# The outer Solar System in 5 billion years

#### Catastrophe

##### "There never was a good war, or a bad peace."
We know that the Sun will expand to become a red giant in approximately 5 billion years time. After that it will shrink to become a white dwarf and, ultimately a black dwarf. Now what I am interested in is, when Mercury, Venus and, possibly, Earth as well have been consumed, at the Sun's maximum extent, where will the frost line (aka snow line etcetera) be?
To quote one very famous astrophysicist (who shall be nameless for the moment) "The planets Jupiter, Saturn, (etc) and possibly Mars, will continue to circle the ancient sun aeons after it has died".
So, in your view, where will the frost line be in 5 billion years time? You see where I am going with this?

Cat

#### Helio

The luminosity determines the HZ, so what happens when the Sun becomes a WD?

It's radius will be about 0.015 what it is now. If we square this we get the reduction in luminosity due to size.

It's temperature will be very hot -- it is the core (even if just ashes) of the Sun after all.

Initially, somewhat, it will be perhaps 150,000K. This is a 4th power factor to luminosity.

It will cool quickly, however, and at about 10,000K the HZ will be about 1% to 4% of what it is now.

Using the 0.015 radius, I get ...

Luminosity changes due to temp. and radius:
150,000K = 102x more luminous than today's Sun.
100,000K = 20x
50,000K = 1.25x
10,000K = 0.002

HZ changes are the sq. root of L so:
150,000k = 10 AU
100,000K = 4.5 AU
50,000K = 1.1 AU
10,000K = 0.04 AU

I think the above is somewhat close to accurate.

But, another problem is that WDs at those higher temperatures produce lots of dangerous UV. In color, these things are blue-white, not white.

Last edited:
Catastrophe

#### Catastrophe

##### "There never was a good war, or a bad peace."
Helio,, first things first. What happens at the red giant stage? The temperature governing the frost line is 270 K. Where will the frost line be when Earth is either burning or charring? Now it is just outside the asteroids and bordering on Jupiter's realm. Then? Will Jupiter's hydrogen and helium be opting out to be dispersed by the solar wind, just as happened with the terrestrial planets (well, similar)?

What happens next?

Cat

Helio

#### Helio

Helio,, first things first. What happens at the red giant stage? The temperature governing the frost line is 270 K. Where will the frost line be when Earth is either burning or charring?
Yes, that's important to know.

But give the answer a try.

1) Square the radius increase since this is the increase in area that is emitting. [New radius/Current radius]
2) Take the fourth power of the temp. ratio. [New temp./5777K]
3) Multiply 1 and 2 to get the revised luminosity.
4) But radiation diminishes by the inv. sq. law., so take the sq. root found in #3 to find the new HZ in AU.

As above, the red giant is strong in red so this will also play a role an how our planet would handle the difference. Our albedo might be less (oceans absorb red far better than blue, for instance).

So throw in one of your Chem E fudge factors for color. (pun intended)

Also, for Earth, the size will be so large that it will be more than 1/2 the Earth affected plus atm. refraction. Hence another factor to consider.

The mass loss is significant in reaching the red giant phase, so much so that our orbit will move outward, as is commonly reported. What is not mentioned, that I've seen, is that the flow of gas the Earth must pass through for millions of years should be a factor in slowing us and, thus, shrinking our orbit. But, since the gas flow is outward, perhaps it will push on the Earth to increase the radius. Good luck figuring the net on that one.

Now it is just outside the asteroids and bordering on Jupiter's realm. Then? Will Jupiter's hydrogen and helium be opting out to be dispersed by the solar wind, just as happened with the terrestrial planets (well, similar)?
I would assume so. The lighter gases in their upper atmospheres are there due to lack of being energized (KE from temp.). But this changes with a red giant, so no doubt you're right.

