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Magnitude of Stars The magnitude $M$ of a star is a measure of how bright a star appears to the human eye. It is defined by $$M=-2.5 \log \left(\frac{B}{B_{0}}\r...

Question

Magnitude of Stars The magnitude $M$ of a star is a measure of how bright a star appears to the human eye. It is defined by $$M=-2.5 \log \left(\frac{B}{B_{0}}\right)$$ where $B$ is the actual brightness of the star and $B_{0}$ is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. (c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright t

Magnitude of Stars The magnitude $M$ of a star is a measure of how bright a star appears to the human eye. It is defined by $$M=-2.5 \log \left(\frac{B}{B_{0}}\right)$$ where $B$ is the actual brightness of the star and $B_{0}$ is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. (c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero.



Answers

Magnitude of Stars The magnitude $M$ of a star is a measure
of how bright a star appears to the human eye. It is defined
by
$$M=-2.5 \log \left(\frac{B}{B_{0}}\right)$$
where $B$ is the actual brightness of the star and $B_{0}$ is a
constant.
(a) Expand the right-hand side of the equation.
(b) Use part (a) to show that the brighter a star, the less its
magnitude.
(c) Betelgeuse is about 100 times brighter than Albiero. Use
part (a) to show that Betelgeuse is 5 magnitudes less
bright than Albiero.


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