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
Earth. Explain your answer.

Answer 1

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

Step-by-step 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

`(b_1)/(b_2) = 2.512^((m_1 - m_2))`

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;

`(b_1)/(b_2) = 2.512^((-0.27 - 0.77))= 0.383689`

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.