What happens next?
Perhaps we shouldn't put all this into Uranus. [sorry]

Catastrophe

#### Catastrophe

##### "There never was a good war, or a bad peace."
Perhaps we should first consider how long the red giant has to burn away the "outer light gas" planets:

"to 1 billion years

Stars spend approximately a few thousand to 1 billion years as a red giant. Eventually, the helium in the core runs out and fusion stops. The star shrinks again until a new helium shell reaches the core.27 Mar 2018

Red Giant Stars: Facts, Definition & the Future of the Sun | Space"

I agree it does not have to be at the billion end, but you can give me an estimate of how long the outer planets have before "the Sun doesn't shine" - well at least not strongly enough to burn or blow away more gas.

I have proposed a model, which I cannot prove, and you cannot disprove, but, accepting this, we can both explore some more if you like.

Cat

Helio

#### Catastrophe

##### "There never was a good war, or a bad peace."
View: https://imgur.com/a/pmGhiV3

A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ( M ☉)) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around 5,000 K (4,700 °C; 8,500 °F) or lower.

Red giant - Wikipedia

Cat

#### Helio

The Sun is, IIRC, expected to just reach 1 AU due to the Sun's current mass. So, many point out that the mass reduction will ease the Earth farther out, so we might not auger in, but we sure will be at least toast!

#### Catastrophe

##### "There never was a good war, or a bad peace."
Sun surface tamperature [Google] = 5,778 K

That seems to be about the same as around 5,000 K (4,700 °C; 8,500 °F) or lower. so I'll just look at the graphic above and leave the calculations to you

Up to that size for up to a billion years.

If I were a hydrogen atom on Jupiter, I'd run like hell

Cat

#### Catastrophe

##### "There never was a good war, or a bad peace."
The Sun is, IIRC, expected to just reach 1 AU due to the Sun's current mass. So, many point out that the mass reduction will ease the Earth farther out, so we might not auger in, but we sure will be at least toast!

Helio, you are talking about the end of the red giant. I am talking about the (up to a ) billion years when it is much larger.

Cat

#### Catastrophe

##### "There never was a good war, or a bad peace."
I was not seriously considering Earth. I am (see heading) referring to the Outer Solar System.

My main concern is hydrogen and helium, and their future in their current domicile.

Cat

#### Helio

Let's use 1 AU for our solar red giant.

Do you have a source on the effective temp. of our red giant?

The 5778K result is the temp. needed to generate the luminosity we observe. It's the effective temperature that generates the Solar Constant of 1361kw/m^2 (from space at 1 AU).

Another temp. to note is 5850K (or close to it). This is the temp. needed to generate a Planck (blackbody) curve that would fit best for the actual energy distribution of the Sun (Spectral Irradiance). It is hotter because the Sun, for one reason, has some excess blue light in its distribution.

#### Catastrophe

##### "There never was a good war, or a bad peace."
This all came from Google "sun surface temperature". See bottom first

Sun/Surface temperature
5,778 K

Feedback
Web results
How Hot Is the Sun? - Space.com
https://www.space.com › 17137-how-hot-is-the-sun

The temperature of the sun at its core is 27 million degrees, but only about 10 million degrees on its surface.
18 Oct 2017

"The fact that the outermost region of the sun's atmosphere is at millions of degrees while the temperature of the underlying photosphere is only 6,000 kelvins ...

Sun - Wikipedia
https://en.wikipedia.org › wiki › Sun

The Sun is a G2V star, with G2 indicating its surface temperature of approximately 5,778 K (5,505 °C, 9,941 °F), and V that it, like most stars, ...
Solar core · ‎Sun (disambiguation) · ‎Sun path · ‎The Sun in culture

How hot is the Sun? | Cool Cosmos

The temperature at the surface of the Sun is about 10,000 Fahrenheit (5,600 Celsius). The temperature rises from the surface of the Sun inward towards the ...

The Sun's Layers and Temperatures - Nasa JPL
https://www.jpl.nasa.gov › nmp › SCIENCE › sun

Core: the temperature at the very center of the Sun is about 27 million degrees Farenheit (F). The temperature cools down through the radiative and ...

