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 Solution (A) The Solar Constant Solution (B) Calculating the Flux Density of an Object Observed Through a Filter

To find the Johnson B-band flux of a star, in this case, the Sun, use the following formula. The value of the fν zero-point for the B filter is given in Table 2 of Section 2.3 in the text. Convert this to SI units: W m-2 Hz-1. The absolute magnitude of the Sun in the B filter is -26.10. Insert the relevant values and solve for fB of the Sun. You will need to use the text found on canismajor.ca to complete this problem.  :  (5.1)

The Sun's B-filter flux is approximately 1.12 * 10-12 W m-2 Hz-1 (= 1.12 * 10-12 N)

To calculate the total energy received by the Earth from the Sun in this band, multiply this figure times the central frequency of the B-band (λ = 0.438 * 10-6 m, from Table 2) and then by half the area of the Earth (the hemisphere facing the Sun) (radius = 6.371 * 106 m.)    (5.2)

or about 6.8 * 1014 Hz. So the luminosity at Earth is  (5.3)

The total luminosity of the Sun in the B band is taken at 1 AU (= 1.496 * 1011 m).  (5.4)

or approximately 1.07 * 1026 W.

The total luminosity of the Sun at all wavelengths (bolometric luminosity) is taken to be approximately 3.862 * 1026 W., as given above. Solution (C) Luminosity, Flux, and Temperature

Luminous flux is related to temperature by the formula: where σ is the Stefan-Boltzmann constant (5.67 * 10-8 W m-2 K-4). Therefore, luminosity may be expressed as: Knowing the luminosity and radius of the Sun, we can calculate its effective surface temperature, as follows:    (6.1)  (6.2)  (6.3)   (6.4) We take the first solution, rejecting the negative and imaginary solutions:  (6.5)     References ----------------------------------------------------------------   Cox, A. (Ed.) (2000). Allen's Astrophysical Quantities, 4th ed. New York: AIP/Springer. 