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Effective radiative disc radius of the Sun
SolarEnergy,Vol.19,p. 387. PergamonPress1977. Printedin GreatBritain
TECHNICAL NOTE Effective radiative disc radius of the Sun CLIFFORD C. O. EZEILO Thermal Sciences Reader, University of Nigeria, Nsukka, Nigeria
(Received 13 February 1976) Loewe and Barbara Van Meurs[1] went into much trouble to arrive at a value of 1.48983 x 108 km as the "effective radiative distance" of the Sun from the Earth. Their result involves mathematical analysis that yields 5.167 x 10' km as the mean radiative radius of the Sun and 0.0451 x 105 km as the corresponding value for the Earth. The correct average Sun-Earth centre-to-centre distance of 1.495042 × 108 km is used in these deductions, With a mean solar surface temperature of 6000°K and considering the Sun as a black-body emitter, a Solar Constant value of 883.876W/m 2 would result on applying the StefanBoltzmann law using the above Loewe and Neur's radiative distance. This is significantly below the measured value of 1353 W/m2. The true centre-to-centre distance (Sun to Earth) of 1.495042 × 10e km is not significantly different from the authors' "effective radiative distance" of 1.48983 × 108kin. The basic assumption must therefore be in error especially since the analysis ignores temperature changes within the Solar Photosphere and the thin Coronasphere where the temperature rises from about 6000°K to nearly 50,000°K in a few thousand kilometres[2]. In short, "digging into the Sun" in order to establish an effective radiative radius cannot be expected to yield an accurate result unless the radial temperature distribution within the Sun is known, A suggestion is therefore made in this contribution that the knowledge of the "effective radiative disc radius of the Sun" is of more practical interest. The Solar Constant value of 1353 W/m2 is first presumed correct to within _+2.5 per cent depending on the
Sunsport Number[3]. With the Sun's surface temperature taken as 6000°K,the effective radiative solar disc radius can then be readily shown to be (6.4152-+0.08)x 105kin. This value is less than the Sun's known outer radius of 6.95 x l& km but since the Sun's radiation intensity drops from the disc centre to the edges, the effective radius quoted above is no more than a computational result to fit the observed facts. It has been reported that the radiative intensity of the Sun drops to about 75 per cent of it's disc centre value at the edges[4]. This implies that the effective temperature of the Sun at the edges is just about 90.36 per cent, i.e. (0.75TM)of its disc-centre value. The effective radiative disc radius must therefore be less than the correct Sun's radius and the value of (6.4152-+ 0.08) x 105 km will be seen to fit the observed data fairly well. The remaining alternative is to ignore edge effects and arrive at 5765°K as the surface temperature of the Sun and this is scarcely acceptable. REFEIIENCKS 1. F. Loewe and B. Van Meurs, The effective radiative distance of the Sun. Solar Energy 15(2), 191 (1973). 2. S. Ruttenberg, The international years of the quiet Sun 1964--65. Solar Energy 7(4), 157 (1963). 3. M. R. Thekaekara, Extraterrestrial solar energy and its possible variations. UNESCO Congress, The Sun in the Service of Mankind,Paper E44, Paris (1973). 4. J. Willis, A convenient graphical method of evaluating field of view obstructions for cosine response detectors. Solar Energy 13, 349 (1971).
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TECHNICAL NOTE Effective radiative disc radius of the Sun CLIFFORD C. O. EZEILO Thermal Sciences Reader, University of Nigeria, Nsukka, Nigeria
(Received 13 February 1976) Loewe and Barbara Van Meurs[1] went into much trouble to arrive at a value of 1.48983 x 108 km as the "effective radiative distance" of the Sun from the Earth. Their result involves mathematical analysis that yields 5.167 x 10' km as the mean radiative radius of the Sun and 0.0451 x 105 km as the corresponding value for the Earth. The correct average Sun-Earth centre-to-centre distance of 1.495042 × 108 km is used in these deductions, With a mean solar surface temperature of 6000°K and considering the Sun as a black-body emitter, a Solar Constant value of 883.876W/m 2 would result on applying the StefanBoltzmann law using the above Loewe and Neur's radiative distance. This is significantly below the measured value of 1353 W/m2. The true centre-to-centre distance (Sun to Earth) of 1.495042 × 10e km is not significantly different from the authors' "effective radiative distance" of 1.48983 × 108kin. The basic assumption must therefore be in error especially since the analysis ignores temperature changes within the Solar Photosphere and the thin Coronasphere where the temperature rises from about 6000°K to nearly 50,000°K in a few thousand kilometres[2]. In short, "digging into the Sun" in order to establish an effective radiative radius cannot be expected to yield an accurate result unless the radial temperature distribution within the Sun is known, A suggestion is therefore made in this contribution that the knowledge of the "effective radiative disc radius of the Sun" is of more practical interest. The Solar Constant value of 1353 W/m2 is first presumed correct to within _+2.5 per cent depending on the
Sunsport Number[3]. With the Sun's surface temperature taken as 6000°K,the effective radiative solar disc radius can then be readily shown to be (6.4152-+0.08)x 105kin. This value is less than the Sun's known outer radius of 6.95 x l& km but since the Sun's radiation intensity drops from the disc centre to the edges, the effective radius quoted above is no more than a computational result to fit the observed facts. It has been reported that the radiative intensity of the Sun drops to about 75 per cent of it's disc centre value at the edges[4]. This implies that the effective temperature of the Sun at the edges is just about 90.36 per cent, i.e. (0.75TM)of its disc-centre value. The effective radiative disc radius must therefore be less than the correct Sun's radius and the value of (6.4152-+ 0.08) x 105 km will be seen to fit the observed data fairly well. The remaining alternative is to ignore edge effects and arrive at 5765°K as the surface temperature of the Sun and this is scarcely acceptable. REFEIIENCKS 1. F. Loewe and B. Van Meurs, The effective radiative distance of the Sun. Solar Energy 15(2), 191 (1973). 2. S. Ruttenberg, The international years of the quiet Sun 1964--65. Solar Energy 7(4), 157 (1963). 3. M. R. Thekaekara, Extraterrestrial solar energy and its possible variations. UNESCO Congress, The Sun in the Service of Mankind,Paper E44, Paris (1973). 4. J. Willis, A convenient graphical method of evaluating field of view obstructions for cosine response detectors. Solar Energy 13, 349 (1971).
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