5. The absolute magnitude of a star, M_(j) is (related to its luminosity, L by the formula M=4.72-log(L)/(L_(0)) , where L_(0) is the luminosity of the sun . The luminosity is the rate at which the star emits light, and is measured in watts. a)Determine M)=4.7z-109(2)/(2)=4.7z-[logL-log10] b) The absolute magnitude of Sirius, the star chrightest from

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5. The absolute magnitude of a star, M_(j) is (related to its luminosity, L by the formula M=4.72-log(L)/(L_(0)) , where L_(0) is the luminosity of the sun . The luminosity is the rate at which the star emits light, and is measured in watts. a)Determine M)=4.7z-109(2)/(2)=4.7z-[logL-log10] b) The absolute magnitude of Sirius, the star chrightest from

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5. The absolute magnitude of a star, M, is related to its luminosity, L, by the formula:M = 4.72 - log(L/L₀),where L₀ is the luminosity of the sun.a) Determine M if L = 2L₀If L = 2L₀, then we substitute this into the formula:M = 4.72 - log(2L₀/L₀)M = 4.72 - log(2)M ≈ 4.72 - 0.301M ≈ 4.42So, the absolute magnitude of the star is approximately 4.42.b) The absolute magnitude of Sirius is 1.4. Determine its luminosity.We are given M = 1.4, and we need to find L. We use the same formula and rearrange it to solve for L:1.4 = 4.72 - log(L/L₀)log(L/L₀) = 4.72 - 1.4log(L/L₀) = 3.32Now, we convert the logarithmic equation to an exponential equation (assuming base 10 logarithm):L/L₀ = 10³·³²L = 10³·³² L₀L ≈ 2089L₀Therefore, the luminosity of Sirius is approximately 2089 times the luminosity of the sun.

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