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
Earth. Explain your answer.

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

Answers ( )

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    2021-08-07T16:10:19+00:00

    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

    \dfrac{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;

    \dfrac{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.

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