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Question:

natersuk
natersuk
Student
Graduate School

Two stars are observed in the sky.

Star A appears 2.5 times brighter than star B, and star A is 4 times nearer than star B. Which star is more luminous, and by how much is it more luminous than the other?

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Posted by natersuk on Friday October 23, 2009 at 8:35 AM and tagged with astronomy, science.

Answers:

  1. krishna-agrawala
    krishna-agrawala Teacher
    Graduate School

    eNotes Editor

    The apparent brightness of the star will be inversely proportional of the real brightness of the star.

    let a be the real brightness of star A and b be the real brightness of star B.

    Then Ratio of apparent brightness of star A and star B can be given by the formula:

    Apparent Brightness of A/Apparent Brightness of B

    = (a/Distance of A)/(b/Distance of b)

    = (a/b)*(Distance of B/Distance of A) ... (1)

    We know that A is 4 times nearer than B. This means:

    Distance of B/Distance of A = 4

    Also it is given that apparent brightness of A is 2.5 times that of B. This means:

    Apparent Brightness of A/Apparent Brightness of B = 2.5

    Substituting this values of (Distance of B/Distance of A), and (Apparent Brightness of A/Apparent Brightness of B) in  equation (1)we get:

    2.5 = (a/b)*4

    Or: b/a = 4/2.5 = 1.6

    Therefore b is 1.6 times a.

    Answer: B is 1.6 times luminous as compared to A

     

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    Posted by krishna-agrawala on Friday October 23, 2009 at 9:04 AM

  2. natersuk
    natersuk Student
    Graduate School

    Are you able to elaborate in simpler terms?

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    Posted by natersuk on Saturday October 24, 2009 at 2:11 AM