What will be the temperature on Earth when Sun finishes its main sequence?












4












$begingroup$


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.










share|improve this question











$endgroup$












  • $begingroup$
    @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
    5 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
    4 hours ago






  • 1




    $begingroup$
    I understand your point. Close vote removed
    $endgroup$
    – arkaia
    3 hours ago
















4












$begingroup$


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.










share|improve this question











$endgroup$












  • $begingroup$
    @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
    5 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
    4 hours ago






  • 1




    $begingroup$
    I understand your point. Close vote removed
    $endgroup$
    – arkaia
    3 hours ago














4












4








4





$begingroup$


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.










share|improve this question











$endgroup$




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






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 1 hour ago









Camilo Rada

13.5k54396




13.5k54396










asked 7 hours ago









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
    5 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
    4 hours ago






  • 1




    $begingroup$
    I understand your point. Close vote removed
    $endgroup$
    – arkaia
    3 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
    5 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
    4 hours ago






  • 1




    $begingroup$
    I understand your point. Close vote removed
    $endgroup$
    – arkaia
    3 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
5 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
5 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
4 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
4 hours ago




1




1




$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
3 hours ago




$begingroup$
I understand your point. Close vote removed
$endgroup$
– arkaia
3 hours ago










1 Answer
1






active

oldest

votes


















4












$begingroup$

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").



enter image description here



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



enter image description here



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.






share|improve this answer











$endgroup$













  • $begingroup$
    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
    4 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
    4 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
    4 hours ago












  • $begingroup$
    I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
    $endgroup$
    – sidharth chhabra
    4 hours ago






  • 1




    $begingroup$
    This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
    $endgroup$
    – Camilo Rada
    4 hours ago











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "553"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fearthscience.stackexchange.com%2fquestions%2f16580%2fwhat-will-be-the-temperature-on-earth-when-sun-finishes-its-main-sequence%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









4












$begingroup$

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").



enter image description here



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



enter image description here



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.






share|improve this answer











$endgroup$













  • $begingroup$
    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
    4 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
    4 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
    4 hours ago












  • $begingroup$
    I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
    $endgroup$
    – sidharth chhabra
    4 hours ago






  • 1




    $begingroup$
    This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
    $endgroup$
    – Camilo Rada
    4 hours ago
















4












$begingroup$

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").



enter image description here



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



enter image description here



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.






share|improve this answer











$endgroup$













  • $begingroup$
    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
    4 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
    4 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
    4 hours ago












  • $begingroup$
    I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
    $endgroup$
    – sidharth chhabra
    4 hours ago






  • 1




    $begingroup$
    This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
    $endgroup$
    – Camilo Rada
    4 hours ago














4












4








4





$begingroup$

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").



enter image description here



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



enter image description here



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.






share|improve this answer











$endgroup$



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").



enter image description here



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



enter image description here



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.







share|improve this answer














share|improve this answer



share|improve this answer








edited 4 hours ago

























answered 5 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
    4 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
    4 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
    4 hours ago












  • $begingroup$
    I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
    $endgroup$
    – sidharth chhabra
    4 hours ago






  • 1




    $begingroup$
    This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
    $endgroup$
    – Camilo Rada
    4 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
    4 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
    4 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
    4 hours ago












  • $begingroup$
    I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
    $endgroup$
    – sidharth chhabra
    4 hours ago






  • 1




    $begingroup$
    This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
    $endgroup$
    – Camilo Rada
    4 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
4 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
4 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
4 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
4 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
4 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
4 hours ago














$begingroup$
I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
$endgroup$
– sidharth chhabra
4 hours ago




$begingroup$
I am trying to understand the future of Earth when the Sun becomes a red giant. Do you have any books or latest papers which discuss the future 5 billion years from now?
$endgroup$
– sidharth chhabra
4 hours ago




1




1




$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
4 hours ago




$begingroup$
This article is nice academic.oup.com/astrogeo/article/42/6/6.26/293074
$endgroup$
– Camilo Rada
4 hours ago


















draft saved

draft discarded




















































Thanks for contributing an answer to Earth Science Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fearthscience.stackexchange.com%2fquestions%2f16580%2fwhat-will-be-the-temperature-on-earth-when-sun-finishes-its-main-sequence%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

Knooppunt Holsloot

Altaar (religie)

Gregoriusmis