Question

The distance from Earth of the red supergiant Betelgeuse is approximately 643 light-years. If it were...

The distance from Earth of the red supergiant Betelgeuse is approximately 643 light-years. If it were to explode as a supernova, it would be one of the brightest stars in the sky. Right now, the brightest star other than the Sun is Sirius, with a luminosity of 26LSun and a distance of 8.6 light-years.

How much brighter in our sky than Sirius would the Betelgeuse supernova be if it reached a maximum luminosity of 8.0×109LSun?

using two significant figures

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Answer #1

To find the ratio of Apparent Brightness for the two object's which is given by,

B = L / 4R2

The Betelgeuse supernova much brighter in our sky than Sirius which would be given as :

BBetelgeuse / BSirius = [LBetelgeuse / 4 (DBetelgeuse)2] / [LSirius / 4 (DSirius)2]

BBetelgeuse / BSirius = [LBetelgeuse (DSirius)2] / [(DBetelgeuse)2 LSirius]

BBetelgeuse / BSirius = [(8 x 109 Lsun) (8.6 Ly)2] / [(643 Ly)2 (26 Lsun)]

BBetelgeuse / BSirius = 55041.6

BBetelgeuse = (55041.6) BSirius

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