The Sun. Fabio Peron Università IUAV - Venezia. Earth-Sun relationships. The Sun. Photosphere (Emits much of the solar radiant power)

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1 Università IUAV Venezia Corso di Fisica Tecnica Ambientale Laboratorio Integrato Innovazione-Sostenibilità Sun and solar radiation Fabio Peron Università IUAV - Venezia The Sun The Sun Earth-Sun relationships Photosphere (Emits much of the solar radiant power) Thickness 500 km; Surface temperature K (corpo nero); Total radiation kw/m 2 D t =12700 km D s =1,39 x 10 6 km The Sun is a mean dimensions star, of a very common type (yellow star spectral type G). Mass M= 2x1030 kg ( times the Earth, 99% of Solar System); Mean density 1410 kg/m 3, in the inner part kg/m 3 ; composition: 98% H e He, 60 elements are present in traces thermonuclear reactions: 4 H 11 He 24 + energy; Power emitted E s = 3,8x10 26 W (4x10 6 tons of matter transformed in energy each second). 1,5 x 10 8 km Given these geometric conditions, only a very small part of the sun radiated power reaches the ground. The Sun-Earth view factor is evaluated as: energy reaching Earth = 2x10 energy emitted by Sun F S T = 9

2 Solar Constant Radiation on Earth surface The radiation reaching a unitary surface disposed perpendicular to the sun's rays at the mean ground-to-sun distance is called Solar Constant, I sc.wehave: W I sc = 1353 m 2 The radiation intensity at the atmosphere limit on a plane perpendicular to the Sun rays, I n, varies during the year and can be evaluated by: 360n In = Isc 1+ 0,033cos 365 n = giulian day: January 1 st n=1, December 31 st n=365 Radiation on Earth surface: the spectrum Radiation on Earth surface: air mass Solar radiation undergoes changes when it crosses the atmosphere for two phenomena: atmospheric absorption (selective reduction of power at specific wavelenghts) scattering (diffusion in every direction) The total spectrum is in the range 0,29 μm -2,5 μm. Below this range ozone in the upper part of the atmosphere absorbs quite completely the radiation. Over this range emitted energy is very low. A=60 AM=0,85 The radiation on the ground is so much smaller that the thickness of the atmosphere crossed. The thickness of the atmosphere got through by sun rays is described by the parameter air mass (AM): 1/sen A with A altitude angle of Sun. Air mass equal to 1 (AM=1) means altitude angle sine equal to 1 or in other words Sun altitude 90 degrees. Also the spectrum vary with the Sun altitude. A=30 AM=0,5

3 as a function of the hour as a function of the hour The apparent diurnal motion of the Sun has as a consequence the fact that radiation reachs Earth surface with different angles during the day. The Earth's rotation around its axis results in the alternation of day and night. It gives origin to the apparent Sun motion during the day and to the apparent stars motion at night Rotation.as a function of the latitude as a function of the season The same energy reach different areas Because of the sphericality of the Earth's surface, the same incident power is spread over different areas. The intensity is greater around the equator and smaller around the poles. The terrestrial axis is inclined at This originates radiation and heating variations with the seasons. During solistices there are poles with 24 hours of light or darkness. In equinoxes across the globe you have 12 hours of night and 12 hours of light.

4 as a function of the latitude as a function of season and hour Equinox Winter solistice As a function fo hour, site and period Sun is in different positions. Climate and Earth motion as a function of latitude The apparent path of the sun in the sky as is observed at different latitudes during equinox and solistice. The sun at noon reaches the maximum height. In the northern hemisphere in summer the sun is higher on the horizon than in the winter. Singapore 14 latitude nord, Noon summer solistice

5 as a function of latitude as a function of latitude During the summer to the north of the Arctic Circle you have 24 hours of light, with the sleek experience of the Midnight Sun. During the summer to the north of the Arctic Circle you have 24 hours of light, with the sleek experience of the Midnight Sun. Sun position in the sky Sun position in the sky You find the South direction and you will find the imaginary plane passing through the station point and the location of the sun. The angle between this plane and the ψ s = sun azimut β = sun altitude β - Sun position in the sky depends on: site south direction on the plane of the horizon is indicated as the solar azimut, ψ s. The angle between the direction joining the station point with the location of the sun and the plane of the horizon is indicated as the solar height, β. ψ s + day sen β = senδ senϕ + cosδ cosϕ cosω hour. cosδ senω sen ψ s = cos β ω = hour angle, at 12 ω = 0, each hour before noon 15, each hour after noon +15 ; ϕ = latitude; δ = solar declination.

