Earth s orbit. 2.2 Celestial mechanics. Earth s orbit. Earth s orbit. Variation of eccentricity over Earth s history. 0 e 1
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1 around the un:. Celestial mechanics Earth's orbit is an ellipse and the sun is located in one of its focal points. Definition Ellipse: The sum of the distances from any point on the ellipse to the two focal points is constant (equal x semi major axis a > un Earth-distance r varies during the course of the year semi major axis major axis minor axis Definitions: Perihelion P: point on the orbit which is closest to the un (Jan 3 Aphelion A: point on the orbit which is farthest from the un (July 5 Eccentricity e: Amount by which orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola. Ratio of the distance between the foci of the ellipse to the length of the major axis of the ellipse. Variation of eccentricity over Earth s history 0 e 1 Today e0.0167
2 Definitions: olar constant (1361 Wm - : olar irradiance obtained per m on a plane perpendicular to the sunbeam at distance a (semi major axis from the un Distance a (semi major axis sometimes also called 1 Astronomical Unit (AU 150 Mio km semi major axis a Earth-un distance varies over the course of a year: Insolation r at distance r: r (r πr s B s πr Using a: semi major Axis r s : radius of the sun πa # % a πr $ r r (a πr s B s B πa s a r s & ( ' r a : solar constant at distance a from sun r is a function of time of the year: r(t Deviation from solar constant due to Earth orbit pecial cases: Earth in Aphel: Earth in Perihel: ra+aea(1+e ra-aea(1-e r a r ( aphel r ( a(1 + e a(1 e + a r ( perihel r ( a(1 e a(1 e > a ( r r (1 + e (1 e
3 r (perihel r (aphel (1 e (1+ e (1+ e (1+ e (1 e (1 e Deviation from solar constant due to Earth orbit Current e0.0167: r (perihel r (aphel (1+ e ( (1 e ( % difference in insolation between Perihel and Aphel max. e in Earth history: 0.06: r ( perihel (1 + e ( aphel (1 e r ( ( % difference in insolation between Perihel and Aphel olar radiation reaching planet Earth Irradiance G(r received per m on average on the Earth sphere a r G( r r olar radiation reaching planet Earth Total solar energy received on Earth: πr G π( m 30*Wm W (17 PetaW (17,000,000,000,000,000 J per second from the sun Compare: 1 average wiss nuclear power plant generates power on the order of 1 GigaW10 9 W > olar energy incident on Earth compares to about 1.7 x 10 8 nuclear power plants (170 Mio. nuclear power plants Total energy taken out of solar flux by Earth disk: R *π Total solar energy per m distributed over Earth sphere R *π / ( R *π / ~ 30 Wm - Compare: World s current energy consumption: 15 TerraW ( W > times smaller than solar energy incident on the planet > solar energy received within less than one hour would be sufficient to cover one year of World s current energy consumption
4 Desertec: olar Power from the Desert Within 6h deserts receive more energy from the sun than humankind consumes within a year less than 0.5% of desert surface can provide enough power to meet energy demand of the entire world Desertec: olar Power from the Desert Desertec: olar Power from the Desert olar thermal power Desertec: olar Power from the Desert parabolic mirrors to generate heat for conventional steam turbines
5 olar radiation reaching planet Earth Effective Temperature Planetary albedo A: Fraction of reflected solar radiation with respect to incoming solar radiation Mean annual energy G A absorbed by the planet per m on the sphere: G A (1 A In equilibrium, absorbed shortwave energy G A is balanced by longwave emission (over the Earth sphere according to the tefan-boltzman law with an effective temperature T eff : A 0.3 for Earth G A (1 AσT eff T eff G A σ 0Wm 55K 5.67*10 8 Wm K Effective Temperature Effective temperature: (blackbody temperature at which the emitted longwave equals the absorbed shortwave radiation. If the radiation temperature of a planet is below the effective temperature it will emit less radiation than it absorbs > planet will warm until it reaches radiative equilibrium and effective temperature. if its radiation temperature is above the effective temperature it will cool toward radiative equilibrium by emitting more radiation than it absorbs. Exercices 3 How does the effective Temperature T eff, P for a given planet depend on its distance r to the sun, T eff T eff (r? planet distance from sun (10 9 m albedo (1-albedo T eff (K Mercury Venus Earth Mars Jupiter
6 Effective Temperature of Planets Habitable Zones T eff (r 1 r T eff 1 r r 1 ( log% r log T eff # $ 1 & ( ' log( T eff 1 log ( r y 0.5x Log Temperature (K Log Distance from sun r Habitable Zones Radiative criteria for life on planets (I Planet with albedo α p and solar constant p : Distance r p to star (with emission Temperature T star and radius r star so that effective planetary Temperature T p eff in a range that allows for liquid water on the planet: Inner limit: T p eff below 373K: T p eff (1 α p p πr starb star r starσt star r σ πr T star star p σ r p σ r p minr p r T star star r T star star *373 T p eff Outer limit: planet heats up above 73K: maxr p r star T star T p eff r T star star *73 ( 1 α P Habitable Zones Radiative criteria for life on planets (II: Not only quantity of radiation important (which determines planetary temperature, but also quality (spectral composition, photon energy If Tstar >> T sun (5778 K: > more emission in shorter wavelenghts (UV range (c.f Wien s law> individual photon highly energetic (more energetic than binding energy of organic molecules > destroyes organic molecules Our sun already too much UV> biosphere in water produced oxygen during Earth history that allowed the build up of ozone layer to shield UV > prerequisite for development of life on land ( Mio years ago > Biosphere itself made our planet habitable
7 Habitable Zones Insolation at a specific location and time Radiative criteria for life on planets (III: Not only quantity of radiation important (which determines planetary temperature, but also quality (spectral composition, photon energy If Tstar << T sun (5778 K: less emission in high frequency (UV ranges > photons have too low energy (Ehv to allow for photochemistery > photosyntheis would not work (1 A σt eff > Medium sized stars have an ideal Planck curve for life on planets Zero-dimensional climate model: Only global mean insolation required Three-dimensional climate model: Insolation required for any given location at any given time
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