Presentation on theme: "MOVEMENTS OF THE EARTH LESSON 1 Teaching Team:"— Presentation transcript:
1 MOVEMENTS OF THE EARTH LESSON 1 Teaching Team: PhysicsEnvironmentalLESSON 1MOVEMENTS OF THE EARTH(Apparent movement of the sun,time determination and geographic coordinates)Teaching Team:Prof. Alfonso Calera Belmonte (Dpt. Applied Physics, UCLM)Prof. Antonio J. Barbero (Dpt. Applied Physics, UCLM)Consultant:Prof. Kathy Walsh (Dpt. Modern Languages, UCLM)
2 PhysicsEnvironmentalCELESTIAL SPHERECelestial sphere: fictitious sphere of arbitrary radius, whose center is the observer’s eye. The positions of the planets and the stars are projected onto it. So, we can measure planet and star positions independently of their distance, using angle units over maximum circles defined over the sphere.Maximum circle:It is a circle defined by the intersection of the sphere with a plane dividing it into two equal parts.Minor circle:It is a circle defined by the intersection of the sphere with a plane dividing it into two non-equal parts.21Real positions
3 Maximum circle perpendicular to the axis of the world PhysicsEnvironmentalREFERENCES IN THE CELESTIAL SPHEREPole Line (axis of the world)Right hand ruleNSMeridiansMaximum circlesperpendicularto equatorSpin of the celestial sphereSpin of the EarthCelestial EquatorMaximum circle perpendicular to the axis of the world
4 is the latitude of this point PhysicsEnvironmentalGEOGRAPHIC COORDINATES: LATITUDEShape of the Earth: very similar to a sphere squashed at the poles and convex at the equator. This shape is called ‘geoide’.Equatorial diameter: 12,756 Km. is the latitude of this pointNSEquatorial length: 40,075 Km.PARALLEL: Minor circle determined by cutting the sphere with a plane parallel to the equator.LATITUDE of a point: It is the angle subtended from the center of the Earth by a radius directed to the point and another radius directed to that point on the equator located on the same meridian ( in the figure).Latitude is measured in degrees:0º (equator) to 90º (north/south pole)All points on the same parallel have the same latitude.
5 L is the longitude of all those points PhysicsEnvironmentalGEOGRAPHIC COORDINATES: LONGITUDEMeridian of referenceEquatorial diameter: 12,756 Km.L is the longitude of all those pointsNSEquatorial length: 40,075 Km.MERIDIAN: Any maximum circle passing throught the poles.Meridian lenght: 40,008 Km.LONGITUDE of a point: It is the angle between the plane of a particular meridian and the plane of another meridian taken as reference.LLongitude L is measured in degrees, from 0º until 180º, either to the East (E) or to the West (W) from the meridian of reference.... really L is the longitude of any point lying on that meridian!
6 ORBIT OF THE EARTH: CHARACTERISTICS PhysicsEnvironmentalORBIT OF THE EARTH: CHARACTERISTICS1º) The orbit of the Earth around the Sun is a slightly eccentic ellipse. The Sun lies on one of its focal points. Because of this, the apparent movement of the Sun around the Earth varies throughout the year: the Sun seems to move faster whenever the Earth is closer to it. The mean distance Earth-Sun is called astronomical unit (1 A.U. Mkm)2º) The time the Earth takes to complete one orbit around the Sun is days (one year). The Earth spins once around its own axis every 24 hours (one day).3º) The Earth’s equator plane is not the same as the Earth’s orbit plane around the Sun: both planes are tilted at an angle of 23º 27’ (ecliptic obliquity).23º 27’
