What will be the temperature on Earth when Sun finishes its main sequence?
$begingroup$
We know that presently Sun is 4.5 billion years into its main sequence. It has another 5 billion years before it enters the Red Giant phase. We also know that Sun's luminosity increases by 10% every billion years during the main sequence. I am interested in finding the temperature rise as we approach the end of main sequence. I got two different values for temperature on Earth.
Wikipedia entry says that temperature on Earth would be 422 k in 2.8 billion years. However, if we use the formula for effective temperature as discussed in this answer
https://earthscience.stackexchange.com/a/4274/15299 and L = 1.8 then, the temperature on Earth would be 330K. Also in this book, the author does the same calculations on page 255.
geophysics hypothetical astronomy energy-balance
$endgroup$
add a comment |
$begingroup$
We know that presently Sun is 4.5 billion years into its main sequence. It has another 5 billion years before it enters the Red Giant phase. We also know that Sun's luminosity increases by 10% every billion years during the main sequence. I am interested in finding the temperature rise as we approach the end of main sequence. I got two different values for temperature on Earth.
Wikipedia entry says that temperature on Earth would be 422 k in 2.8 billion years. However, if we use the formula for effective temperature as discussed in this answer
https://earthscience.stackexchange.com/a/4274/15299 and L = 1.8 then, the temperature on Earth would be 330K. Also in this book, the author does the same calculations on page 255.
geophysics hypothetical astronomy energy-balance
$endgroup$
$begingroup$
@arkaia I have shared another answer in the question which is similar and was answered by experts here. I request you to let my question stay here as there are many intelligent folks here who may resolve this question quickly.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
@arkaia It is true that this question has a lot of astronomy, but heat balance and effective temperature is Earth Science-ish, and if somebody masters an answer including greenhouse effect, that would definitely be Earth Sciences.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
21 hours ago
add a comment |
$begingroup$
We know that presently Sun is 4.5 billion years into its main sequence. It has another 5 billion years before it enters the Red Giant phase. We also know that Sun's luminosity increases by 10% every billion years during the main sequence. I am interested in finding the temperature rise as we approach the end of main sequence. I got two different values for temperature on Earth.
Wikipedia entry says that temperature on Earth would be 422 k in 2.8 billion years. However, if we use the formula for effective temperature as discussed in this answer
https://earthscience.stackexchange.com/a/4274/15299 and L = 1.8 then, the temperature on Earth would be 330K. Also in this book, the author does the same calculations on page 255.
geophysics hypothetical astronomy energy-balance
$endgroup$
We know that presently Sun is 4.5 billion years into its main sequence. It has another 5 billion years before it enters the Red Giant phase. We also know that Sun's luminosity increases by 10% every billion years during the main sequence. I am interested in finding the temperature rise as we approach the end of main sequence. I got two different values for temperature on Earth.
Wikipedia entry says that temperature on Earth would be 422 k in 2.8 billion years. However, if we use the formula for effective temperature as discussed in this answer
https://earthscience.stackexchange.com/a/4274/15299 and L = 1.8 then, the temperature on Earth would be 330K. Also in this book, the author does the same calculations on page 255.
geophysics hypothetical astronomy energy-balance
geophysics hypothetical astronomy energy-balance
edited 20 hours ago
Camilo Rada
13.5k54396
13.5k54396
asked yesterday
sidharth chhabrasidharth chhabra
1634
1634
$begingroup$
@arkaia I have shared another answer in the question which is similar and was answered by experts here. I request you to let my question stay here as there are many intelligent folks here who may resolve this question quickly.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
@arkaia It is true that this question has a lot of astronomy, but heat balance and effective temperature is Earth Science-ish, and if somebody masters an answer including greenhouse effect, that would definitely be Earth Sciences.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
21 hours ago
add a comment |
$begingroup$
@arkaia I have shared another answer in the question which is similar and was answered by experts here. I request you to let my question stay here as there are many intelligent folks here who may resolve this question quickly.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
@arkaia It is true that this question has a lot of astronomy, but heat balance and effective temperature is Earth Science-ish, and if somebody masters an answer including greenhouse effect, that would definitely be Earth Sciences.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
21 hours ago
$begingroup$
@arkaia I have shared another answer in the question which is similar and was answered by experts here. I request you to let my question stay here as there are many intelligent folks here who may resolve this question quickly.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
@arkaia I have shared another answer in the question which is similar and was answered by experts here. I request you to let my question stay here as there are many intelligent folks here who may resolve this question quickly.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
@arkaia It is true that this question has a lot of astronomy, but heat balance and effective temperature is Earth Science-ish, and if somebody masters an answer including greenhouse effect, that would definitely be Earth Sciences.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
@arkaia It is true that this question has a lot of astronomy, but heat balance and effective temperature is Earth Science-ish, and if somebody masters an answer including greenhouse effect, that would definitely be Earth Sciences.
