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MOVEMENTS OF THE EARTH (Apparent movement of the sun,

Environmental. Physics. LESSON 1. MOVEMENTS 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 :

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MOVEMENTS OF THE EARTH (Apparent movement of the sun,

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  1. Environmental Physics LESSON 1 MOVEMENTS 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. Environmental Maximum circle: It is a circle defined by the intersection of the sphere with a plane dividing it into two equal parts. Physics 2 1 Real positions CELESTIAL SPHERE Celestial 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. Minor circle: It is a circle defined by the intersection of the sphere with a plane dividing it into two non-equal parts.

  3. Environmental N Spin of the celestial sphere Spin of the Earth Physics S REFERENCES IN THE CELESTIAL SPHERE Pole Line (axis of the world) Right hand rule Meridians Maximum circles perpendicular to equator Celestial Equator Maximum circle perpendicular to the axis of the world

  4. Environmental  is the latitude of this point N  Physics S GEOGRAPHIC COORDINATES: LATITUDE Shape 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. Equatorial 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. Meridian of reference L is the longitude of all those points Environmental N L Physics S GEOGRAPHIC COORDINATES: LONGITUDE Equatorial diameter: 12,756 Km. Equatorial 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. Longitude 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. Environmental Physics 23º 27’ ORBIT OF THE EARTH: CHARACTERISTICS 1º) 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.  149.5 Mkm) 2º) The time the Earth takes to complete one orbit around the Sun is 365.25 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).

  7. June 21/22 Summer solstice Ecliptic plane March 20/21 Spring equinox Environmental  = 23º 27’ 23º 27’  = 0 April 4 23º 27’ January 3 PERIHELION 1 U.A. 1.017 U.A. 0.983 U.A. July 4 APHELION 1 U.A. 23º 27’ October 5 September 21/22 Fall equinox Physics December 21/22 Winter solstice 23º 27’  = 0  = -23º 27’ THE ORBIT OF THE EARTH: THE SEASONS 1 A.U.. = (149597890±500) km  1.496108 km

  8. Environmental Daily angle (radians) Inverse relative distance J = day of the year Eccentricity factor (J = 1 .. 365) Physics EARTH-SUN DISTANCE Spencer Formula r0 = 1 U.A. Duffie y Beckman Formula

  9. Environmental Physics Earth-Sun distance

  10. Environmental Physics EARTH-SUN DISTANCE: XY representation Calculus from Duffie-Beckman formula

  11. Celestial north pole Fall equinox Apparent path of the Sun on the ecliptic plane Environmental Declination angle  Summer solstice 23º27’ 23º27’ Winter solstice Physics Spring equinox Celestial equator plane Celestial south pole YEARLY APPARENT MOVEMENT OF THE SUN Declination angle

  12. 23º 27’ Environmental 23º 27’ 23º 27’ 23º 27’ Physics SOLSTICES SUMMER WINTER

  13. Spencer formula for declination Environmental  (degrees) Daily angle (radians) Physics On equinoxes  = 0 On the summer solstice  = +23º27’ On the winter solstice  = -23º27’

  14. Declination formula (Crop Evapotranspiration/FAO)  (degrees) Environmental Crop Evapotranspiration Spencer Day of the year Physics http://www.fao.org/docrep/X0490E/x0490e00.htm

  15. Summer solstice Environmental Spencer Crop Evap. Winter solstice Spring equinox Fall equinox Physics COMPARING RESULTS FOR DECLINATION FROM SPENCER FORMULA AND CROP FORMULA  (degrees) Number of day of the year

  16. Celestial equator Environmental Celestial north pole 90-  horizon  Physics CELESTIAL EQUATOR AND CELESTIAL NORTH POLE  latitude Observer in Northern hemisphere

  17. Zenit Celestial north pole  Environmental 90- W N S  Physics E CELESTIAL EQUATOR AND CELESTIAL NORTH POLE (II) Observer in northern hemisphere

  18. Polar Environmental Celestial NP Physics CIRCUMPOLAR STARS

  19. Zenit  Celestial south pole Environmental W  90- Physics S N E CELESTIAL EQUATOR AND CELESTIAL SOUTH POLE Observer in southern hemisphere

  20. Celestial equator Zenit Celestial north pole Tropic of Capricorn Tropic of Cancer Environmental 23º 27’ W -23º 27’ N S  Physics E APPARENT PATH OF THE SUN IN THE NORTHERN HEMISPHERE SKY Equinoxes Summer solstice Winter solstice

  21. Zenit  Celestial north pole Environmental  W N S  Physics E APPARENT PATH OF THE SUN Any day Observer in northern hemisphere  declination  latitude Season: spring/summer