7 THE ORBIT OF THE EARTH: THE SEASONS PhysicsEnvironmentalTHE ORBIT OF THE EARTH: THE SEASONS1 A.U.. = ( ±500) km 1.496108 kmJune 21/22Summer solstice = 23º 27’Ecliptic planeMarch 20/21Spring equinox = 023º 27’April 423º 27’January 3PERIHELION1 U.A.0.983 U.A.1.017 U.A.July 4APHELION23º 27’December 21/22Winter solstice = -23º 27’23º 27’September 21/22Fall equinox = 0October 5
8 Inverse relative distance PhysicsEnvironmentalEARTH-SUN DISTANCESpencer FormulaEccentricity factorr0 = 1 U.A.Daily angle (radians)Inverse relative distanceDuffie y Beckman FormulaJ = day of the year(J = )
10 Calculus from Duffie-Beckman formula PhysicsEnvironmentalEARTH-SUN DISTANCE: XY representationCalculus from Duffie-Beckman formula
11 YEARLY APPARENT MOVEMENT OF THE SUN PhysicsEnvironmentalYEARLY APPARENT MOVEMENT OF THE SUNDeclination angleCelestial south poleCelestial north poleFall equinoxApparent path of the Sun on the ecliptic planeDeclination angle 23º27’Summer solsticeWinter solsticeSpring equinoxCelestial equator plane
13 Spencer formula for declination PhysicsEnvironmentalSpencer formula for declination (degrees)Daily angle (radians)On equinoxes = 0On the summer solstice = +23º27’On the winter solstice = -23º27’
14 Declination formula (Crop Evapotranspiration/FAO) PhysicsEnvironmentalDeclination formula (Crop Evapotranspiration/FAO) (degrees)SpencerCrop EvapotranspirationDay of the year
15 Physics Environmental COMPARING RESULTS FOR DECLINATION FROM SPENCER FORMULA AND CROP FORMULA (degrees)Summer solsticeSpencerCrop Evap.Spring equinoxFall equinoxWinter solsticeNumber of day of the year
16 CELESTIAL EQUATOR AND CELESTIAL NORTH POLE PhysicsEnvironmentalCELESTIAL EQUATOR AND CELESTIAL NORTH POLECelestial equator latitudeCelestial north pole90-horizonObserver inNorthern hemisphere
17 CELESTIAL EQUATOR AND CELESTIAL NORTH POLE (II) PhysicsEnvironmentalCELESTIAL EQUATOR AND CELESTIAL NORTH POLE (II)ZenitCelestial north poleObserver in northern hemisphereSNEW90-
19 CELESTIAL EQUATOR AND CELESTIAL SOUTH POLE PhysicsEnvironmentalCELESTIAL EQUATOR AND CELESTIAL SOUTH POLEZenitCelestial south poleObserver in southern hemisphereNSEW90-
20 APPARENT PATH OF THE SUN IN THE NORTHERN HEMISPHERE SKY PhysicsEnvironmentalAPPARENT PATH OF THE SUN IN THE NORTHERN HEMISPHERE SKYCelestial equatorZenitTropic of CancerTropic of CapricornCelestial north pole23º 27’Equinoxes-23º 27’SNEWWinter solsticeSummer solstice
21 APPARENT PATH OF THE SUN PhysicsEnvironmentalAPPARENT PATH OF THE SUNZenitAny dayObserver in northern hemisphereCelestial north pole declination latitudeSNEWSeason: spring/summer
22 POSITION OF THE SUN RELATED TO A HORIZONTAL SURFACE PhysicsEnvironmentalZenit latitude declinationSeason: spring/summerCelestial north polezObserver in northern hemisphere solar altitudez zenith angle solar azimutSNEW Hour angle15º/hourCOORDINATES measuredfrom the center of sun disc
23 MAXIMUM SOLAR ALTITUDE PhysicsEnvironmentalMAXIMUM SOLAR ALTITUDEZenit latitude declinationCelestial north poleObserver in northern hemisphere max = 0SNEWSeason Spring / Summer
24 HOUR ANGLE AT THE SUNRISE PhysicsEnvironmentalHOUR ANGLE AT THE SUNRISEZenit latitude declinationCelestial north polez = 90º solar altitudez zenith angle solar azimutSNEWss Hour angleat the sunriseSeason Spring / SummerObserver in northern hemisphere = 0
25 It varies from 0º (horizon) to 90º (zenit) PhysicsEnvironmentalSIGN CRITERION solar altitudeIt varies from 0º (horizon) to 90º (zenit)z zenith angleIt varies from 0º (cénit) to 90º (horizonte) solar azimutIt varies from 0º (south) to 180º (north).Sign: + towards E, - towards W hour angleIt varies 0º (Sun on the meridian) to a value dependenton the day of the year and on the latitude.Sign: + before noon, - after noons hour angleat the sunriseValue dependent on the day of the yearand on the latitude.
