Lifetime of a main sequence star (i.e., a hydrogen-burning star) is proportional

Question

Lifetime of a main sequence star (i.e., a hydrogen-burning star) is proportional to 1/M2.5. Because we know that our Sun's lifetime (lifetime) is about 10 billion years, we can determine a star's lifetime (lifetime,) in years using the following ratio:. Lifetime/lifetime = (M/M)2.5. What is the lifetime of a main sequence star with a mass half that of the Sun?. Express your answer in years. A height rod star Antares in Constellation Scorpius has a mass 15.5 times that of our sun. Find the lifetime of Antares in years.

Explanation / Answer

Given The life time of sun it    10 billion years the relation between life time of sun and life time of star is                      life time of star / life time of sun = ( MS / M star ) 2.5      a) life time of a main sequence star with a mass half that of the sun                          that is    Mstar = M S / 2             there fore                    life time of star   = ( life time of sun ) ( MS / (MS / 2 ) ) 2.5                                                = ( 10 billion years ) ( 2 ) 2.5                                              = 5.6568 billion years   b) given the mass of bright red star Antares   Mstar = 15.5 MS                 Life time of Antares    = ( life time of sun ) ( MS / 15.5 MS ) 2.5                                                = ( 10 billion years ) ( 1/15.5) 2.5                                              = ( 10 *109 years ) ( 0.001057)                                              = ( 10 billion years ) ( 1/15.5) 2.5                                              = ( 10 *109 years ) ( 0.001057)                                              = 1.0572*10 7 years

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