## Alpha Centauri has an apparent magnitude of -0.27, whereas the apparent magnitude of Alpha Crucis is 0.77. Identify which star appears

Question

Alpha Centauri has an apparent magnitude of -0.27, whereas the apparent
magnitude of Alpha Crucis is 0.77. Identify which star appears brighter when observed from

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6 months 2021-08-07T16:08:45+00:00 1 Answers 27 views 0

The star, Alpha Crucis, is brighter than the star, Alpha Centauri, when observed from Earth

Explanation:

The given parameters are;

The apparent magnitude of the star Alpha Centauri = -0.27

The apparent magnitude of  the star Alpha Crucis = 0.77

Let relative brightness of two stars is given by the relation Where;

m₁ = The apparent magnitude of the star Alpha Centauri = -0.27

m₂ = The apparent magnitude of  the star Alpha Crucis = 0.77

b₁ = The brightness of the star Alpha Centauri

b₂ = The brightness of the star Alpha Crucis

Which gives; Therefore;

b₁/b₂ = 0.383689 and

b₁ = b₂ × 0.383689

b₂ = b₁/0.383689 = 2.606×b₁

b₂ = 2.606×b₁

b₂ > b₁, b₂ is brighter than b₁, that is the star, Alpha Crucis is brighter than the star, Alpha Centauri, when observed from Earth.