26 RELATIONSHIPS BETWEEN THE POSITION ANGLES PhysicsEnvironmentalRELATIONSHIPS BETWEEN THE POSITION ANGLESZenital angle / solar elevation vs declination, latitude and hour angleAzimut angle vs solar elevation, declination and latitudeHour angle at the sunrise vs declination and latitudeWhat rate does the hour angle vary?
27 THIS INTERVAL IS NOT NECESSARY A 24-HOURS INTERVAL! PhysicsEnvironmentalSOLAR DAYSolar day is the time interval the Sun takes to verify a complete revolution around a stationary observer lying on the Earth.THIS INTERVAL IS NOT NECESSARY A 24-HOURS INTERVAL!An observer located on the northern hemisphere is looking at the south and turns on a clock which goes on uniformly when the Sun lies directly on the local meridian (then it’s noon!).That observer may find 24 hours later that... the Sun does not lie on the meridian. Maybe the Sun has already passed the meridian, maybe the Sun has not yet reached the meridian. It depends on the day of the year!When moving in the ecliptic plane, the Earth sweeps different areas at different dates because its velocity varies depending on the distance Earth-Sun.The duration of the solar day varies throughout the year for the two main following reasons:The axis of the Earth is tilted a constant angle onto the ecliptic plane.
28 ALL MEAN SOLAR DAYS HAVE THE SAME DURATION PhysicsEnvironmentalMEAN SOLAR DAYMean Solar Day is the average of the solar days and corresponds to a fictitious sun moving on the equatorial plane, whose apparent movement around the Earth have a constant orbital velocity.ALL MEAN SOLAR DAYS HAVE THE SAME DURATIONCenitSNEWCelestial equator
29 TIME EQUATION = SOLAR MEAN TIME - SOLAR APPARENT TIME PhysicsEnvironmentalTIME EQUATIONThe disagreement between the movement of the mean sun (fully homogeneous, with 24-hours intervals for every two next passes across the local meridian) and the apparent movement of the real Sun, is taken into account for calculus by defining the TIME EQUATION.TIME EQUATION = SOLAR MEAN TIME - SOLAR APPARENT TIMEThe time equation reaches its maximum value (about 16 minutes) in november and its minimum in february (about 14 minutes).SPENCER FORMULA FOR TIME EQUATIONWe can obtain data for each day of the year from this one or some similar formulaJ number of the day of the yearDaily angle0 to 365, or 0 to 366 for leap year
30 TIME EQUATION: GRAPHICS PhysicsEnvironmentalTIME EQUATION: GRAPHICSTIME EQUATION = SOLAR MEAN TIME - SOLAR APPARENT TIMEfisiqui/relojsol/horas.htm
31 DETERMINATION OF TIME: GMT PhysicsEnvironmentalDETERMINATION OF TIME: GMTGMT = Greenwich Mean TimeGMT is the Greenwich time according to the fictitious movement of the mean sun.0ºIt counts from midnight, when the mean sun passes across the lower Greenwich meridian.When the mean sun passes across the upper Greenwich meridian, it is noon:GMT = 12:00:00
32 DETERMINATION OF TIME: UNIVERSAL TIME PhysicsEnvironmentalDETERMINATION OF TIME: UNIVERSAL TIMEUT = Universal TimeUTC = Universal Time CoordinatedUT measurements are based on the standard second.Actual definition for a second (1967): a second equals to periods of the radiation from a particular transition between two hiperfine levels of the ground state of cesium 133.Universal time coordinated (UTC) is GMT updated by adding additional seconds (“leap seconds”) to having in mind the lack of uniformity in the rotation of the Earth.UTC means the average value from a certain number of measurements made using different atomic clocks around the world.In aviation UTC is called ZULU time.Definition UTC
33 DETERMINACIÓN OF TIME: GREENWICH OBSERVATORY PhysicsEnvironmentalDETERMINACIÓN OF TIME: GREENWICH OBSERVATORY
34 UTC = 12:00:00 GMT = 12:00:00 UTC = 00:00:00 GMT = 00:00:00 PhysicsEnvironmentalDETERMINATION OF TIME: GMT y UTCZenitSNEWUTC = 12:00:00GMT = 12:00:00UTC = 00:00:00GMT = 00:00:00
35 DETERMINATION OF TIME: LOCAL APPARENT TIME (LAT) PhysicsEnvironmentalDETERMINATION OF TIME: LOCAL APPARENT TIME (LAT)HORA SOLAR LOCAL (HSL) / LOCAL APPARENT TIME (LAT)It refers to the position of the Sun from the local meridian.CenitSun apparent movement:HSL = 12:00:00 = 0ºExample: = 30ºSNEWHSL = 10:00:00
36 DETERMINATION OF TIME: LOCAL STANDARD TIME (LST) PhysicsEnvironmentalDETERMINATION OF TIME: LOCAL STANDARD TIME (LST)HORA SOLAR ESTÁNDAR (HSE) / LOCAL STANDARD TIME (LST)It refers to the standard meridian time (taken as a reference) on each point of a particular zone.All standard meridians are multiple of 15º either E or W from Greenwich.
