The mass luminosity relation L  M 3.5 describes the mathematical relationship between luminosity and mass for main sequence stars. It descr

Question

The mass luminosity relation L  M 3.5 describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 2 M⊙ would have a luminosity of _____________ L⊙ while a star with luminosity of 3,160 L⊙ would have an approximate mass of ________________ M⊙.

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Trung Dũng 6 months 2021-08-22T05:50:11+00:00 1 Answers 5 views 0

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    2021-08-22T05:51:16+00:00

    Answer:

    (a) 11.3 L

    (b) 10 M

    Explanation:

    The mass-luminosity relationship states that:

    Luminosity ∝ Mass^3.5

    Luminosity = (Constant)(Mass)^3.5

    So, in order to find the values of luminosity or mass of different stars, we take the luminosity or mass of sun as reference. Therefore, write the equation for a star and Sun, and divide them to get:

    Luminosity of a star/L = (Mass of Star/M)^3.5 ______ eqn(1)

    where,

    L = Luminosity of Sun

    M = mass of Sun

    (a)

    It is given that:

    Mass of Star = 2M

    Therefore, eqn (1) implies that:

    Luminosity of star/L = (2M/M)^3.5

    Luminosity of Star = (2)^3.5 L

    Luminosity of Star =  11.3 L

    (b)

    It is given that:

    Luminosity of star = 3160 L

    Therefore, eqn (1) implies that:

    3160L/L = (Mass of Star/M)^3.5

    taking ln on both sides:

    ln (3160) = 3.5 ln(Mass of Star/M)

    8.0583/3.5 = ln(Mass of Star/M)

    Mass of Star/M = e^2.302

    Mass of Star = 10 M

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