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Help Needed Over Stellar Magnitude Issue

GeeKay
in Astronomy and Cosmology

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I am tying up the loose ends of a SF short story I wrote last year, featuring a neutron star. Right now, though, I'm stuck over a long-term problem concerning the star's luminosity. It's surface temperature is 8,200 K and has a diameter of 20 kms. My problem has consisted of trying (and failing) to calculate what the star's absolute magnitude would be. I'm afraid this is beyond my abilities to solve, and unfortunately I don't know anyone among my friends who has the mathematical nous to help me out here.  So I would be extremely appreciative if someone here could put me out of my misery. Many Thanks!

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swansont - many thanks for your succinct answer to what has been a long-term headache for me. Much appreciated! :)

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