6 Time angle The Earth spins around its axis in 24 hours. Sun declination As a result of the revolution motion around the sun and the inclination of the Earth's axis, the sun seems to move into the sky during the year, resulting in noon at zenith along the different latitudes between N and S. In one hour the earth rotates 360/24 degrees = 15 degrees. In a place at 30 degrees latitude to the east of the site considered, there is a local time that differs for two hours later. In a place at 30 degrees latitude more west there is a local time that differs for two hours back. Earlier Later ω is the hour angle, 0 at 12, every hour before midday they are taken away15, every hour before midday are sum 15. It is defined as solar declination, δ, on a certain day the latitude of places where the sun at noon is on zenith on that day (es. 0 at equinoxes). Sun declination at 21 June, summer solistice, the sun is at noon at the zenith along the tropic of cancer, N; at 21 December, winter solistice, the sun is at noon at the zenith along the tropic of capricorn S; at 21 March and at 22 September, spring and autumn equinoxes, the sun is at noon at the zenith along the equator. Geographic coordinates Longitude Latitude The geographic coordinates allow you to locate a site on the Earth's surface. Latitudine ϕ is the angle between the equator and the site considered measured along the meridian passing through the site itself. North and South latitudes are distinguished from the equator. Solar declination is a function of the day: n δ = 23,45 sen Finding the solar declination on a certain day of the year corresponds to knowing how to describe the geometric relationships between sun and earth as a whole on that day. Longitudine L is the angle between the meridian passing through the site and the fundamental meridian (Greenwich Meridian) measured along the parallel across the site. East and West longitudes are distinguished from Greenwich.

7 Geographic coordinates Geographic coordinates N Pole = latitude 90 N Arctic Circle 66.5 N meridiano Tropic of Cancer 23.5 N West of Greenwich West of Greenwich Equator = latitude 0 Tropic of Capricorn 23.5 S Latitude: at equator is equal to 0 Mitad del Mundo Quito-Ecuador Greenwich Meridian = 0 Latitude at poles is 90 Antarctic Circle 66.5 S S Pole = latitude 90 S paralleli Longitudine: L Osservatorio Reale di Greenwich è a 0 di longitudine Geographic coordinates Measuring time Local Solar Time, LST: refers to the culmination of the sun in the sky at the place considered, in other words at the local real midday. It will be the same for all sites on the same meridian. Solar Mean Time, LCT: if you compare during the year the culmination with noon of a precise watch pointed at the beginning of the observations on the noon local time, it turns out that at some moments the noon of the sun takes a few minutes before the clock and in a few more minutes later. The average time of day and then the average solar time were used as a reference for the time measurement. The difference between average solar time and local solar time is dictated equation of time, EOT: LST = LCT + EOT The meridian Royal Observatory of Greenwich

8 Equation of time Measuring time Analemma Standard time, ST (U.T.): To facilitate exchanges from place to place, you have chosen to divide the Earth's surface into extended zones of 15 longitude and to equalize the time of the entire "time zone" to the average solar time of the central meridian. if you compare the year of the culmination with the noon of a watch: LST= ST + 4 (L L mc )+EOT with L mc longitude of the central meridian of the zone. Greenwich Etna Date change EOT= -0, ,4197cos x 3,2265 cos 2x 0,0903 cos 3x 7,351 sen x 9,3912 sen 2x 0,3361 sen 3x with x = 2πn / 366; result is expressed in minutes The angle of incidence of radiation The angle of incidence of radiation θ cos ϑ = cos β sen χ cos - + ( ψ ψ ) sen β cos χ s

9 Sun position and radiation intensity Solar radiation A common measure of radiation intensity is W/m 2. The intensity of radiation affecting the atmosphere limit (Solar Constant) is around 1380 Wm -2. When the solar rays impact on a surface at a different angle from perpendicularity they disperse on a larger surface, resulting in lesser intensity. Solar radiation Solar radiation