Why is the sun's atmosphere hotter than its surface? - EarthSky
https://earthsky.org › Sun

The visible surface of the sun, or the photosphere, is around 6,000 degrees Celsius (11,000 degrees Fahrenheit). But a few thousand kilometers ...
30 May 2021 · Uploaded by ScienceAtNASA

How hot is the Sun? | Surface Temperature & Variance
https://nineplanets.org › Space Questions

The Sun is nearly a perfect sphere of hot plasma. The average surface temperatures are at around 5.778 K. Click for even more facts and information.

How is the temperature of the Sun's surface measured through ...
https://astronomy.com › measuring-the-suns-temperature

31 Jan 2018 — These different methods all show that the effective temperature of the Sun's surface is around 5,800 kelvins (9,980 degrees Fahrenheit [5,520 ...

How hot is the Sun?
https://www.thesun.co.uk › tech › how-hot-sun

29 Mar 2021 — The Sun is a blistering 15 million degrees Celsius (27 million degrees Fahrenheit) at its very centre, known as its core. The hottest parts of ...

Why the Sun's atmosphere is hotter than its surface
https://www.sciencedaily.com › releases › 2015/06

17 Jun 2015 — The Sun's temperature, which reaches around 15 million degrees Celsius in its core, steadily decreases with distance from the core, falling to ...

Sun
Star

Description
Description
The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy mainly as visible light, ultraviolet light, and infrared radiation. Wikipedia
Magnitude: -26.74
Mass: 1.989 × 10^30 kg
Luminosity: 1 L☉
Absolute magnitude: 4.83
Surface temperature: 5,778 K
Spectral type: G2V

Sun/Surface temperature
5,778 K

Feedback
Web results
How Hot Is the Sun? - Space.com
https://www.space.com › 17137-how-hot-is-the-sun

The temperature of the sun at its core is 27 million degrees, but only about 10 million degrees on its surface.
18 Oct 2017

"The fact that the outermost region of the sun's atmosphere is at millions of degrees while the temperature of the underlying photosphere is only 6,000 kelvins ...

Sun - Wikipedia
https://en.wikipedia.org › wiki › Sun

The Sun is a G2V star, with G2 indicating its surface temperature of approximately 5,778 K (5,505 °C, 9,941 °F), and V that it, like most stars, ...
Solar core · ‎Sun (disambiguation) · ‎Sun path · ‎The Sun in culture

How hot is the Sun? | Cool Cosmos

The temperature at the surface of the Sun is about 10,000 Fahrenheit (5,600 Celsius). The temperature rises from the surface of the Sun inward towards the ...

The Sun's Layers and Temperatures - Nasa JPL
https://www.jpl.nasa.gov › nmp › SCIENCE › sun

Core: the temperature at the very center of the Sun is about 27 million degrees Farenheit (F). The temperature cools down through the radiative and ...

Why is the sun's atmosphere hotter than its surface? - EarthSky
https://earthsky.org › Sun

The visible surface of the sun, or the photosphere, is around 6,000 degrees Celsius (11,000 degrees Fahrenheit). But a few thousand kilometers ...
30 May 2021 · Uploaded by ScienceAtNASA

How hot is the Sun? | Surface Temperature & Variance
https://nineplanets.org › Space Questions

The Sun is nearly a perfect sphere of hot plasma. The average surface temperatures are at around 5.778 K. Click for even more facts and information.

How is the temperature of the Sun's surface measured through ...
https://astronomy.com › measuring-the-suns-temperature

31 Jan 2018 — These different methods all show that the effective temperature of the Sun's surface is around 5,800 kelvins (9,980 degrees Fahrenheit [5,520 ...

How hot is the Sun?
https://www.thesun.co.uk › tech › how-hot-sun

29 Mar 2021 — The Sun is a blistering 15 million degrees Celsius (27 million degrees Fahrenheit) at its very centre, known as its core. The hottest parts of ...

Why the Sun's atmosphere is hotter than its surface
https://www.sciencedaily.com › releases › 2015/06

17 Jun 2015 — The Sun's temperature, which reaches around 15 million degrees Celsius in its core, steadily decreases with distance from the core, falling to ...

