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How long do stars last?
For main sequence stars, the luminosity L increases with the mass M according to the approximate power law:
Although the index 3.5 is used here, a more conservative approach used by a number of astronomy texts is to use a relationship with the power left as a range of values between 3 and 4.
Basic Assumptions:
Luminosity is energy released per second [J/s] or Watts.
Luminosity is proportional to the mass of the star.
3. Hotter Stars = Burn fuel (H + He) faster
The temperature of a star is related to the rate at which nuclear fusion happens within it's core.
Larger stars 'burn' hotter due to excessive pressure from gravitational forces acting on particles. Causing the fusion to occur at a faster rate (rxn/sec).
4. Energy produced by nuclear fusion reactions proportional to the mass of the star.
5. Combining the above relationships, results in the following proportion:
6. Substituting
7. Using the sun as a reference:
Summarize why more massive main sequence stars have relatively shorter life times.
The expected lifetime of the Sun is about 1x1010 y. Estimate the lifetime of a star which has a mass 10 times smaller that the Sun.
ANS: 3.16x1012 y
Determine the relative mass of a star which will have a lifetime which is only 0.01% of that of the Sun.
ANS: Ms = 39.8M☉
Use the HR diagram to estimate the surface temperature of the star.
ANS: Ls = 631L☉ ∴ T≅20 000K
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