Planet Destruction

[neufer]

... if most stars go through the Red Giant phase ...

• Most stars DO NOT go through the Red Giant phase:

<<Red dwarfs are by far the most common type of star in the Milky Way, at least in the neighborhood of the Sun. According to some estimates, red dwarfs make up three-quarters of the stars in the Milky Way. Because of the comparatively short age of the universe, no red dwarfs exist at advanced stages of evolution.>>

Um, pardon me, but from that same Wikipedia article:

Red giants are evolved from main-sequence stars with masses
in the range from about 0.3 M☉ to around 8 M☉.

Wouldn't that mass range include a majority of stars? It includes Red Dwarf stars from .3 to .5 solar.

If you want to be pedantic:

• Stars less than 1.0 M_☉ HAVE NOT YET GONE through the Red Giant phase.

[BDanielMayfield]

I'd rather not argue past and present, it gets me tense. I'd much rather have seen a solution to the question using integral calculus.

Bruce

[neufer]

I'd rather not argue past and present, it gets me tense.

tense (adj.) "stretched tight," 1660s, from Latin tensus, past participle of tendere "to stretch, extend."
Figurative sense of "in a state of nervous tension" is first recorded 1821.

tense (n.) "form of a verb showing time of an action or state," early 14c., tens "time," also "tense of a verb" (late 14c.), from Old French tens "time, period of time, era; occasion, opportunity; weather" (11c., Modern French temps), from Latin tempus "a portion of time" (also source of Spanish tiempo, Italian tempo; see temporal).

I'd much rather have seen a solution to the question using integral calculus.

A solution to the question of finding the specific point in time representing a maximum in the number of planets would involve differential calculus. However, there is no guarantee that the math will yield a solution.

“At the most basic level, though everything came down to the ‘body count” – the preeminent statistic that served in those years as both the military’s scorecard and its raison d’etre. How else could you tell if the crossover point [when American soldiers would be killing more enemies than their Vietnamese opponents could replace] was within reach unless you tallied the enemy dead? The war managers, of course, gave little thought to what this strategy – basing the entire military effort on such an indicator as Vietnamese corpses – might mean for Vietnamese civilians.”

• - Kill Anything That Moves: The Real American War in Vietnam.
  (New York: Metropolitan Books/Henry Holt and Co., 2013), pp. pp. 42-3).

[BDanielMayfield]

I'd much rather have seen a solution to the question using integral calculus.

A solution to the question of finding the specific point in time representing a maximum in the number of planets would involve differential calculus. However, there is no guarantee that the math will yield a solution.

That's good to know, but I was referring to the more recent question about how many stars will pass through a Red Giant phase at some point in their stellar evolution. As in, if F(m) is the percent of main-sequence stars of solar mass m, what is the summation of F(m) over the range 0.3 to 8. Is this sum > or < than 50%?

Bruce

[neufer]

If F(m) is the percent of main-sequence stars of solar mass m,
what is the summation of F(m) over the range 0.3 to 8.
Is this sum > or < than 50%?

I don't know.

Red dwarfs ( 0.07 < m < 0.5) are presumed to make up 75% of the stars in the Milky Way.

Hence the summation of F(m) over the range 0.07 to 0.5 is 75% of the stars in the Milky Way.

[BDanielMayfield]

What happens to planets and the elements they are made of when they are engulfed by stars becoming Red Giants?

I think it's unclear. Terrestrial planets might survive for a time orbiting inside a red giant. But the drag may cause such planets to end up deeper inside the star, where they would not survive intact. In that case their elements would mix with the star and be partly dispersed ...

Yes, at least some of the swallowed planet's lighter elements would be blown back out into the interstellar medium by the star's stellar wind and especially when the star blows off its outer layers in the planetary nebula phase. So we're probably made, not just of "star stuff", but of at least a little recycled planet material too.

It is interesting to consider the case of a planetary remnant that is orbiting INSIDE a swollen star's photosphere. Is it still a planet? I wouldn't think so, but if the star blows its outer envelope away before the former planet has totally melted/evaporated away or spiraled down into the star's core then the remains of the planet might become a planet again orbiting a White Dwarf.

Bruce

[Chris Peterson]

It is interesting to consider the case of a planetary remnant that is orbiting INSIDE a swollen star's photosphere. Is it still a planet?

I'd say so. Just like a rogue planet, no longer attached to a star, is reasonably called a planet. For classification purposes, the origin and evolutionary history of a body is probably the most rational system to use in most cases.