<p>In short: No. Unless multi-million timescales are considered.</p>

<p>The reason we keep teaching Newtonian mechanics, is because it is a VERY accurate approximation of a more general theory (general relativity) within the regimes of speed and gravity acceleration found in everyday life. Therefore, all the relativistic corrections to Newtonian mechanics in the Earth system are negligible. Both, for the internal operations of the climate and for the evolution of its orbital parameters on timescales of hundreds of millennia or shorter.</p>

<p>One effect, would be the minor role that apsidal precession have on the change of distribution of incoming solar energy described by the <a href="https://en.wikipedia.org/wiki/Milankovitch_cycles#Orbital_shape_(eccentricity)" rel="noreferrer">Milankovic cycles</a>. But that can arguably considered negligible. </p>

<p>But perhaps the most important contribution would be the influence of relativistic corrections in Earth's orbit eccentricity variations on multi-million years timescales.</p>

<p>State-of-the-art orbital solutions for the long-term motion of the Earth like <a href="https://www.aanda.org/articles/aa/pdf/2011/08/aa16836-11.pdf" rel="noreferrer">La2010</a>, do use relativistic correction, however they are rather small. The way the corrections are included in the model are described by <a href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1994AJ....108.1962S&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf" rel="noreferrer">Saha &amp; Tremaine (1994)</a>, where they point that:</p>

<blockquote>
  <p>General relativistic effects in planetary motion have fractional
  amplitude of order $\frac{k^2}{c^2 r} \sim 10^{-8}$ at $r = 1 \,  \textbf{AU}$.</p>
</blockquote>

<p>Meaning that the correction correspond to a 0.000001% of the total variation of the orbital parameters. Unquestionably, even such small corrections have a cumulative effect over multi-million years timescales. <a href="http://iopscience.iop.org/article/10.1086/375560/pdf" rel="noreferrer">Varadi et. at. (2003)</a>, compares the output of a model using relativistic corrections (solid line) with one not using them (dashed line), and the following figure show the results over 3 million years, where can be observed that significant differences arise after 300,000 years.</p>

<p><a href="https://i.sstatic.net/6GSFD.png" rel="noreferrer"><img src="https://i.sstatic.net/6GSFD.png" alt="enter image description here"></a></p>

<p>However, it is reasonable to consider that such small corrections would have been overcome at some point in the past by some other unaccounted effects, like large meteorite impacts (or fly-by), solar storms, etc. Remember that La2010 go back 50 million years and <a href="https://www.aanda.org/articles/aa/full/2004/46/aa1335/aa1335.html" rel="noreferrer">other models go back several billion years</a>, when such events were rather common. So, I would still argue that relativistic corrections are not very significant. However, in a chaotic system like Earth's climate, you can never rule out that a negligible forcing could have had an important effect.</p>

<p>Of course the answer would be different (and the relative importance higher) if we consider a planet orbiting extremely close to a super-massive star. But, I'm assuming you are mostly considering planets similar to Earth in that regard.</p>

<p>There are also some claims (the <a href="http://lasp.colorado.edu/sorce/news/2008ScienceMeeting/posters/P4_01_Lynch_Poster.pdf" rel="noreferrer">Damhsa Theory</a>) that gravitational waves might have play a role in the very long term climate evolution of Earth. However, I'm not capable to really assess the validity of such theory, but I have to admit I'm skeptical about it. I've posted <a href="https://physics.stackexchange.com/questions/394552/damhsa-theory-can-gravitational-waves-really-affect-the-long-term-climatic-evo">a question about that</a> in Physics SE, an there seem to be wide consensus that such effect would be exceedingly small to ever deserve any kind of consideration.</p>

CC BY-SA 3.0
2018-03-20T21:30:42.593Z
To me the "Damhsa theory" looks somewhere between "wrong" and "not even wrong" (i.e. so vague it's un-falsifiable) but as far as I can tell relativity does become relevant at multi-Myr timescales -- I assume this because the [La2010 orbital model](https://www.aanda.org/articles/aa/pdf/2011/08/aa16836-11.pdf) and its predecessor take the trouble to account for relativity. I guess that in a Newtonian solar system we'd get similar Milankovitch cycles but with different timings (I have no idea how different). Might be interesting to compare La2010 with earlier Newtonian models...
Pont
CC BY-SA 3.0
2018-03-20T22:21:00.647Z
@Pont I had a look into that paper, and the corrections are rather small, probably borderline in what could be considered negligible. I'll add few sentences about that.
Camilo Rada
CC BY-SA 3.0
2018-03-20T22:44:14.597Z
@Pont I just added some comments in that regard.
Camilo Rada
CC BY-SA 3.0
2018-03-20T23:26:43.003Z
After reading Varadi et. al. paper I've changed my mind on the relevance of relativity, so I've changed the answer accordingly.
Camilo Rada
CC BY-SA 3.0
2018-03-21T00:17:25.600Z
What is "My"? Million years?
Pedro A
CC BY-SA 3.0
2018-03-21T00:19:43.940Z
@Hamsterrific Yes, in non academic environments I never know if to use Ma, My, Myr or Myrs, you can find all options and the former is the one used in academic publication, but many of my students don't really know what annus means
Camilo Rada
CC BY-SA 3.0
2018-03-20T20:17:11.807Z
2018-03-21T00:22:14.277Z
2018-03-21T00:22:14.277Z
Camilo Rada
<p>The latest positions that I am aware of say yes, but not in any useful way.</p>

