Answer:
a) 46.76 Lsun
b) 2187 Lsun
c ) You can easily estimate the luminosity of a 3-solar massed giant star because its luminosity is close to the luminosity of the sun
Explanation:
To estimate the luminosity of a celestial body in terms of solar luminosity we use the expression below
= [tex]\frac{L}{Lsun} = (\frac{M}{Msun} )^{3.5}[/tex]
a) Estimate the luminosity of a 3 solar mass main sequence star
= [tex]\frac{L}{Lsun} = (\frac{3M}{Msun} )^{3.5}[/tex]
Hence ; L(luminosity of a 3 solar mass star ) = 46.76 Lsun
b) Estimate the luminosity of a 9-solar-mass main sequence star
= [tex]\frac{L}{Lsun} = (\frac{9M}{Msun} )^{3.5}[/tex]
hence L( luminosity of a 9-solar mass star ) = 2187 Lsun
c ) You can easily estimate the luminosity of a 3-solar massed giant star because its luminosity is close to the luminosity of the sun
A) The luminosity of a 3 -solar-mass main-sequence star is; L = 46.765L_sun
B) The luminosity of a 9 -solar-mass main-sequence star is; L = 2187L_sun
C) Yes, we can easily estimate the luminosity of a 3 -solar-mass main-sequence star.
We want to find luminosity of a solar body which in this case is a main sequence star. The formula in terms of solar luminosity is;
L/L_sun = (M/M_sun)^(3.5)
Where;
L is luminosity of the solar body
L_sun is luminosity of the sun
M is mass of the solar body
M_sun is mass of the sun
A) Thus;
For a 3 -solar-mass main-sequence star;
M = 3M_sun
Therefore;
L/L_sun = (3M_sun/M_sun)^(3.5)
L/L_sun = 3^(3.5)
L/L_sun = 46.765
L = 46.765L_sun
B) For a 9-solar-mass main-sequence star;
L/L_sun = (9M_sun/M_sun)^(3.5)
L/L_sun = 9^(3.5)
L/L_sun = 2187
L = 2187L_sun
C) We can see from answer A above that the luminosity of a 3 solar mass body is 46.765 times of the luminosity of sun. Since it's not so much bigger than the luminosity of sun, then it is easy to estimate.
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