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Sunset Phenomena. Roger Bailey North American Sundial Society Hartford Oct 1999. Sunset Phenomena. Sunset Phenomena. Simple spherical trigonometry can be used to determine for any location and day of the year When sunset occurs, Where the sun sets on the horizon, - PowerPoint PPT Presentation

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  • Sunset PhenomenaRoger BaileyNorth American Sundial SocietyHartford Oct 1999

  • Sunset Phenomena

  • Sunset PhenomenaSimple spherical trigonometry can be used to determine for any location and day of the yearWhen sunset occurs, Where the sun sets on the horizon,The path of the setting sun, and How long it takes for the sun to set.

  • Spherical TrigonometryHigh school math butNon Euclidian geometryParallel lines meetAngles in triangle > 180Sides are anglesYour position is fixedSun, stars, planets move with celestial sphereAbducted by NASS aliens, Prof. Bailey is forced to write gnomic equations in center ring

  • Navigational trianglePZ=CoL, PM=CoD, ZM=CoHCosine rule: 2 sides and angleCos A=Cos A Cos B+Sin A Sin B Cos c Sin X= Cos 90-X=Cos XSin H=Sin L Sin D+Cos L Cos D Cos tSin D=Sin H Sin L+Cos H Cos L Cos ZSin L=Sin H Sin D+Cos H Cos D Cos Sine rule: Sin Z=Cos D Sin t / Cos HPZenithDQMZtHorizon

  • Navigators EquationAltitude HSin H = Sin L x Sin D + Cos L x Cos D x Cos tAzimuth ZSin Z = Cos D x Sin t / Cos HL = LatitudeD = Declination of Sunt = time angle from local noon (15 / hour)

  • Sunset EquationAt sunrise and sunset, altitude is zero, neglecting refraction and semi-diameterI f H = 0, then Sin H = 0Sin L x Sin D + Cos L x Cos D x Cos t = 0Cos t = -Tan L x Tan D Time of sunset is determined by the latitude and solar declinationSunrise is - t

  • Sun as the Essence of TimeYear: one full orbital periodFull Declination cycle +/- 23.5 solstices & equinoxesFull Equation of Time cycleDay: one full rotation 360 in 24 hoursTime as an angle360/24 = 15/hour = 1/4 minutesSun at Zenith, time angle t = 0Clocks are wrong!

  • Clock Time CorrectionsLongitude correctionMod (Longitude / 15) as a time angleExample (Canmore) 115/15 = 7 hours and 10 or 40Daylight Saving Time +1 hour in the summerEquation of Time Correction Solar noon is 1:40 pm MDST on a sunny summer afternoon in Canmore AB

  • Sunset TimeSunset Equation: Cos t = -Tan L x Tan DEquinox: (21 March, 21 Sept) Declination = 0If D = 0, Cos t = 0, t = 90 or 6 hoursSunrise 6 AM, Sunset 6 PM for any latitudeEquator: Latitude = 0If L = 0, Cos t = 0, t = 90 or 6 hoursSunrise 6 AM, Sunset 6 PM for any declination

  • Time to SunsetItalian Hours Sunset to SunsetCountdown Italian Hours gives time till sunsetAirports: Visual Flying RulesRASC Alberta Star PartyEccles Ranch ObservatoryCaroline AB (52.1, 114.7)0

  • Endless DayJohn DunnArctic Light

  • Polar CirclesSunrise Equation Cos t = -Tan L x Tan DPolar Circle, sun does not riseAt noon, t = 0, Cos t = 1 = -Tan L x Tan DTan D = 1/Tan L = Cot L = Tan (90-L)Extreme Declination = +/- 23Extreme Latitude = -/+ 66 (90-23)

  • Sunset Location What is the azimuth of the setting sun?Cosine Rule for the Navigational TriangleSin D=Sin L Sin H + Cos L Cos H Cos ZFor H = 0, Sin H = 0 & Cos H = 1 Cos Z = Sin D / Cos L

  • Sunset LocationCos Z = Sin D / Cos LFor the equator, L = 0, Cos L = 1Cos Z = Sin D = Cos (90-D) and Z = 90-DThe azimuth of the setting sun is the co-declinationFor equinox D = 0, Cos Z= 0, then Z = 90 for all LThe sun rises due east and sets due west on the equinox for all latitudes

  • Sunset Path

  • Sunset PathAngle with horizon is Cos = Sin L / Cos DAt equator, L = 0Cos = 0, so = 90 for all declinationsAt equinox, D =0Cos = Sin L = Cos (90-L) = Co-latitudeHorizon

  • Sunset Path Reality CorrectionsSemidiameter 16Refraction 34Time Correction 50 x 4 / Sin Azimuth Correction50 x Cos Theoretical HorizonApparent HorizonAzimuth CorrectionTime Correction16 SD34Refraction

  • Dip CorrectionEarths curvature and the height of observer affect the apparent horizonDip = 0.97 x height (ft)Height Dip10 ft 3 100 ft 9.71000 ft 30HeightDip

  • Green FlashHave you seen the Green Flash at the instant of sunset?Can you climb fast enough to increase the dip and see multiple Green Flashes ?Depends on initial height, and climb rateHeight = 0Climb = 2 fps

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  • Sunset RateSunset rate = Solar rate (/minute) x Sin Equator: = 90, the sun always sets at 15/At Latitude 51, the sun sets at :Equinox, D = 0, = 39, rate is 9.44/Solstice, D = 23.44, = 32.1, rate is 7.97/Time flies when you are having fun! Tropical sunsets are half as long!

  • Sunset PhenomenaFunctions of Latitude and Declination solvable with high school trig and a pocket calculatorTime: Cos t = -Tan L x Tan DLocation: Cos Z = Sin D / Cos LPath: Cos = Sin L / Cos D Rate: Sin x / minute (15/)Reality checks applicable