Related searches

Description

The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy mainly as visible light, ultraviolet light, and infrared radiation. Wikipedia
Magnitude: -26.74
Mass: 1.989 × 10^30 kg
Luminosity: 1 L☉
Absolute magnitude: 4.83
Surface temperature: 5,778 K
Spectral type: G2V

Cat

Last edited:

#### Helio

Yes, we have today's temp. but how hot is your run-of-the-mill red giant with a mass of say 0.5 to 0.8 solar masses (to account for loss)?

If you want to go deeper -- apparently puns are big for me today -- the Sun has a range of surface temperatures. At the limb it is ~ 5000K and at the center ~ 6,390K. This is because we can look through about 200km or so deeper into its interior when observing the central zone vs. only the upper atm. at the limb.

#### Catastrophe

##### "There never was a good war, or a bad peace."
Helio, you are the acknowledged expert regarding the Sun, and I will bow to your superior knowledge. I started this thread hoping for interesting discussions, and I think I am succeeding. I sincerely, honestly want to explore the question of the frost line (270 K) as the Sun goes red dwarf, and stays there for a long time.

Cat

#### Catastrophe

##### "There never was a good war, or a bad peace."
"Yes, we have today's temp. but how hot is your run-of-the-mill red giant with a mass of say 0.5 to 0.8 solar masses (to account for loss)?"

I Googled surface temperature red giant.

A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ( M ☉)) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around 5,000 K (4,700 °C; 8,500 °F) or lower.
Red giant - Wikipedia

Description
The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy mainly as visible light, ultraviolet light, and infrared radiation. Wikipedia
Magnitude: -26.74
Mass: 1.989 × 10^30 kg
Luminosity: 1 L☉
Absolute magnitude: 4.83
Surface temperature: 5,778 K
Spectral type: G2V

Cat

#### Catastrophe

##### "There never was a good war, or a bad peace."
Apolpgies for frame #13. It was copied from a multiformat Google result. I have tried to tidy it up.

So, where are we? Helio, you are the expert. I am asking the relative surface temperatures of the Sun now and after about 5 billion years to being a red giant for a long time. You know more than I, so I am relying on your guidance.

This is what I am after The outer Solar System in 5 billion years

I want to know where the frost line would be (270 K) and I really would greatly value your assistance. The only important things are facts, and you have more than I do.

Cat

Last edited:

#### Catastrophe

##### "There never was a good war, or a bad peace."
At last I have found something which illustrates my questions:

Friendly Giants Have Cozy Habitable Zones Too - Universe Today

View: https://imgur.com/a/CAw05CB

This illustrates what I mean.,

The frost line is at 270 K. If Jupiter is close to this temperature, will it retain its hydrogen and helium (and its moons)? Looking at the upper diagram, the frost line is currently just on the outside of the asteroid belt, corresponding to the outer extent of the habitable zone. Apply this to the lower diagram, complete with frost line temperature of 270 K (-3 C), and then ask whether Jupiter and Saturn will retain their hydrogen, helium and methane. (Not to mention their satellites) This seems to blow out the ideas of a habitable paradise in 5 billion years time, unless the near Earth size remains of Jupiter and Saturn can be colonised." NASA gives: "The resulting core masses are then expected to be in the range 0-10 M⊕, and 6-17 M⊕ for Jupiter and Saturn, respectively. Would they be water worlds?

N.B. "until it is 200 times its current size and several thousands times more luminous". This will be blasting away at the outer planets - obviously Jupiter and Saturn especially.
My emphasis.

Cat

Last edited:

#### Pogo

We also have to realize that the Sun is not at a constant luminosity, it has increased by about 1/3 since its birth. About a billion years or so will see the Sun with an increased luminosity, and the oceans will have vaporized, sorta like Venus. Now, if we can just pipe some air and water to Mars . . .

#### Helio

There is another article by the same authors preceding the above as follows:

Will Earth Survive When the Sun Becomes a Red Giant? - Universe Today

The previous post shows diagrams of exactly what I mean by the title of this thread. I am really so pleased to have found it.