  22. POSITION OF THE SUN RELATED TO A HORIZONTAL SURFACE Zenit  Celestial north pole Environmental z  W  N S 15º/hour   Physics  E  latitude  declination Season: spring/summer Observer in northern hemisphere  solar altitude z zenith angle  solar azimut  Hour angle COORDINATES measured from the center of sun disc

  23. Zenit  Celestial north pole Environmental   = 0 W max N S  Physics E MAXIMUM SOLAR ALTITUDE  latitude  declination Observer in northern hemisphere Season Spring / Summer

  24. Zenit  Celestial north pole Environmental  W sHour angle at the sunrise z = 90º N S s  Physics E  HOUR ANGLE AT THE SUNRISE  latitude  declination  solar altitude z zenith angle  solar azimut Season Spring / Summer Observer in northern hemisphere  = 0

  25. Environmental shour angle at the sunrise Physics SIGN CRITERION It varies from 0º (horizon) to 90º (zenit)  solar altitude It varies from 0º (cénit) to 90º (horizonte) z zenith angle It varies from 0º (south) to 180º (north). Sign: + towards E, - towards W  solar azimut  hour angle It varies 0º (Sun on the meridian) to a value dependent on the day of the year and on the latitude. Sign: + before noon, - after noon Value dependent on the day of the year and on the latitude.

  26. Environmental Physics RELATIONSHIPS BETWEEN THE POSITION ANGLES Zenital angle / solar elevation vs declination, latitude and hour angle Azimut angle vs solar elevation, declination and latitude Hour angle at the sunrise vs declination and latitude What rate does the hour angle vary?

  27. Environmental Physics SOLAR DAY Solar 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. Environmental Cenit Celestial equator W N S Physics E MEAN SOLAR DAY Mean Solar Dayis 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 DURATION

  29. Environmental Physics We can obtain data for each day of the year from this one or some similar formula TIME EQUATION The 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 TIME The time equation reaches its maximum value (about 16 minutes) in november and its minimum in february (about 14 minutes). SPENCER FORMULA FOR TIME EQUATION J number of the day of the year Daily angle 0 to 365, or 0 to 366 for leap year

  30. Environmental Physics TIME EQUATION: GRAPHICS TIME EQUATION = SOLAR MEAN TIME - SOLAR APPARENT TIME http://averroes.cec.junta-andalucia.es/ies_gaviota/ fisiqui/relojsol/horas.htm

  31. Environmental www.greenwichmeantime.com Physics 0º DETERMINATION OF TIME: GMT GMT = Greenwich Mean Time GMT is the Greenwich time according to the fictitious movement of the mean sun. It 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. Environmental Physics http://www.hyperdictionary.com/search.aspx?Dict=&define=UTC&search.x=32&search.y=10 Definition UTC http://www.its.bldrdoc.gov/fs-1037/dir-009/_1277.htm DETERMINATION OF TIME: UNIVERSAL TIME UTC = Universal Time Coordinated UT = Universal Time UT measurements are based on the standard second. Actual definition for a second (1967): a second equals to 9 192 631770 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.

  33. Environmental Physics DETERMINACIÓN OF TIME: GREENWICH OBSERVATORY

  34. Zenit UTC = 12:00:00 GMT = 12:00:00 Environmental W N S Physics E UTC = 00:00:00 GMT = 00:00:00 DETERMINATION OF TIME: GMT y UTC

  35. Cenit Environmental Sun apparent movement: W  N S Physics HSL = 10:00:00 E DETERMINATION 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. HSL = 12:00:00  = 0º  = 30º Example:

  36. Environmental Physics DETERMINATION 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. http://stj.chihuahua.gob.mx/asamblea/horarios.htm

  37. Environmental Time equation Longitude correction Ls Standard meridian longitude Le Local meridian longitude 4 min / degree LAT = LST + 4·(Ls-Le) + Et Physics >0 towards W Degrees Longitude correction in minutes Ls, Le <0 towards E DETERMINATION 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) - Et (minutes) Sun apparent movement 15 degrees / hour

  38. Environmental Physics >0 towards W Ls, Le <0 towards E www.greenwichmeantime.com 1º52’ 0º 4·(-1.867) =- 7.47 min = -7 min 28 s DETERMINATION 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. Le Ls Albacete Find LST in Albacete when it is 12:00:00 LAT on January 1st. (Longitude of Albacete 1º52’ W) Greenwich LST = LAT - Et - 4·(Ls-Le) Longitud correction -7.47 min Jan 1st Et = -2.90 min LST = 12:00:00 -(-7.47) -(-2.90) LST = 12:00:00 +10.37 min = 1º52’ = 1.87º = 12:10:23

