Presentation on theme: "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)"— Presentation transcript:
1 The sunDue to the earth’s tilt and its orbit around the sun, the declination of the sun changes with time of year23.45o 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 year.
2 Over the course of a year In a given dayTo a good approximation:The sun moves like a star withA fixed declinationA fixed Sidereal Hour AngleOver the course of a yearTo a good approximation:The sun moves against the background of fixed starsDeclination changes like a sinusoidSHA changes by approx. 1o per day
4 Declination as a function of date Summer Solstice+23.45o-23.45oWinter Solstice
5 Meridian height is related to latitude and declination 90o+Decl-Meridian heightDue South
6 Day = number of days after 21 March Calculating declination on a “desert island”d = declinationDay = number of days after 21 MarchWhat if you don’t have a calculator or a tableof sines or MS Exel?
7 Graphically – draw approximation to sine curve and interpolate visuallyRule of 12ths: changes are 1:2:3:3:2:1 for sine curves
8 Draw a circle, and measure angles (Burch) Could approximate angleas days after 21 MarchRadius=23.45
9 Something you won’t remember on a desert island: This varies from the other formula by as much as 2 degreesBlame: orbital parameters of the earth, leap year differences, eccentricityof orbit…..buyer beware!!
10 Who are you going to trust? - Declination for Oct. 16th from various sourcesSourceDeclination(degrees)Length of day(hours)Simple form.Complex formRandom websiteNOAA online-9.25Another NOAA-9.0211.000NB – if you tried to estimate latitude from length of day,you would see variations of 360 nautical miles!! Also- changesmost rapidly this time of year.
11 The sun moves across the sky at 15o per hour With a compass can be used to tell local timeWith a shadow stick can be used to find dueSouth (shortest shadow) or latitude
12 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 watchNB works only when the sun is below 45o in the horizon.When sun is high, lines of azimuth converge - inaccurateSee tables in Gatty’s book for more accurate numbers using a compass
14 Precision of altitude measurements These are limited by 1.) height of sun and 2.) measuringinstrumentWith hands – only if very low in the sky (arctic) can one geta degree or so.With shadow stick – dependson the geometry – maybe 1oWith quadrant – maybe 1oWarning – do not look directlyat noon-day sun – use smokedglass etcWith sextant – maybe 2-4’
16 Example: Shadow stick work compared with GPS on trip from Orlando to PA
17 The sun will look like a star that has a declination that varies with time of year – hence rising/setting azimuthchangesRising and setting angles are (90o-Latitude) at the equinoxAt any latitude – the maximum rising/setting angle north or south ofdue east/wests called the sun’s amplitudeWinter Solsticerises S of EEquinox, risesdue eastSummer Solsticerises N of EθDue East
18 Found in Greenland by the Viking sun compassFound in Greenland by thearcheologist C. L. VebækIndicates 32 compass points.Hole in the center is wherethe gnomon (or pointer forSun-shadow) goes.Markings on surface areInterpreted as guides forsunrise and sunset angles.
19 Interpretation of the scratches are hyperbolae that give the position of the gnomon’s shadowat different times of the day
20 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 circle
21 Terminator of earth – sunset in the summer over Europe and AfricaDirection of sunset isperpendicular to terminator
22 Length of day from latitude and declination Side viewTop viewdecyouddaynightTerminatorLength of day = 24*d/360o
23 Example: Boston – constant lat, different dates
24 16-Oct-2008, Decl. of sun = -10.28o hours of daylight
25 Time Need a watch – typical wristwatches are pretty accurate Can calibrate – NIST time service:Keep track of gain/lossPrecision of a few seconds possible (less than a nautical mile)Limiting factors become accuracy of sightings