Cat
Yes, that's a nice article.

"This new habitable zone will stretch from 49.4 AU to 71.4 AU – well into the Kuiper Belt – which means the formerly icy worlds will melt, and liquid water will be present beyond the orbit of Pluto."

The key to finding out who is right is to learn what the red giant's temperature will be, since we can use about 1AU for its radius. [Some suggest smaller.]

Red stars look red because they are cooler. 5000K is too hot to look red, just like 5850K (bb #) is too hot to look yellow.

I would expect the more accurate temp. to be close to what we see in other red-looking stars (ie red dwarfs), which are the coolest stars and are around 3000K. So something between 2750K and 3500K would make far more sense than 5000K.

Indeed, here is an article that states:
"Since a red giant star’s energy spreads across a larger area, its surface temperatures are cooler, reaching only 2,200 to 3,200 degrees Celsius / ..."

But, and based on your prior temp. quote, they also suggest 5000K in direct conflict with themselves. "...and the surface temperature is usually around 5,000 K."

Wiki seems no better as it appears to do the same thing.

The temp. difference here is nothing trivial to determine the HZ. Since temp is a 4th power rule, then these differences can throw us off by a factor up to about 12x!

Perhaps I'll have time to do a simple graph showing the HZ distance as a function of temp. and size.

As for H & He being removed from the giants, this might be more up your alley. If the new hotter temperatures jump the KE of atoms and molecules to that close to the escape velocity of the respective planet, then off they go. My guess is they sure might, at least H and H2. If hydrogen is a big chunk of the mass of Jupiter, then this mass loss would lower its escape velocity allowing perhaps He to be ejected, or some heavier molecule.

Catastrophe

#### Helio

Further, I keep seeing the use of "further" when I'm convinced the correct word to use for their distance reference is "farther". I never really paid attention to this in years past, but now that I learned the difference, it's striking to see its abuse. Or am I wrong?

#### Helio

Here is a table of HZ zones based on the calculator in your Habitable tab Exoplanet Excel program. [I think I included it.]

Wiki's page on giants shows a limited abs. mag. range of 0 to -1, so we can use that work sheet using these values. Since these are abs. values, the distance to use is simply 10 pc. Simple inputs, but the results aren't too encouraging as far as accuracy, at least in my view.

 Stellar Class BC Abs. Mag. Inner HZ, AU Outer HZ, AU K5 -0.6 0 11 16 K5 -0.6 -1 18 25 M0 -1.28 0 15 22 M0 -1.28 -1 24 35

The BC value comes from Princeton and from the Planetary Biology folks. I favor Princeton's. This is the correction factor needed to determine actual luminosity.

The M0 results push the HZ outward because they have greater luminosity if we see them at the same visual magnitude. I think this is the explanation.

Catastrophe

#### Catastrophe

##### "There never was a good war, or a bad peace."
Many thanks Helio, for those calculations.

Looking at #18, and this is a key whether or not it needs slight modification, it seems that at least Jupiter would be in the HZ. There is some variation, but the highest figure I have seen (above) for our Sun is 2AU diameter; thus 1 AU would have the Sun just reaching Earth (current) orbit.

If Jupiter were in the habitable zone, then the temperature would be at least 270 K or -3 C. My initial response is that H and He would be leaving very quickly, but I will seek data on this. I agree this is a complex picture with loss of gases (mass) changing both planets and (ergo) moons' orbits.

I really do appreciate your expert participation, especially on the star (Sun) involvement.

Cat

#### Pogo

But then again, there are a number of ‘hot Jupiters’ in other systems that are still hot Jupiters; really close to their suns, very hot, but apparently massive enough to retain the atmosphere. Maybe Saturn, Uranus, and Neptune May melt, but could Jupiter be massive enough to retain itself?

Replies
1
Views
325
Replies
0
Views
252
Replies
9
Views
554
Replies
17
Views
1K
Replies
8
Views
1K