$endgroup$
– Camilo Rada
22 hours ago
1
1
$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
21 hours ago
$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
21 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Answers will be different because they must be tied to a model of solar evolution, and all models are a bit different.
So to answer your question we have to select a model. A pretty standard and trusted one, is the one used in the paper Stellar evolution models for Z = 0.0001 to 0.03. Where Z stands for the metalicity of the star, that for the Sun they indicate would be 0.0188.
In figure 2, they show the trajectory of a star like the sun in the H-R diagram (look for the line labeled "1.0").
The data output of this model is available at the VizieR catalog. I just downloaded the data for starts of one solar mass and Z=0.02 (like the Sun), and computed the effective temperature of Earth using the formula in the linked question
$Large frac{T}{T_0}=left(frac{L}{L_0}right)^{frac{1}{4}}$
Using a current effective temperature $T_0$ of -19°C (you will find values between -18 and -21°C), we get that the plot pf Luminosity and temperature versus time looks like this
And given that you are interested in specific values here is some tabulated data including also the solar radius. Note that most of these points are linear interpolations of the original data, that had only six points in this age range.
Age Radius Lumin. Temperature
[Billion [solar [Solar [°C]
years] radius] Lumin.]
0.00 0.89 0.7 -41.4
0.25 0.90 0.7 -40.2
0.50 0.91 0.7 -39.0
0.75 0.91 0.7 -37.8
1.00 0.92 0.8 -36.6
1.25 0.93 0.8 -35.4
1.50 0.94 0.8 -34.2
1.75 0.95 0.8 -32.9
2.00 0.95 0.8 -31.7
2.25 0.96 0.8 -30.4
2.50 0.97 0.8 -29.2
2.75 0.98 0.9 -27.9
3.00 0.99 0.9 -26.7
3.25 1.00 0.9 -25.4
3.50 1.00 0.9 -24.1
3.75 1.01 0.9 -22.8
4.00 1.02 1.0 -21.5
4.25 1.03 1.0 -20.2
4.50 1.04 1.0 -18.9
4.75 1.05 1.0 -17.6
5.00 1.06 1.0 -16.3
5.25 1.07 1.1 -15.0
5.50 1.08 1.1 -13.7
5.75 1.08 1.1 -12.3
6.00 1.09 1.1 -11.0
6.25 1.10 1.2 -9.6
6.50 1.11 1.2 -8.3
6.75 1.12 1.2 -6.9
7.00 1.13 1.2 -5.5
7.25 1.14 1.3 -4.1
7.50 1.15 1.3 -2.8
7.75 1.16 1.3 -1.4
8.00 1.17 1.3 0.0
8.25 1.18 1.4 1.4
8.50 1.19 1.4 2.9
8.75 1.20 1.4 4.3
9.00 1.21 1.4 5.7
9.25 1.22 1.5 7.2
9.50 1.26 1.5 9.2
9.75 1.32 1.6 11.9
10.00 1.38 1.6 14.7
10.25 1.44 1.7 17.5
10.50 1.51 1.8 20.3
10.75 1.58 1.8 23.1
11.00 1.66 1.9 25.9
11.25 1.74 2.0 28.8
11.50 1.82 2.1 31.7
11.75 1.90 2.2 34.7
12.00 2.40 3.1 65.0
12.25 4.08 7.8 151.9
12.50 6.94 19.6 261.2
12.75 11.68 57.8 427.2
Note that you can only know the effective temperature, the actual temperature will depend on the strength of the greenhouse effect, and modeling that is a whole new problem with huge uncertainties.
