<p>Differential equations describing the dynamics of celestial bodies (rotation, nutation, precession and other effects) can be solved numerically, which makes it possible to study their general non-linear behavior.</p>
<p>My question is this: suppose we want to study the <em>change in time</em> of a planet's orbit with a specific time frame 100-1000 years and at the same study the <em>change in time</em> of its nutation with a period of 0.1-0.5 years. What is the general approach to computing and representing such different time-scale processes?</p>
<p><strong>Remark:</strong> In the article <a href="https://www.researchgate.net/publication/253254901_The_Influence_of_the_Planets_Sun_and_Moon_on_the_Evolution_of_the_Earth%27s_Axis" rel="nofollow noreferrer">The Influence of the Planets, Sun and Moon on the Evolution of the Earth's Axis</a> provides a picture <em>Figure 3. Action of the Sun on the Earth’s rotation</em>. Plot show precession rates and nutation amplitudes on a large time-frame. It can be seen that if these processes differ by orders at time-scale, plot become extremely unreadable. Should we then use a hierarchy of dynamic effects over time for greater clarity?</p>
<p><a href="https://i.sstatic.net/o6qa1.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/o6qa1.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2023-02-01T13:30:06.640Z
This is a very broad question. There are multiple books on this subject. There are undergraduate and graduate level classes devoted to this subject. There are multiple scientific journals that are at least in part devoted to this subject.
David Hammen
CC BY-SA 4.0
2023-02-01T13:46:20.247Z
What do you mean by "long term"? A thousand years? 30 thousand? A million? 30 million? A billion? Beyond this is well into chaotic behavior, so it gets dicey.
David Hammen
CC BY-SA 4.0
2023-02-01T13:49:32.010Z
Those are very different problems, demanding very different techniques.
David Hammen
CC BY-SA 4.0
2023-02-01T16:37:18.760Z
I suggest narrowing the scope of this question to a specific time frame and either to orbital (e.g. precession) or rotational changes (e.g. nutation).  As is, this question is too big in scope and is subject to closure.
Connor Garcia
CC BY-SA 4.0
2023-02-01T17:16:08.850Z
I have also voted to close until the question is edited to focus on a small enough scope that it can be answered here. dtn - for reference, "discussion" is NOT what this site is for, almost the opposite, in fact, which is why we need you to define your question specifically.
Rory Alsop
CC BY-SA 4.0
2023-02-02T06:05:15.407Z
@ConnorGarcia I've narrowed this question down to a specific time frame.
ayr
CC BY-SA 4.0
2023-02-02T06:05:34.683Z
@RoryAlsop I tried to focus on a fairly small issue.
ayr
CC BY-SA 4.0
2023-02-02T08:20:59.233Z
Wikipedia has a brief article on [Multi-time-step integration](https://en.wikipedia.org/wiki/Multi-time-step_integration). It doesn't say much, but it has several promising-looking references.
PM 2Ring
CC BY-SA 4.0
2023-02-03T21:36:37.803Z
@ConnorGarcia I disagree with you and DH, there can certainly be an answer that explains the differences in dynamical calculation techniques between short timescale and long timescale. Short would be direct numerical, long would be more like perturbation/evolution of the mean orbital elements. Instead of handwringing one should welcome this question; it can have a clear, concise and well-sourced, fact-based answer.
uhoh
CC BY-SA 4.0
2023-02-04T11:55:26.723Z
@uhoh thank you for your support!
ayr
<orbital-mechanics><celestial-mechanics><n-body-simulations><resource-request><modeling>
Different techniques for calculation of celestial bodies dynamics with different time-scales
ayr
# Different techniques for calculation of celestial bodies dynamics with different time-scales

(Asked by: username_0 on 2023-02-01)

Differential equations describing the dynamics of celestial bodies (rotation, nutation, precession and other effects) can be solved numerically, which makes it possible to study their general non-linear behavior.

My question is this: suppose we want to study the *change in time* of a planet's orbit with a specific time frame 100-1000 years and at the same study the *change in time* of its nutation with a period of 0.1-0.5 years. What is the general approach to computing and representing such different time-scale processes?

**Remark:** In the article [The Influence of the Planets, Sun and Moon on the Evolution of the Earth's Axis](https://www.researchgate.net/publication/253254901_The_Influence_of_the_Planets_Sun_and_Moon_on_the_Evolution_of_the_Earth%27s_Axis) provides a picture *Figure 3. Action of the Sun on the Earth’s rotation*. Plot show precession rates and nutation amplitudes on a large time-frame. It can be seen that if these processes differ by orders at time-scale, plot become extremely unreadable. Should we then use a hierarchy of dynamic effects over time for greater clarity?

[![enter image description here](https://i.sstatic.net/o6qa1.png)](https://i.sstatic.net/o6qa1.png)

**Tags:** orbital-mechanics, celestial-mechanics, n-body-simulations, resource-request, modeling

> **Comments:**
> **username_1**: This is a very broad question. There are multiple books on this subject. There are undergraduate and graduate level classes devoted to this subject. There are multiple scientific journals that are at least in part devoted to this subject.  
> **username_1**: What do you mean by "long term"? A thousand years? 30 thousand? A million? 30 million? A billion? Beyond this is well into chaotic behavior, so it gets dicey.  
> **username_1**: Those are very different problems, demanding very different techniques.  
> **username_2**: I suggest narrowing the scope of this question to a specific time frame and either to orbital (e.g. precession) or rotational changes (e.g. nutation).  As is, this question is too big in scope and is subject to closure.  
> **username_3**: I have also voted to close until the question is edited to focus on a small enough scope that it can be answered here. dtn - for reference, "discussion" is NOT what this site is for, almost the opposite, in fact, which is why we need you to define your question specifically.  
> **username_0**: @username_2 I've narrowed this question down to a specific time frame.  
> **username_0**: @username_3 I tried to focus on a fairly small issue.  
> **username_4**: Wikipedia has a brief article on [Multi-time-step integration](https://en.wikipedia.org/wiki/Multi-time-step_integration). It doesn't say much, but it has several promising-looking references.  
> **username_5**: @username_2 I disagree with you and DH, there can certainly be an answer that explains the differences in dynamical calculation techniques between short timescale and long timescale. Short would be direct numerical, long would be more like perturbation/evolution of the mean orbital elements. Instead of handwringing one should welcome this question; it can have a clear, concise and well-sourced, fact-based answer.  
> **username_0**: @username_5 thank you for your support!  

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## 0 answers

