MOVEMENTS OF THE EARTH LESSON 1 Teaching Team:

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MOVEMENTS OF THE EARTH LESSON 1 Teaching Team:
Physics Environmental 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)

Physics Environmental 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. 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. 2 1 Real positions

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

 is the latitude of this point
Physics Environmental 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.  is the latitude of this point N S 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.

L is the longitude of all those points
Physics Environmental GEOGRAPHIC COORDINATES: LONGITUDE Meridian of reference Equatorial diameter: 12,756 Km. L is the longitude of all those points N S 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. L 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!

ORBIT OF THE EARTH: CHARACTERISTICS
Physics Environmental 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.  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’

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

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

Physics Environmental Earth-Sun distance

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

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

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

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

Declination formula (Crop Evapotranspiration/FAO)
Physics Environmental Declination formula (Crop Evapotranspiration/FAO)  (degrees) Spencer Crop Evapotranspiration Day of the year

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

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

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

Physics Environmental CIRCUMPOLAR STARS Polar Celestial NP

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

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

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

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

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

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

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

RELATIONSHIPS BETWEEN THE POSITION ANGLES
Physics Environmental 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?

THIS INTERVAL IS NOT NECESSARY A 24-HOURS INTERVAL!
Physics Environmental 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.

ALL MEAN SOLAR DAYS HAVE THE SAME DURATION
Physics Environmental MEAN SOLAR DAY Mean 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 DURATION Cenit S N E W Celestial equator

TIME EQUATION = SOLAR MEAN TIME - SOLAR APPARENT TIME
Physics Environmental 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 We can obtain data for each day of the year from this one or some similar formula J number of the day of the year Daily angle 0 to 365, or 0 to 366 for leap year

TIME EQUATION: GRAPHICS
Physics Environmental TIME EQUATION: GRAPHICS TIME EQUATION = SOLAR MEAN TIME - SOLAR APPARENT TIME fisiqui/relojsol/horas.htm

DETERMINATION OF TIME: GMT
Physics Environmental 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

DETERMINATION OF TIME: UNIVERSAL TIME
Physics Environmental DETERMINATION OF TIME: UNIVERSAL TIME UT = Universal Time UTC = Universal Time Coordinated UT 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

DETERMINACIÓN OF TIME: GREENWICH OBSERVATORY
Physics Environmental DETERMINACIÓN OF TIME: GREENWICH OBSERVATORY

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

DETERMINATION OF TIME: LOCAL APPARENT TIME (LAT)
Physics Environmental 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. Cenit Sun apparent movement: HSL = 12:00:00  = 0º Example:  = 30º S N E W HSL = 10:00:00

DETERMINATION OF TIME: LOCAL STANDARD TIME (LST)
Physics Environmental 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.

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

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

DETERMINATION OF TIME: LOCAL APPARENT TIME (EXEMPLE 2)
Physics Environmental 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. Reference meridian 4·( ) = 6.08 min LAT = LST + 4·(Ls-Le) + Et = 10:00:00 + 6.08 = 10 h min 10 h min = 10:20:42 16th Oct Et = min

DETERMINATION OF TIME: LEGAL TIME
Physics Environmental 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). 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

GEOGRAPHIC POSITION: LATITUDE DETERMINATION
Physics Environmental 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 Zenit S N E W

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

GEOGRAPHIC POSITION: LONGITUDE DETERMINATION
Physics Environmental 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 LAT measurement on the point Having in mind the daily correction LST on Ls meridian

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

GEOGRAPHIC POSITION: LONGITUDE DETERMINATION. EXEMPLE
Physics Environmental 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) LAT – LST – Et = 4 (Ls-Le) = L Difference LAT-LST = -13 m Le Ls 1 4 = (-6.4) 1 4 = (Ls-Le) = L (-13 – (-6.60)) L < 0 (Ls-Le) = L = -1.6º = -1º36’ 1º 36’ Le = Ls + 1º36’ W E

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

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

SOLAR ALTITUDE ANGLE CORRECTION ON SUNRISE AND SUNSET (II)
Physics Environmental 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

Royal Greenwich bservatory
Physics Environmental 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 U.S. Naval Observatory Horas de salida y puesta de Sol en coordenadas cualesquiera Royal Greenwich bservatory

BIBLIOGRAFÍA y DOCUMENTACIÓN (II)
Physics Environmental BIBLIOGRAFÍA y DOCUMENTACIÓN (II) Spain hour zones Sunrise and sunset corrections Glossary and definitions (English) (no longer available) The problem of the longitude W J H Andrewes, “Crónica de la medición del tiempo”, Investigación y Ciencia, nov 2002 See also quotations on the text.