According to this model, the terminal age main sequence of the Sun would be 9.38 Billion years, and according to the data above, the effective temperature then would be 8.2 °C (281 K), that's 27.2 °C hotter than today.
$endgroup$
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
|
show 2 more comments
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1 Answer
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1 Answer
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$begingroup$
Answers will be different because they must be tied to a model of solar evolution, and all models are a bit different.
So to answer your question we have to select a model. A pretty standard and trusted one, is the one used in the paper Stellar evolution models for Z = 0.0001 to 0.03. Where Z stands for the metalicity of the star, that for the Sun they indicate would be 0.0188.
In figure 2, they show the trajectory of a star like the sun in the H-R diagram (look for the line labeled "1.0").
The data output of this model is available at the VizieR catalog. I just downloaded the data for starts of one solar mass and Z=0.02 (like the Sun), and computed the effective temperature of Earth using the formula in the linked question
$Large frac{T}{T_0}=left(frac{L}{L_0}right)^{frac{1}{4}}$
Using a current effective temperature $T_0$ of -19°C (you will find values between -18 and -21°C), we get that the plot pf Luminosity and temperature versus time looks like this
And given that you are interested in specific values here is some tabulated data including also the solar radius. Note that most of these points are linear interpolations of the original data, that had only six points in this age range.
Age Radius Lumin. Temperature
[Billion [solar [Solar [°C]
years] radius] Lumin.]
0.00 0.89 0.7 -41.4
0.25 0.90 0.7 -40.2
0.50 0.91 0.7 -39.0
0.75 0.91 0.7 -37.8
1.00 0.92 0.8 -36.6
1.25 0.93 0.8 -35.4
1.50 0.94 0.8 -34.2
1.75 0.95 0.8 -32.9
2.00 0.95 0.8 -31.7
2.25 0.96 0.8 -30.4
2.50 0.97 0.8 -29.2
2.75 0.98 0.9 -27.9
3.00 0.99 0.9 -26.7
3.25 1.00 0.9 -25.4
3.50 1.00 0.9 -24.1
3.75 1.01 0.9 -22.8
4.00 1.02 1.0 -21.5
4.25 1.03 1.0 -20.2
4.50 1.04 1.0 -18.9
4.75 1.05 1.0 -17.6
5.00 1.06 1.0 -16.3
5.25 1.07 1.1 -15.0
5.50 1.08 1.1 -13.7
5.75 1.08 1.1 -12.3
6.00 1.09 1.1 -11.0
6.25 1.10 1.2 -9.6
6.50 1.11 1.2 -8.3
6.75 1.12 1.2 -6.9
7.00 1.13 1.2 -5.5
7.25 1.14 1.3 -4.1
7.50 1.15 1.3 -2.8
7.75 1.16 1.3 -1.4
8.00 1.17 1.3 0.0
8.25 1.18 1.4 1.4
8.50 1.19 1.4 2.9
8.75 1.20 1.4 4.3
9.00 1.21 1.4 5.7
9.25 1.22 1.5 7.2
9.50 1.26 1.5 9.2
9.75 1.32 1.6 11.9
10.00 1.38 1.6 14.7
10.25 1.44 1.7 17.5
10.50 1.51 1.8 20.3
10.75 1.58 1.8 23.1
11.00 1.66 1.9 25.9
11.25 1.74 2.0 28.8
11.50 1.82 2.1 31.7
11.75 1.90 2.2 34.7
12.00 2.40 3.1 65.0
12.25 4.08 7.8 151.9
12.50 6.94 19.6 261.2
12.75 11.68 57.8 427.2
Note that you can only know the effective temperature, the actual temperature will depend on the strength of the greenhouse effect, and modeling that is a whole new problem with huge uncertainties.
According to this model, the terminal age main sequence of the Sun would be 9.38 Billion years, and according to the data above, the effective temperature then would be 8.2 °C (281 K), that's 27.2 °C hotter than today.
$endgroup$
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
|
show 2 more comments
$begingroup$
Answers will be different because they must be tied to a model of solar evolution, and all models are a bit different.