37 DETERMINATION OF TIME: LOCAL STANDARD TIME (LST) (II) PhysicsEnvironmentalDETERMINATION OF TIME: LOCAL STANDARD TIME (LST) (II)Relationship between local apparent time (LAT, HSL) and local standard time (LST, HSE)LST = LAT- 4·(Ls-Le)- EtLongitude correctionTime equation(minutes)Ls Standard meridian longitudeLe Local meridian longitudeSun apparent movement15 degrees / hour4 min / degreeLs, Le>0 towards W<0 towards ELAT = LST + 4·(Ls-Le) + EtDegreesLongitude correction in minutes
38 DETERMINATION OF TIME: LOCAL STANDARD TIME (EXEMPLE) PhysicsEnvironmentalDETERMINATION OF TIME: LOCAL STANDARD TIME (EXEMPLE)The local standard time is the same for all points in the same time zone.... but the local apparent time is NOT the same! Each point has yours.LeLs1º52’0ºAlbaceteFind LST in Albacete when it is 12:00:00 LAT on January 1st. (Longitude of Albacete 1º52’ W)GreenwichLST = LAT- 4·(Ls-Le)- EtLs, Le>0 towards W<0 towards ELongitud correction minJan 1st Et = minLST = 12:00:00 -(-7.47) -(-2.90)LST = 12:00: min =1º52’ = 1.87º4·(-1.867) = min = -7 min 28 s= 12:10:23
39 DETERMINATION OF TIME: LOCAL APPARENT TIME (EXEMPLE 2) PhysicsEnvironmentalDETERMINATION OF TIME: LOCAL APPARENT TIME (EXEMPLE 2)Find the local apparent time at 10:00:00 h LST on the 16th October in a city where the longitude is 58º 29’ W.Reference meridian4·( ) = 6.08 minLAT = LST+ 4·(Ls-Le)+ Et= 10:00:00+ 6.08= 10 h min10 h min = 10:20:4216th OctEt = min
40 DETERMINATION OF TIME: LEGAL TIME PhysicsEnvironmentalDETERMINATION OF TIME: LEGAL TIMELegal time is the time corresponding to a reference meridian on each time zone (on a general sense, it is the time corresponding to a certain time zone).DETERMINATION OF TIME: OFFICIAL TIMEOfficial time is the time established by the government. It can differ from the legal time by an enter number having in mind criteria of energetic sparing (it is usual having different times on winter and on summer).Spain belongs to the center european time zone..Winter time: OFFICIAL TIME = LEGAL TIME = GMT + 1Summer time: OFFICIAL TIME = LEGAL TIME + 1 = GMT + 2
41 GEOGRAPHIC POSITION: LATITUDE DETERMINATION PhysicsEnvironmentalGEOGRAPHIC POSITION: LATITUDE DETERMINATIONFor determining the latitude we must know the altitude over the horizon of some fixed reference. We will see two of them:1º) SOLAR ALTITUDE WHEN THE SUN IS CROSSING THE LOCAL MERIDIANZenitSNEW
42 GEOGRAPHIC POSITION: LATITUDE DETERMINATION (II) PhysicsEnvironmentalGEOGRAPHIC POSITION: LATITUDE DETERMINATION (II)2º) POLAR STAR ALTITUDE: THIS IS A DIRECT MEASUREMENT OF LATITUDEApplication: at night, only on the northern hemisphereZenitSNEWCelestial North Pole
43 GEOGRAPHIC POSITION: LONGITUDE DETERMINATION PhysicsEnvironmentalGEOGRAPHIC POSITION: LONGITUDE DETERMINATIONTo determine the longitude of a point we must know simultaneously LAT on that point and LST on some reference meridian, in orden to obtain Le from the equation:LAT = LST + 4(Ls-Le) + EtLAT measurementon the pointHaving in mind thedaily correctionLST on Ls meridian
