sun around
    the time of the equinox
  • Website for moon phases
  • http//

Bright face of moon always faces the sun phase
of the moon tells you the angle to the sun
Direction of sun 14.5o per hour
Horns of moon point south
Due South
Moon opposite Sun 180o to 270o
270o to 0o
New Moon
0o to 90o
90o to 180o