So to answer your question we have to select a model. A pretty standard and trusted one, is the one used in the paper Stellar evolution models for Z = 0.0001 to 0.03. Where Z stands for the metalicity of the star, that for the Sun they indicate would be 0.0188.
In figure 2, they show the trajectory of a star like the sun in the H-R diagram (look for the line labeled "1.0").
The data output of this model is available at the VizieR catalog. I just downloaded the data for starts of one solar mass and Z=0.02 (like the Sun), and computed the effective temperature of Earth using the formula in the linked question
$Large frac{T}{T_0}=left(frac{L}{L_0}right)^{frac{1}{4}}$
Using a current effective temperature $T_0$ of -19°C (you will find values between -18 and -21°C), we get that the plot pf Luminosity and temperature versus time looks like this
And given that you are interested in specific values here is some tabulated data including also the solar radius. Note that most of these points are linear interpolations of the original data, that had only six points in this age range.
Age Radius Lumin. Temperature
[Billion [solar [Solar [°C]
years] radius] Lumin.]
0.00 0.89 0.7 -41.4
0.25 0.90 0.7 -40.2
0.50 0.91 0.7 -39.0
0.75 0.91 0.7 -37.8
1.00 0.92 0.8 -36.6
1.25 0.93 0.8 -35.4
1.50 0.94 0.8 -34.2
1.75 0.95 0.8 -32.9
2.00 0.95 0.8 -31.7
2.25 0.96 0.8 -30.4
2.50 0.97 0.8 -29.2
2.75 0.98 0.9 -27.9
3.00 0.99 0.9 -26.7
3.25 1.00 0.9 -25.4
3.50 1.00 0.9 -24.1
3.75 1.01 0.9 -22.8
4.00 1.02 1.0 -21.5
4.25 1.03 1.0 -20.2
4.50 1.04 1.0 -18.9
4.75 1.05 1.0 -17.6
5.00 1.06 1.0 -16.3
5.25 1.07 1.1 -15.0
5.50 1.08 1.1 -13.7
5.75 1.08 1.1 -12.3
6.00 1.09 1.1 -11.0
6.25 1.10 1.2 -9.6
6.50 1.11 1.2 -8.3
6.75 1.12 1.2 -6.9
7.00 1.13 1.2 -5.5
7.25 1.14 1.3 -4.1
7.50 1.15 1.3 -2.8
7.75 1.16 1.3 -1.4
8.00 1.17 1.3 0.0
8.25 1.18 1.4 1.4
8.50 1.19 1.4 2.9
8.75 1.20 1.4 4.3
9.00 1.21 1.4 5.7
9.25 1.22 1.5 7.2
9.50 1.26 1.5 9.2
9.75 1.32 1.6 11.9
10.00 1.38 1.6 14.7
10.25 1.44 1.7 17.5
10.50 1.51 1.8 20.3
10.75 1.58 1.8 23.1
11.00 1.66 1.9 25.9
11.25 1.74 2.0 28.8
11.50 1.82 2.1 31.7
11.75 1.90 2.2 34.7
12.00 2.40 3.1 65.0
12.25 4.08 7.8 151.9
12.50 6.94 19.6 261.2
12.75 11.68 57.8 427.2
Note that you can only know the effective temperature, the actual temperature will depend on the strength of the greenhouse effect, and modeling that is a whole new problem with huge uncertainties.
According to this model, the terminal age main sequence of the Sun would be 9.38 Billion years, and according to the data above, the effective temperature then would be 8.2 °C (281 K), that's 27.2 °C hotter than today.
$endgroup$
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
|
show 2 more comments
$begingroup$
Answers will be different because they must be tied to a model of solar evolution, and all models are a bit different.
So to answer your question we have to select a model. A pretty standard and trusted one, is the one used in the paper Stellar evolution models for Z = 0.0001 to 0.03. Where Z stands for the metalicity of the star, that for the Sun they indicate would be 0.0188.
In figure 2, they show the trajectory of a star like the sun in the H-R diagram (look for the line labeled "1.0").
