Question

A main-sequence star is 18 times more massive than the Sun. Its luminosity is 24743 times that of the Sun. If the Sun's main-sequence lifetime is 10 billion years, how many years will this star live?

Answer 1

Star will live  for 7.27 million years.

A main-sequence Star is 18 times more massive than the Sun.

Mass of Sun = $M_{sun}$

Mass of Star = $M_{star}$

$M_{star}$ = 18 *  $M_{sun}$

Luminosity of the Sun =  $L_{sun}$

Luminosity of the Star =  $L_{star}$

 $L_{star}$ = 24743 * $L_{sun}$

Luminosity refers to the total amount of energy produced by various celestial bodies (stars, galaxies) per unit time and is generally measured in joules per second or watts in SI units.

According to the luminosity and mass of the star relationship

$\frac{L_{star} }{L_{sun} } = (\frac{M_{star} }{M_{sun} } )^{3.5}$

This shows star is more massive than the sun.

Lifetime of the Sun = $T_{sun}$ = 10 billion years

Lifetime of the Star =  $T_{star}$

Also the mass and the lifetime of the star relationship says that

$\frac{T_{star} }{T_{sun} } = (\frac{M_{sun} }{M_{star} } )^{2.5}$

$\frac{T_{star} }{10 billion} } = (\frac{M_{sun} }{M_{sun * 18} } )^{2.5}$

$\frac{T_{star} }{10 billion} } = \frac{1}{18^{2.5} }$

$T_{star}$ = $\frac{10 billion}{1374.615}$

$T_{star}$ = 72,74,764.2067 years

$T_{star}$ = 7.27 million years

Star will live for 7.27 million years.

To know more about Luminosity,

https://brainly.com/question/26559085

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