26 Close up of daylight on Oct. 16 near latitude of Boston1o of Latitude =0.04 hours = 2.4 min.
27 Comments on latitude from length of day Angular diameter of the sun is 32.5’ (2 minutes)At horizon, must factor in refraction effectsWorks best around the solsticesAlmost impossible to use around equinoxDaylight the same at all latitudesAccuracy of declination, other factorsDistortion of sunsetfrom refraction
28 Comparison – naïve approach (mine) to NOAA calculation at solstice and Oct 16thOct 16th – 1o = 2.4 minutes of daylightSolstice – 1o = 15 minutes of daylightOct 16th – 1o error in declinationSolstice – no error in declinationOct 16th – 28 minutes difference in daylightSolstice – 8.4 minutes difference in daylightOct 16th – difference in latitude = 6oSolstice – difference in latitude = 0.56oHuge difference!!
29 Special considerations for areas near the North or South Pole
30 Midnight above the arctic circle – perfect for determining latitude from horizon grazing!!
31 Mean Solar TimeThe 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 longitudeGreenwich Mean Time (GMT) is used as prime meridianVariations caused byAxial tilt of earthEccentricity of earth’s orbit (speeds up and slows down)Position within time zoneLeap year effects – one year is not precisely days (minor for the primitive navigator)Tidal forces from moon slows down the earth’s rotation ever so slightly (VERY minor)
32 Time zones are approx. 15o wide in longitude centered on local noon (modulo political boundaries)
33 Equation of time describes deviations of the sun’s true position at noon from mean solar time(negative means the sun is late relative to mean solar time)
34 Memorization trick for E. o. T. – 14 minutes late on Feb 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
35 Longitude from local noon Variation of height of sun at meridian crossing is very slow – not accurateMid-point between a time of sunrise and sunset is most accurateWith a watch – measure identical height above horizon at sunrise and sunset using hands or kamal for accuracy
36 The kamal – used by ancient Arab sea traders Based on same principle as use of hands to measureanglesKnotted string allows for range of anglesBoard at end is calibrated in degreesHold knot in teeth and read off elevation from horizon
37 Local Area NoonCorrection from equation of timeThen – knowing watch time zone (from GMT) – caclulatetime difference from of LAN from GMT, and convertto degrees from prime meridianAccuracy of sighting of sunrise and sunset with a kamalshould be fairly accurate – much better than 1 degree.Fraction of the sun’s diameter (10’ = 10 nautical miles)
38 A simultaneous plot of solar declination and time of the sun The analemaA photo of the sun at the same timeevery day for a yearA simultaneous plot of solardeclination and time of the sun(relative to mean solar time)produces a figure 8 called ananalema
39 An “analemmatic” sundial corrects for the equation of time – with different locations of the gnomon (shadow stick) dependingon date.
40 Why the sky is blue and polarized? The light reaching your eyes from the sky is the resultof a single scatter off of air molecules. This scatteringis called “Rayleigh scattering”. It is larger at higherFrequencies (shorter wavelengths) – so blue scatters best.Also, light is polarized when scattered at 90oScattered light is polarizedat 90o scatteringIncoming
41 At sunset, light has all the blue scattered out of it, and is red.
42 Polarization of the sky depends on the location of the sunSun at zenithSun at horizon
44 The Viking sun stone From Harafns Saga: “the weather was thick and stormy…The king looked about and saw no blue sky…then 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.
45 Calcite is “birefringent” – meaning that two different polarization states of light have two different refractiveindices
46 Speculation on the sun stone The sun was often low on the horizon during the voyaging seasonA lot of fog also was low in the sky and could obscure the sunSky polarization would be observable overhead, and could have been usedLarge sources of calcite on east coast of Iceland.
47 The moonAlthough the moon can be used for celestial navigation, it can’t 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 moon’s rotation until it shows the same face to us.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 hourThe lit side of the moon always faces the sunFull moon rises opposite the setting sun around the time of the equinoxWebsite for moon phases:
48 Bright face of moon always faces the sun – phase of the moon tells you the angle to the sun Direction of sun14.5o per hourHorns of moonpoint southDue South
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