<p>From what I have read, the current prevailing opinion is that the weather of Earth is a chaotic system.  Chaotic systems are known to be very sensitive to initial conditions.  Eddys in the atmosphere that are mere milimeters in size may change whether it rains or shines on the other side of the planet in a few months.</p>

<p>From this concept, we can assume that GR affects the weather.  However, we have to be cautious with what we draw from that conclusion.  I believe it was von Neuman who is quoted as saying that when he first heard of the idea of weather as a chaotic system, sensitive to initial conditions, he had the idea that we might soon have weather control simply by doing small adjustments.  Only later did he finally understand chaos theory: such perturbations were like giving a well shuffled desk another shuffle.  It certainly changes your luck, but you couldn't possibly know if it was for better or for worse.</p>

<p>So to your question, as to whether GR would have <em>any</em> effect, the answer is yes.  If you were to rephrase the question to ask whether it had any measurable effects that might be tested with empirical evidence, then I would have to defer to Camilo's answer.</p>

CC BY-SA 3.0
2018-03-21T00:28:24.900Z
I agree, but you could answer basically the same if I ask "Does my dog affects Earth's climate?"
Camilo Rada
CC BY-SA 3.0
2018-03-21T00:38:03.340Z
@CamiloRada Yes, you can =)  Myself, I find the distinction rather interesting.  That I cannot predict whether it's going to rain or shine in Seattle in a month, and yet you can look at multi-million year timescales and provide useful answers is fascinating, and I think it's an important part of climate study.  This is especially true in an era where climate change is a highly contentious topic.  (Oh, and just kidding. I can predict: it'll be raining in Seattle.  Don't worry ;-)  )
Cort Ammon
CC BY-SA 3.0
2018-03-21T00:41:10.530Z
Yes, that's a fascinating point. Weather forecasting is also quite easy here in Vancouver, BC: 99% chances of rain =)
Camilo Rada
CC BY-SA 3.0
2018-03-21T03:42:24.060Z
@Cort Ammon: Look up the term "chaotic attractor".  Essentially, chaotic systems have limits.  You can't make long-term predictions of exactly where within those limits it will be, but you can confidently predict that it will be somewhere within them.  So you could accurately predict that 100 years from now there's a 90% chance it will rain in Seattle on any given Saturday, but you have no chance of predicting which Saturday will be the clear one.
jamesqf
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2018-03-21T06:38:57.357Z
@jamesqf Oh, I do understand them, but that doesn't make them any less fascinating.
Cort Ammon
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2018-03-23T21:26:40.820Z
I am not sure you can say that GR has an effect on climate from the fact that the whole system is chaotic, because in that case this would be quite meaningless since anything has an effect. I meant that GR would have an effect in the sense that despite the chaotic behavior of climate, GR would have a in imprint on the average weather patterns.
user85659
CC BY-SA 3.0
2018-03-23T22:06:57.520Z
@TTFarreo Does that mean we should read the phrase "any influence" in the question as "any predictable influence?"
Cort Ammon
CC BY-SA 3.0
2018-03-24T18:45:24.430Z
@Cort Ammon Yes, you're right.
user85659
CC BY-SA 3.0
2018-03-21T00:18:32.230Z
2018-03-21T00:18:32.230Z
Cort Ammon
<p>I don't see this point made, so I'll just add it.   In very high gravitation situations orbital energy can be lost to "relativity" or more specifically, gravity waves.  The primary relativistic effect that the Sun's gravity has on Mercury is an increase in it's precession, as @CamiloRada pointed out, and <a href="https://physics.stackexchange.com/questions/26408/what-did-general-relativity-clarify-about-mercury">see more details here</a>.</p>