44 The sun spends 4 minutes to go over a degree PhysicsEnvironmentalGEOGRAPHIC POSITION: LONGITUDE DETERMINATION. SIGNSThe sun spends 4 minutes to go over a degreeLAT = LST + 4(Ls-Le) + EtdegreesminutesHSL – HSE – Et=4(Ls-Le)= L4 (Ls-Le) = LAT – LST – Etminutesminutes/degreeLeLsLsLeL < 0L > 0WEWE
45 GEOGRAPHIC POSITION: LONGITUDE DETERMINATION. EXEMPLE PhysicsEnvironmentalGEOGRAPHIC POSITION: LONGITUDE DETERMINATION. EXEMPLEOn July 28th the sun passes across the local meridian at 12:13 LST. Find the longitude of that point respect to the reference meridian.Whenever the sun passes across the meridian it is 12:00 LATTime equation on July 28th: Et = –6.60 m (-6 m 36 s)LAT – LST – Et=4(Ls-Le)= LDifference LAT-LST= -13 mLeLs14=(-6.4)14=(Ls-Le) = L(-13 – (-6.60))L < 0(Ls-Le) = L = -1.6º = -1º36’1º 36’Le = Ls + 1º36’WE
46 THE LENGTH OF THE DAY (SUNRISE AND SUNSET TIME) PhysicsEnvironmentalTHE LENGTH OF THE DAY (SUNRISE AND SUNSET TIME)The time (in hours) the sun takes to reach the local meridian isLack of somecorrections(because the sun goes over 15º/hour in its path on the sky)SNEWCenitLAT = 12:00:00 = 0ºThe maximum of hours of sun for a day is twicesSUNSETLenght ofthe daySUNRISE
47 SOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSET PhysicsEnvironmentalSOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSETI. CORRECTION BY ATMOSPHERIC REFRACTIONSolar altitude(solar disc center) = 0-16’-34’-50’-16’Sunrise ahead of timeSunset behind timeCorrection 3-5 minutos
48 SOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSET (II) PhysicsEnvironmentalSOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSET (II)II. Correction by variation of declinationThroughout a day the apparent movement of the sun goes on, so its declination varies continuously. As a consequence, the declination is not the same at sunrise than at sunset.So, the lenght of a day is not exactly 2s/15 hours.Associated variation 1 minuteIII. OPTICAL EFFECTS BY THERMAL INVERSIONS
49 Royal Greenwich bservatory PhysicsEnvironmentalBIBLIOGRAFÍA y DOCUMENTACIÓNMain text:M. Iqbal, An Introduction to Solar Radiation, Academic Press (1983)Yearbooks and tables. Sunrise and sunset time.Observatorio astronómico nacionalHoras de salida y puesta de Sol en capitales provincia EspañaU.S. Naval ObservatoryHoras de salida y puesta de Sol en coordenadas cualesquieraRoyal Greenwich bservatory
50 BIBLIOGRAFÍA y DOCUMENTACIÓN (II) PhysicsEnvironmentalBIBLIOGRAFÍA y DOCUMENTACIÓN (II)Spain hour zonesSunrise and sunset correctionsGlossary and definitions (English)(no longer available)The problem of the longitudeW J H Andrewes, “Crónica de la medición del tiempo”, Investigación y Ciencia, nov 2002See also quotations on the text.