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
Earth. Explain your answer.

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.