<p>A secondary relativistic effect is orbital decay, or spiraling in.  This is <a href="https://www.forbes.com/sites/chadorzel/2015/07/22/three-experiments-that-show-relativity-is-real/2/#72c35a8443a9" rel="nofollow noreferrer">observable in tight orbits around neutron stars</a> or black holes.  The effect around a regular star would be tiny but non zero.   </p>

<p>This <a href="https://www.forbes.com/sites/startswithabang/2016/12/27/gravitational-waves-from-discovery-of-the-year-to-science-of-the-century/#6ee4dfe5087f" rel="nofollow noreferrer">article gives some numbers for this effect on the Earth</a>.</p>

<blockquote>
  <p>Gravitational radiation is incredibly subtle and weak in its effects.
  The Earth, as it orbits the Sun, loses energy due to this radiation
  and spirals inwards. But it will take 10^150 years for this process to
  occur.</p>
</blockquote>

<p>That's a preposterously long period of time.  Mercury would certainly be effected significantly more than Earth, (I can't do the math, maybe someone here will step up), but even at mercury distance the energy loss to gravity waves and spiraling-in would be slow to the point of irrelevance compared to other effects.</p>

<p>Our sun, for example, grows larger and brighter over it's lifetime. Planets atmosphere's change, either stripped off or in the case of Earth, affected by photosynthesis and other processes, and the Sun loses mass over it's lifetime, which causes the planets, on average to move outwards, though inward migration is also thought to be possible and the planets can affect each other's orbits.  These changes to climate are all likely to be significantly greater than relativistic spiraling-in.</p>

<p>For maximum "spiral-in" effect, you'd probably want a small star and a planet with a very tight orbit of just days, but even that would likely be too small to have significant effects and a planet that orbited faster than it's star rotates would likely experience some tidal forces drawing it inwards.  The tidal drawing-in would likely be far greater.   It's hard to imagine a situation where the relativistic spiraling-in would have much effect between a planet and star.</p>

<p>Now a planet in a super-tight orbit around a white-dwarf star . . . maybe, but the planet would likely get torn apart inside the Roche limit long before you got it close enough for any measurably interesting relativistic spiraling-in.  </p>

<hr>

<p>A word on precession, precession affects the Earth's climate because the Earth has a land dominant hemisphere and a water dominant hemisphere.  Precession also works with the seasons leading to warmer or colder winters or summers.   If there's low axial tilt, then precession won't have much effect on a planet's climate.  Mercury has minimal axial tilt and no significant variation between it's two hemispheres, so it's unlikely that Mercury's precession changes it's climate much.  Certainly not like the effect it has on Earth, such as turning ice ages on or off.  </p>

<p>Precession is also mostly Newtonian.   Relativity just adds a percentage point or two to the rate of precession in the case of Mercury.  </p>

CC BY-SA 3.0
2018-03-21T13:25:49.713Z
2018-03-21T13:25:49.713Z
userLTK
<p>That may sounds like a silly question but here it is.</p>

<p>One of the early great successes of general relativity was to explain the discrepancy between the prehilion advance of Mercury predicted by Newtonian mechanics and the results of its actual measurement.</p>

<p>I was wondering if this kind of effect could have any influence on the climate of a planet experiencing it.</p>

<climate><paleoclimatology><astronomy><milankovitch-cycles><orbit>
Does general relativity influence climate (vs Newtonian mechanics)
user85659
# Does general relativity influence climate (vs Newtonian mechanics)

(Asked by: username_0 on 2018-03-20)

That may sounds like a silly question but here it is.

One of the early great successes of general relativity was to explain the discrepancy between the prehilion advance of Mercury predicted by Newtonian mechanics and the results of its actual measurement.

I was wondering if this kind of effect could have any influence on the climate of a planet experiencing it.

**Tags:** climate, paleoclimatology, astronomy, milankovitch-cycles, orbit


---

## 3 answers

### Answer by username_1 on 2018-03-20. Score: 10

In short: No. Unless multi-million timescales are considered.

The reason we keep teaching Newtonian mechanics, is because it is a VERY accurate approximation of a more general theory (general relativity) within the regimes of speed and gravity acceleration found in everyday life. Therefore, all the relativistic corrections to Newtonian mechanics in the Earth system are negligible. Both, for the internal operations of the climate and for the evolution of its orbital parameters on timescales of hundreds of millennia or shorter.

One effect, would be the minor role that apsidal precession have on the change of distribution of incoming solar energy described by the [Milankovic cycles](https://en.wikipedia.org/wiki/Milankovitch_cycles#Orbital_shape_(eccentricity)). But that can arguably considered negligible.