  39. Environmental Reference meridian 4·(60.00-58.48) = 6.08 min Et = +14.62 min 16th Oct Physics 10 h + 20.70 min = 10:20:42 DETERMINATION 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. + 4·(Ls-Le) = 10:00:00 + 6.08 + Et LAT = LST + 14.62 = 10 h + 20.70 min

  40. Environmental Physics DETERMINATION OF TIME: LEGAL TIME Legal 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 TIME Official 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). http://nist.time.gov/ Spain belongs to the center european time zone.. Winter time: OFFICIAL TIME = LEGAL TIME = GMT + 1 Summer time: OFFICIAL TIME = LEGAL TIME + 1 = GMT + 2

  41. Environmental W Zenit S N E Physics GEOGRAPHIC POSITION: LATITUDE DETERMINATION For 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 MERIDIAN

  42. Environmental W Celestial North Pole Zenit S N E Physics GEOGRAPHIC POSITION: LATITUDE DETERMINATION (II) 2º) POLAR STAR ALTITUDE: THIS IS A DIRECT MEASUREMENT OF LATITUDE Application: at night, only on the northern hemisphere

  43. Environmental Having in mind the daily correction Physics LAT measurement on the point LST on Ls meridian GEOGRAPHIC POSITION: LONGITUDE DETERMINATION To 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) + Et

  44. Environmental degrees minutes minutes minutes/degree HSL – HSE – Et (Ls-Le) = L = 4 Le Le Ls Ls Physics E E W W GEOGRAPHIC POSITION: LONGITUDE DETERMINATION. SIGNS The sun spends 4 minutes to go over a degree LAT = LST + 4(Ls-Le) + Et 4 (Ls-Le) = LAT – LST – Et L < 0 L > 0

  45. Environmental LAT – LST – Et (Ls-Le) = L = 4 Le Ls (-6.4) Physics 1 1 E W = = 4 4 GEOGRAPHIC POSITION: LONGITUDE DETERMINATION. EXEMPLE On 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 LAT Time equation on July 28th: Et = –6.60 m (-6 m 36 s) = -13 m Difference LAT-LST (Ls-Le) = L (-13 – (-6.60)) L < 0 (Ls-Le) = L = -1.6º = -1º36’ 1º 36’ Le = Ls + 1º36’

  46. Lack of some corrections Environmental Cenit W The maximum of hours of sun for a day is twice Lenght of the day N S Physics s E THE LENGTH OF THE DAY (SUNRISE AND SUNSET TIME) The time (in hours) the sun takes to reach the local meridian is (because the sun goes over 15º/hour in its path on the sky) LAT = 12:00:00  = 0º SUNSET SUNRISE

  47. Environmental Solar altitude (solar disc center) -34’  = 0 Sunrise ahead of time -16’ -50’ Physics Sunset behind time -16’ SOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSET I. CORRECTION BY ATMOSPHERIC REFRACTION Correction  3-5 minutos

  48. Environmental Physics SOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSET (II) II. Correction by variation of declination Throughout 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 2s/15 hours. Associated variation  1 minute III. OPTICAL EFFECTS BY THERMAL INVERSIONS http://www.astrored.org/usuarios/xgarciaf/orto1.htm

  49. Royal Greenwich bservatory http://greenwichmeantime.com/ Environmental Physics BIBLIOGRAFÍA y DOCUMENTACIÓN Main text: M. Iqbal, An Introduction to Solar Radiation, Academic Press (1983) Yearbooks and tables. Sunrise and sunset time. Observatorio astronómico nacional Horas de salida y puesta de Sol en capitales provincia España http://www.oan.es/servicios/agenda/2003/index.html U.S. Naval Observatory Horas de salida y puesta de Sol en coordenadas cualesquiera http://aa.usno.navy.mil/data/docs/RS_OneYear.html#formb

  50. Environmental Spain hour zones Sunrise and sunset corrections http://www.rediris.es/red/zona_horaria.es.html http://www.astrored.org/usuarios/xgarciaf/orto1.htm Glossary and definitions (English) http://www.sundialsoc.org.uk/glossary/frameset.htm http://www.infoplease.com/ce6/society/A0850108.html The problem of the longitude http://www.sunlitdesign.com/infosearch/hourangle.htm?indexref=3 http://rubens.anu.edu.au/student.projects97/naval/home.htm (no longer available) Physics W J H Andrewes, “Crónica de la medición del tiempo”, Investigación y Ciencia, nov 2002 BIBLIOGRAFÍA y DOCUMENTACIÓN (II) See also quotations on the text.

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