The data output of this model is available at the VizieR catalog. I just downloaded the data for starts of one solar mass and Z=0.02 (like the Sun), and computed the effective temperature of Earth using the formula in the linked question
$Large frac{T}{T_0}=left(frac{L}{L_0}right)^{frac{1}{4}}$
Using a current effective temperature $T_0$ of -19°C (you will find values between -18 and -21°C), we get that the plot pf Luminosity and temperature versus time looks like this
And given that you are interested in specific values here is some tabulated data including also the solar radius. Note that most of these points are linear interpolations of the original data, that had only six points in this age range.
Age Radius Lumin. Temperature
[Billion [solar [Solar [°C]
years] radius] Lumin.]
0.00 0.89 0.7 -41.4
0.25 0.90 0.7 -40.2
0.50 0.91 0.7 -39.0
0.75 0.91 0.7 -37.8
1.00 0.92 0.8 -36.6
1.25 0.93 0.8 -35.4
1.50 0.94 0.8 -34.2
1.75 0.95 0.8 -32.9
2.00 0.95 0.8 -31.7
2.25 0.96 0.8 -30.4
2.50 0.97 0.8 -29.2
2.75 0.98 0.9 -27.9
3.00 0.99 0.9 -26.7
3.25 1.00 0.9 -25.4
3.50 1.00 0.9 -24.1
3.75 1.01 0.9 -22.8
4.00 1.02 1.0 -21.5
4.25 1.03 1.0 -20.2
4.50 1.04 1.0 -18.9
4.75 1.05 1.0 -17.6
5.00 1.06 1.0 -16.3
5.25 1.07 1.1 -15.0
5.50 1.08 1.1 -13.7
5.75 1.08 1.1 -12.3
6.00 1.09 1.1 -11.0
6.25 1.10 1.2 -9.6
6.50 1.11 1.2 -8.3
6.75 1.12 1.2 -6.9
7.00 1.13 1.2 -5.5
7.25 1.14 1.3 -4.1
7.50 1.15 1.3 -2.8
7.75 1.16 1.3 -1.4
8.00 1.17 1.3 0.0
8.25 1.18 1.4 1.4
8.50 1.19 1.4 2.9
8.75 1.20 1.4 4.3
9.00 1.21 1.4 5.7
9.25 1.22 1.5 7.2
9.50 1.26 1.5 9.2
9.75 1.32 1.6 11.9
10.00 1.38 1.6 14.7
10.25 1.44 1.7 17.5
10.50 1.51 1.8 20.3
10.75 1.58 1.8 23.1
11.00 1.66 1.9 25.9
11.25 1.74 2.0 28.8
11.50 1.82 2.1 31.7
11.75 1.90 2.2 34.7
12.00 2.40 3.1 65.0
12.25 4.08 7.8 151.9
12.50 6.94 19.6 261.2
12.75 11.68 57.8 427.2
Note that you can only know the effective temperature, the actual temperature will depend on the strength of the greenhouse effect, and modeling that is a whole new problem with huge uncertainties.
According to this model, the terminal age main sequence of the Sun would be 9.38 Billion years, and according to the data above, the effective temperature then would be 8.2 °C (281 K), that's 27.2 °C hotter than today.
$endgroup$
Answers will be different because they must be tied to a model of solar evolution, and all models are a bit different.
So to answer your question we have to select a model. A pretty standard and trusted one, is the one used in the paper Stellar evolution models for Z = 0.0001 to 0.03. Where Z stands for the metalicity of the star, that for the Sun they indicate would be 0.0188.
In figure 2, they show the trajectory of a star like the sun in the H-R diagram (look for the line labeled "1.0").
The data output of this model is available at the VizieR catalog. I just downloaded the data for starts of one solar mass and Z=0.02 (like the Sun), and computed the effective temperature of Earth using the formula in the linked question
$Large frac{T}{T_0}=left(frac{L}{L_0}right)^{frac{1}{4}}$
Using a current effective temperature $T_0$ of -19°C (you will find values between -18 and -21°C), we get that the plot pf Luminosity and temperature versus time looks like this
And given that you are interested in specific values here is some tabulated data including also the solar radius. Note that most of these points are linear interpolations of the original data, that had only six points in this age range.
