c Betelgeuse is about 100 times brighter than Albiero Use pa

(c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero. Let B1 be the brightness of the star Albiero and M1 be its magnitude. Then 100B1 is the brightness of Betelgeuse, and its magnitude is M= 2.5 log( )

= -2.5[log ( ? )+log(B₁/B₀)] =-2.5[ ? +log(B₁/B₀)] = ? - 2.5 log (B₁/B₀) = ? + M₁

Solution

M= 2.5 log( B/B0 )

M= 2.5 log(B)+2.5log(B0 )

Betelgeuse is about 100 times brighter than Albiero.

B=100B1

MBetelgeuse= 2.5 log(100B1)+2.5log(B0 )

log ab =log a +log b

MBetelgeuse= 2.5 log(100) 2.5 log(B1)+2.5log(B0 )

MBetelgeuse= 2.5 log(10²) 2.5 (log(B1)-log(B0 ))

log a^b =b log a

MBetelgeuse= 2.5*2 log(10) 2.5 (log(B1/B0 ))

MBetelgeuse= 5 2.5 (log(B1/B0 ))

MBetelgeuse= 5 +MAlbiero

Therefore Betelgeuse is 5 magnitudes less bright than Albiero