Help with Life expectancy of Main Sequence stars.

In summary: This is because the pressure in the core is greater and the temperature is higher, which leads to a higher probability of nuclear fusion. The Sun is about halfway through it's life as a main sequence star. It will eventually evolve into a red giant and then a white dwarf.
  • #1
irk_t_great
2
0
If the nuclear fusion reaction of converting 4 H ! He occurs at an
efficiency of 0.7%, and that mass is converted into energy according
to the equation E = mc2, then estimate the Main Sequence lifetime
of the Sun (spectral type G2) in years if the luminosity of the Sun is
3.83×1033 ergs s−1. Assume the Sun’s core (10% of the total mass) is
converted from H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g.

t=1/M^2.5

t=1/(91.9891x10^32)^2.5
t= the wrong answer.

What are we doing wrong?
 
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  • #2
I have no particular knowledge relating to your question. However, your expression for t leads to a t with dimension g^-2.5. Since t is supposed to be in years, I presume that there must be, at a minimum, a conversion constant of some sort.
 
  • #3
That could be the wrong equation altogether...
 
  • #4
The life expectancy of a main sequence star is inversely proportional to it's mass - i.e., large stars live fast and die hard, tiny brown dwarfs live dang near forever.
 
  • #5
Assuming that this is just a homework assignment, what you must do is use Einstein’s equation to determine the amount of mass you get from 3.83×10^33 ergs/second(or rather 3.83 x 10^33 erg/s=mass x c^2, and solve for the mass). BTW, according to the value in the Wiki, this should be 3.85 x 10^33 ergs/sec, but its your homework :). Then divide the Sun’s core mass (which is described as 10% of the value you are given or .1989 x 10^33 grams) by this figure. This is how many seconds it takes to convert the core’s H into He. Finally, just convert seconds to years.
However, the Sun isn’t just going to fuse itself out of existence. It will eventually become a White Dwarf star and remain so for perhaps more than 10^100 years.
 
Last edited:
  • #6
There's a nice "car" analogy to this problem. Your gas tank holds 20 gallons. You burn 2 gallons per hour. How long until you run out of gas? It's really the same question.
 
  • #7
Fusion in small stars is a much more efficient process compared to large stars.
 

1. What is the main sequence of a star?

The main sequence is a stage in the life cycle of a star where it is actively fusing hydrogen into helium in its core. This is the longest and most stable period of a star's life and is characterized by a relatively constant luminosity and temperature.

2. How does a star's mass affect its life expectancy on the main sequence?

A star's mass directly affects its life expectancy on the main sequence. The more massive a star is, the faster it consumes its fuel and the shorter its main sequence lifespan. Smaller stars have a longer main sequence lifespan since they burn their fuel at a slower rate.

3. What factors can influence the life expectancy of a main sequence star?

Aside from mass, other factors that can influence the life expectancy of a main sequence star include its composition, rotation rate, and environment. A star with a higher metallicity (amount of elements heavier than helium) may have a shorter main sequence lifespan due to increased nuclear reactions. A faster rotating star may have a shorter lifespan due to increased mixing of fuel in its core. And a star in a binary system may have its lifespan affected by interactions with its companion.

4. How long can a star remain on the main sequence?

The length of time a star remains on the main sequence depends on its mass. For a star with the same composition as our Sun, it will spend approximately 10 billion years on the main sequence. However, more massive stars with shorter lifespans can spend as little as a few million years on the main sequence, while smaller stars can spend hundreds of billions of years.

5. What happens to a star after it leaves the main sequence?

Once a star has exhausted its hydrogen fuel on the main sequence, it will start to evolve into a different stage of its life cycle. The exact path it takes depends on its mass. Smaller stars will become red giants, while more massive stars may go through a supernova explosion before becoming a white dwarf or neutron star. Ultimately, the fate of a star is determined by its mass and composition.

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