But perhaps the most important contribution would be the influence of relativistic corrections in Earth's orbit eccentricity variations on multi-million years timescales.

State-of-the-art orbital solutions for the long-term motion of the Earth like [La2010](https://www.aanda.org/articles/aa/pdf/2011/08/aa16836-11.pdf), do use relativistic correction, however they are rather small. The way the corrections are included in the model are described by [Saha & Tremaine (1994)](http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1994AJ....108.1962S&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf), where they point that:

> General relativistic effects in planetary motion have fractional
> amplitude of order $\frac{k^2}{c^2 r} \sim 10^{-8}$ at $r = 1 \, \textbf{AU}$.

Meaning that the correction correspond to a 0.000001% of the total variation of the orbital parameters. Unquestionably, even such small corrections have a cumulative effect over multi-million years timescales. [Varadi et. at. (2003)](http://iopscience.iop.org/article/10.1086/375560/pdf), compares the output of a model using relativistic corrections (solid line) with one not using them (dashed line), and the following figure show the results over 3 million years, where can be observed that significant differences arise after 300,000 years.

[![enter image description here](https://i.sstatic.net/6GSFD.png)](https://i.sstatic.net/6GSFD.png)

However, it is reasonable to consider that such small corrections would have been overcome at some point in the past by some other unaccounted effects, like large meteorite impacts (or fly-by), solar storms, etc. Remember that La2010 go back 50 million years and [other models go back several billion years](https://www.aanda.org/articles/aa/full/2004/46/aa1335/aa1335.html), when such events were rather common. So, I would still argue that relativistic corrections are not very significant. However, in a chaotic system like Earth's climate, you can never rule out that a negligible forcing could have had an important effect.

Of course the answer would be different (and the relative importance higher) if we consider a planet orbiting extremely close to a super-massive star. But, I'm assuming you are mostly considering planets similar to Earth in that regard.

There are also some claims (the [Damhsa Theory](http://lasp.colorado.edu/sorce/news/2008ScienceMeeting/posters/P4_01_Lynch_Poster.pdf)) that gravitational waves might have play a role in the very long term climate evolution of Earth. However, I'm not capable to really assess the validity of such theory, but I have to admit I'm skeptical about it. I've posted [a question about that](https://physics.stackexchange.com/questions/394552/damhsa-theory-can-gravitational-waves-really-affect-the-long-term-climatic-evo) in Physics SE, an there seem to be wide consensus that such effect would be exceedingly small to ever deserve any kind of consideration.

> **Comments:**
> **username_2**: To me the "Damhsa theory" looks somewhere between "wrong" and "not even wrong" (i.e. so vague it's un-falsifiable) but as far as I can tell relativity does become relevant at multi-Myr timescales -- I assume this because the [La2010 orbital model](https://www.aanda.org/articles/aa/pdf/2011/08/aa16836-11.pdf) and its predecessor take the trouble to account for relativity. I guess that in a Newtonian solar system we'd get similar Milankovitch cycles but with different timings (I have no idea how different). Might be interesting to compare La2010 with earlier Newtonian models...  
> **username_1**: @username_2 I had a look into that paper, and the corrections are rather small, probably borderline in what could be considered negligible. I'll add few sentences about that.  
> **username_1**: @username_2 I just added some comments in that regard.  
> **username_1**: After reading Varadi et. al. paper I've changed my mind on the relevance of relativity, so I've changed the answer accordingly.  
> **username_3**: What is "My"? Million years?  
> **username_1**: @Hamsterrific Yes, in non academic environments I never know if to use Ma, My, Myr or Myrs, you can find all options and the former is the one used in academic publication, but many of my students don't really know what annus means  

---

### Answer by username_4 on 2018-03-21. Score: 3

The latest positions that I am aware of say yes, but not in any useful way.

From what I have read, the current prevailing opinion is that the weather of Earth is a chaotic system. Chaotic systems are known to be very sensitive to initial conditions. Eddys in the atmosphere that are mere milimeters in size may change whether it rains or shines on the other side of the planet in a few months.

From this concept, we can assume that GR affects the weather. However, we have to be cautious with what we draw from that conclusion. I believe it was von Neuman who is quoted as saying that when he first heard of the idea of weather as a chaotic system, sensitive to initial conditions, he had the idea that we might soon have weather control simply by doing small adjustments. Only later did he finally understand chaos theory: such perturbations were like giving a well shuffled desk another shuffle. It certainly changes your luck, but you couldn't possibly know if it was for better or for worse.

So to your question, as to whether GR would have *any* effect, the answer is yes. If you were to rephrase the question to ask whether it had any measurable effects that might be tested with empirical evidence, then I would have to defer to username_1's answer.