Age Radius Lumin. Temperature
[Billion [solar [Solar [°C]
years] radius] Lumin.]
0.00 0.89 0.7 -41.4
0.25 0.90 0.7 -40.2
0.50 0.91 0.7 -39.0
0.75 0.91 0.7 -37.8
1.00 0.92 0.8 -36.6
1.25 0.93 0.8 -35.4
1.50 0.94 0.8 -34.2
1.75 0.95 0.8 -32.9
2.00 0.95 0.8 -31.7
2.25 0.96 0.8 -30.4
2.50 0.97 0.8 -29.2
2.75 0.98 0.9 -27.9
3.00 0.99 0.9 -26.7
3.25 1.00 0.9 -25.4
3.50 1.00 0.9 -24.1
3.75 1.01 0.9 -22.8
4.00 1.02 1.0 -21.5
4.25 1.03 1.0 -20.2
4.50 1.04 1.0 -18.9
4.75 1.05 1.0 -17.6
5.00 1.06 1.0 -16.3
5.25 1.07 1.1 -15.0
5.50 1.08 1.1 -13.7
5.75 1.08 1.1 -12.3
6.00 1.09 1.1 -11.0
6.25 1.10 1.2 -9.6
6.50 1.11 1.2 -8.3
6.75 1.12 1.2 -6.9
7.00 1.13 1.2 -5.5
7.25 1.14 1.3 -4.1
7.50 1.15 1.3 -2.8
7.75 1.16 1.3 -1.4
8.00 1.17 1.3 0.0
8.25 1.18 1.4 1.4
8.50 1.19 1.4 2.9
8.75 1.20 1.4 4.3
9.00 1.21 1.4 5.7
9.25 1.22 1.5 7.2
9.50 1.26 1.5 9.2
9.75 1.32 1.6 11.9
10.00 1.38 1.6 14.7
10.25 1.44 1.7 17.5
10.50 1.51 1.8 20.3
10.75 1.58 1.8 23.1
11.00 1.66 1.9 25.9
11.25 1.74 2.0 28.8
11.50 1.82 2.1 31.7
11.75 1.90 2.2 34.7
12.00 2.40 3.1 65.0
12.25 4.08 7.8 151.9
12.50 6.94 19.6 261.2
12.75 11.68 57.8 427.2
Note that you can only know the effective temperature, the actual temperature will depend on the strength of the greenhouse effect, and modeling that is a whole new problem with huge uncertainties.
According to this model, the terminal age main sequence of the Sun would be 9.38 Billion years, and according to the data above, the effective temperature then would be 8.2 °C (281 K), that's 27.2 °C hotter than today.
edited 22 hours ago
answered 23 hours ago
Camilo RadaCamilo Rada
13.5k54396
13.5k54396
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
|
show 2 more comments
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
Thank you for the detailed answer. Can you suggest any recent papers which have modeled the actual temperature? or any books which discuss compare various models for actual temperatures.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
I'm doubt anyone have dare to model greenhouse effect in multi-billion years timescale. Or at least I'm not aware of such research. I don't know why exactly do you need this number, but I think you are better off, figuring our at what temperature using normal green house effects, a runaway greenhouse effect would be inevitable.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
Or as a mental exercise, it would be possible to calculate what would be the temperature if we have the same greenhouse effect than today but the solar luminosity of four billion years in the future.
$endgroup$
– Camilo Rada
22 hours ago
1
1
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
22 hours ago
1
1
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
$begingroup$
@undefined 1 Billion = $10^9$=1,000,000,000
$endgroup$
– Camilo Rada
10 hours ago
|
show 2 more comments
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$begingroup$
@arkaia I have shared another answer in the question which is similar and was answered by experts here. I request you to let my question stay here as there are many intelligent folks here who may resolve this question quickly.
$endgroup$
– sidharth chhabra
23 hours ago
$begingroup$
@arkaia It is true that this question has a lot of astronomy, but heat balance and effective temperature is Earth Science-ish, and if somebody masters an answer including greenhouse effect, that would definitely be Earth Sciences.
$endgroup$
– Camilo Rada
22 hours ago
1
$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
21 hours ago