How many generations old is our system?

[Chrisg1960]

I understand that elements heavier than hydrogen and helium require the life span of a solar system to be created through fusion. With a rough estimate of the universe's age of 13.8 B years and our system's rough age of 4.5 B years, how many generations of star formation and collapse do we believe were required to create the elements in our system? Also related, what percentage of this matter may have originated from a single system? Or in other words, is our system a homogeneous conglomeration of the ejecta from numerous systems or is it more likely that the bulk of the matter in our system came from a single ancestor system? It would seem to be too time consuming for several systems to cast their matter to the skies and have enough matter coalesce into a system to be several generations old. I know this is getting long and multi-pronged here but lastly, when our sun becomes a red giant and casts off roughly 2/3rds of it's mass, what is the likelihood that Jupiter or Saturn may collect enough mass to approach the minimum required to form a new star?

 

[rootone]

We don't have any information about long extinct stars which contributed material to the formation of our solar system.
Obviously more of the material will have come from systems located in the same general region of the galaxy as our Sun.
I think it's more likely that several interacting dust clouds led to the formation of our solar system rather than the coalescing of debris emitted by a single progenitor.
If it is the case that several dust clouds contributed, they could be of quite different ages.

As to whether Jupiter could accrete enough mass from a dying Sun to become a star itself, I'd say that's unlikely since only a small part of the material ejected by the Sun will be heading in a direction that leads it eventually to being captured by Jupiter

 

[newjerseyrunner]

Our sun is a third generation star, we know it based on how much metal there is in it.
Not all generations were equal, the first generation stars did not last ten billion years like our sun will, most of the early stars were monsters, they lived fasted and died young. In the early universe there was a massive amount of interstellar hydrogen so when a star got big, it sucked everything near it in, making them humungous. Humungous stars can explode in as little as a few million years.

Metal in this case isn't the same as metal in chemistry, it means anything heavier than helium. https://en.wikipedia.org/wiki/Metallicity

 

[phyzguy]

The stars which generate heavy elements and spread them through space by exploding as supernovae are much more massive than our sun, typically 10-100 times as massive. The lifetime of a star is roughly proportional to 1/Mass^3. So these massive stars only live a few million to a few 10's of millions of years. So there have been many 'generations' of these massive stars since the universe began. For this reason, the material from which our sun was born likely contained ejecta from many prior supernovae.

 

[Chronos]

Stars in the very early universe could have been very more massive than the sun due to the lack of metallicity. They may have only lived for a handful of millions of year before spewing their metallized gut into the cosmos. IOW, what phyzguy said. The solar system probably includes remains of dozens of generations of star.