> **Comments:**
> **username_1**: I agree, but you could answer basically the same if I ask "Does my dog affects Earth's climate?"  
> **username_4**: @username_1 Yes, you can =)  Myself, I find the distinction rather interesting.  That I cannot predict whether it's going to rain or shine in Seattle in a month, and yet you can look at multi-million year timescales and provide useful answers is fascinating, and I think it's an important part of climate study.  This is especially true in an era where climate change is a highly contentious topic.  (Oh, and just kidding. I can predict: it'll be raining in Seattle.  Don't worry ;-)  )  
> **username_1**: Yes, that's a fascinating point. Weather forecasting is also quite easy here in Vancouver, BC: 99% chances of rain =)  
> **username_5**: @username_4: Look up the term "chaotic attractor".  Essentially, chaotic systems have limits.  You can't make long-term predictions of exactly where within those limits it will be, but you can confidently predict that it will be somewhere within them.  So you could accurately predict that 100 years from now there's a 90% chance it will rain in Seattle on any given Saturday, but you have no chance of predicting which Saturday will be the clear one.  
> **username_4**: @username_5 Oh, I do understand them, but that doesn't make them any less fascinating.  
> **username_0**: I am not sure you can say that GR has an effect on climate from the fact that the whole system is chaotic, because in that case this would be quite meaningless since anything has an effect. I meant that GR would have an effect in the sense that despite the chaotic behavior of climate, GR would have a in imprint on the average weather patterns.  
> **username_4**: @TTFarreo Does that mean we should read the phrase "any influence" in the question as "any predictable influence?"  
> **username_0**: @username_4 Yes, you're right.  

---

### Answer by username_6 on 2018-03-21. Score: 3

I don't see this point made, so I'll just add it. In very high gravitation situations orbital energy can be lost to "relativity" or more specifically, gravity waves. The primary relativistic effect that the Sun's gravity has on Mercury is an increase in it's precession, as @username_1 pointed out, and [see more details here](https://physics.stackexchange.com/questions/26408/what-did-general-relativity-clarify-about-mercury).

A secondary relativistic effect is orbital decay, or spiraling in. This is [observable in tight orbits around neutron stars](https://www.forbes.com/sites/chadorzel/2015/07/22/three-experiments-that-show-relativity-is-real/2/#72c35a8443a9) or black holes. The effect around a regular star would be tiny but non zero.

This [article gives some numbers for this effect on the Earth](https://www.forbes.com/sites/startswithabang/2016/12/27/gravitational-waves-from-discovery-of-the-year-to-science-of-the-century/#6ee4dfe5087f).

> Gravitational radiation is incredibly subtle and weak in its effects.
> The Earth, as it orbits the Sun, loses energy due to this radiation
> and spirals inwards. But it will take 10^150 years for this process to
> occur.

That's a preposterously long period of time. Mercury would certainly be effected significantly more than Earth, (I can't do the math, maybe someone here will step up), but even at mercury distance the energy loss to gravity waves and spiraling-in would be slow to the point of irrelevance compared to other effects.

Our sun, for example, grows larger and brighter over it's lifetime. Planets atmosphere's change, either stripped off or in the case of Earth, affected by photosynthesis and other processes, and the Sun loses mass over it's lifetime, which causes the planets, on average to move outwards, though inward migration is also thought to be possible and the planets can affect each other's orbits. These changes to climate are all likely to be significantly greater than relativistic spiraling-in.

For maximum "spiral-in" effect, you'd probably want a small star and a planet with a very tight orbit of just days, but even that would likely be too small to have significant effects and a planet that orbited faster than it's star rotates would likely experience some tidal forces drawing it inwards. The tidal drawing-in would likely be far greater. It's hard to imagine a situation where the relativistic spiraling-in would have much effect between a planet and star.

Now a planet in a super-tight orbit around a white-dwarf star . . . maybe, but the planet would likely get torn apart inside the Roche limit long before you got it close enough for any measurably interesting relativistic spiraling-in.

---

A word on precession, precession affects the Earth's climate because the Earth has a land dominant hemisphere and a water dominant hemisphere. Precession also works with the seasons leading to warmer or colder winters or summers. If there's low axial tilt, then precession won't have much effect on a planet's climate. Mercury has minimal axial tilt and no significant variation between it's two hemispheres, so it's unlikely that Mercury's precession changes it's climate much. Certainly not like the effect it has on Earth, such as turning ice ages on or off.

Precession is also mostly Newtonian. Relativity just adds a percentage point or two to the rate of precession in the case of Mercury.


---

