To determine which of these stars will stay on the main sequence for the shortest time, we must consider the relationship between a star's mass and its lifespan on the main sequence. In stellar evolution, more massive stars exhaust their nuclear fuel faster and thus spend less time on the main sequence compared to less massive stars.
Here are the initial masses of the four stars:
- Star 1: [tex]\(9\)[/tex] Solar masses
- Star 2: [tex]\(0.9\)[/tex] Solar masses
- Star 3: [tex]\(5\)[/tex] Solar masses
- Star 4: [tex]\(0.3\)[/tex] Solar masses
The star with the highest mass will stay on the main sequence for the shortest time.
Let's compare the given masses:
- Star 1 has a mass of [tex]\(9\)[/tex] Solar masses.
- Star 2 has a mass of [tex]\(0.9\)[/tex] Solar masses.
- Star 3 has a mass of [tex]\(5\)[/tex] Solar masses.
- Star 4 has a mass of [tex]\(0.3\)[/tex] Solar masses.
Among these, Star 1 has the highest mass of [tex]\(9\)[/tex] Solar masses.
Therefore, the star that will stay on the main sequence for the shortest time is Star 1.
