<h3 id="there-will-be-major-limitations-much-worse-than-quantum-effects-c78r">There will be major limitations much worse than quantum effects.</h3>
<p>There is always uncertainty in input variables; we only know the standard gravitational masses, positions and velocities to some amount of accuracy.</p>
<p>The chaotic nature of n-body dynamics as discussed in Wikipedia's <a href="https://en.wikipedia.org/wiki/N-body_problem#Planetary_problem" rel="nofollow noreferrer">N-body problem#; Planetary problem</a> may cause the seemingly small uncertainty in results to diverge exponentially over the long run.</p>
<p>Chaotic motion is also discussed in <a href="https://astronomy.stackexchange.com/a/33437/7982">@astrosnapper's answer</a> and references therein.</p>
<ol>
<li>We can get some insight into that by considering that if two planets reach a state of resonance (e.g. 3:2) their gravitational perturbations on each other can suddenly become much larger, and often one of them is promoted/demoted to a substantially different orbit. Where it ends up can depend on very small changes in input conditions.</li>
<li>Since gravity varies with <span class="math-container">$1/r^2$</span>, close approaches can have huge effects, again a small different in the approach distance can result in a huge difference a million years later.</li>
</ol>
<p>Therefore when talking about millions of years, people don't often use raw numerical techniques propagation exact motion, but instead use perturbations of orbital elements; for example Jupiter may increase the eccentricity of a planet's orbit and change its semimajor axis and line of nodes over time, and it's only these kinds of parameter evolutions that are simulated.</p>
<p>A good <em>and fun</em> example of that is discussed in <a href="https://arstechnica.com/science/2019/04/starman-is-out-there-but-we-probably-wont-see-him-again-until-2047/" rel="nofollow noreferrer">Starman is out there, but we probably won’t see him again until 2047</a> which links to <a href="https://www.mdpi.com/2226-4310/5/2/57" rel="nofollow noreferrer">The Random Walk of Cars and Their Collision Probabilities with Planets</a> (open access, also in <a href="https://arxiv.org/abs/1802.04718" rel="nofollow noreferrer">arXiv</a>):</p>
<blockquote>
<p>On February 6th, 2018 SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster's orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.</p>
</blockquote>

CC BY-SA 4.0
2021-07-14T01:03:04.007Z
2021-07-14T08:20:21.480Z
2021-07-14T08:20:21.480Z
uhoh
<p>I was wondering whether planetary orbits can be predicted with our classical theories, or whether quantum randomness comes into play making the unpredictable in the long run?</p>

CC BY-SA 4.0
2021-07-13T19:48:33.573Z
Someone more qualified will give a real answer, but generally, no. Quantum effects will not play a role in orbital prediction. You could maybe argue that the evaporation of black holes via Hawking radiation could effect orbital predictions on very long timescales.
franz_lyre
CC BY-SA 4.0
2021-07-13T20:42:30.757Z
It depends how long you mean by “long run.” However, f_n_lyre is right in that there are no quantum effects—the scale is too large.
Pierre Paquette
CC BY-SA 4.0
2021-07-13T21:46:32.317Z
Partial answer in my answer https://astronomy.stackexchange.com/a/33437/23748 to the [Propagate Earth trajectory for 1 Myr](https://astronomy.stackexchange.com/questions/33433/propagate-earth-trajectory-for-1-myr/33437#33437) question
astrosnapper
<orbit><solar-system>
Are we able to accurately predict planetary orbits over a longer period of time?
Raheemsterling
# Are we able to accurately predict planetary orbits over a longer period of time?

(Asked by: username_0 on 2021-07-13)

I was wondering whether planetary orbits can be predicted with our classical theories, or whether quantum randomness comes into play making the unpredictable in the long run?

**Tags:** orbit, solar-system

> **Comments:**
> **username_1**: Someone more qualified will give a real answer, but generally, no. Quantum effects will not play a role in orbital prediction. You could maybe argue that the evaporation of black holes via Hawking radiation could effect orbital predictions on very long timescales.  
> **username_2**: It depends how long you mean by “long run.” However, f_n_lyre is right in that there are no quantum effects—the scale is too large.  
> **username_3**: Partial answer in my answer https://astronomy.stackexchange.com/a/33437/23748 to the [Propagate Earth trajectory for 1 Myr](https://astronomy.stackexchange.com/questions/33433/propagate-earth-trajectory-for-1-myr/33437#33437) question  

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## 1 answers

### Answer by username_4 on 2021-07-14. Score: 4

### There will be major limitations much worse than quantum effects.

There is always uncertainty in input variables; we only know the standard gravitational masses, positions and velocities to some amount of accuracy.

The chaotic nature of n-body dynamics as discussed in Wikipedia's [N-body problem#; Planetary problem](https://en.wikipedia.org/wiki/N-body_problem#Planetary_problem) may cause the seemingly small uncertainty in results to diverge exponentially over the long run.

Chaotic motion is also discussed in [@username_3's answer](https://astronomy.stackexchange.com/a/33437/7982) and references therein.

1. We can get some insight into that by considering that if two planets reach a state of resonance (e.g. 3:2) their gravitational perturbations on each other can suddenly become much larger, and often one of them is promoted/demoted to a substantially different orbit. Where it ends up can depend on very small changes in input conditions.
2. Since gravity varies with $1/r^2$, close approaches can have huge effects, again a small different in the approach distance can result in a huge difference a million years later.

Therefore when talking about millions of years, people don't often use raw numerical techniques propagation exact motion, but instead use perturbations of orbital elements; for example Jupiter may increase the eccentricity of a planet's orbit and change its semimajor axis and line of nodes over time, and it's only these kinds of parameter evolutions that are simulated.

A good *and fun* example of that is discussed in [Starman is out there, but we probably won’t see him again until 2047](https://arstechnica.com/science/2019/04/starman-is-out-there-but-we-probably-wont-see-him-again-until-2047/) which links to [The Random Walk of Cars and Their Collision Probabilities with Planets](https://www.mdpi.com/2226-4310/5/2/57) (open access, also in [arXiv](https://arxiv.org/abs/1802.04718)):

> On February 6th, 2018 SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster's orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.


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