Je me demande si les excentricités des orbites planétaires pourraient rester constantes dans le futur sans subir aucune variation.
Planetary orbits

Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies that are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet.

Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune.

As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.)

In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The paths of all the star's satellites are elliptical orbits about that barycenter. Each satellite in that system will have its own elliptical orbit with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and the sum of those two energies is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases.
Orbite étranges

Les mathématiciens ont découvert qu'il est en principe possible d'avoir plusieurs corps en orbites non elliptiques qui se répètent périodiquement, bien que la plupart de ces orbites ne soient pas stables face à de petites perturbations de la masse, de la position ou de la vitesse. Cependant, certains cas stables particuliers ont été identifiés, notamment une orbite en forme de huit sur un plan occupée par trois corps en mouvement. Des études ultérieures ont révélé que des orbites non planes sont également possibles, notamment une impliquant 12 masses se déplaçant dans 4 orbites approximativement circulaires et imbriquées, topologiquement équivalentes aux arêtes d'un cubo-octaèdre.

On considère qu'il est extrêmement improbable de trouver de telles orbites se produisant naturellement dans l'univers, en raison de l'improbabilité que les conditions requises surviennent par hasard.
### Query ###
Je me demande si les excentricités des orbites planétaires pourraient rester constantes dans le futur sans subir aucune variation.

### Main Text ###
Planetary orbits

Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies that are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet.

Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune.

As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.)

In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The paths of all the star's satellites are elliptical orbits about that barycenter. Each satellite in that system will have its own elliptical orbit with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and the sum of those two energies is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases.

### Supplementary Text ###
Orbite étranges

Les mathématiciens ont découvert qu'il est en principe possible d'avoir plusieurs corps en orbites non elliptiques qui se répètent périodiquement, bien que la plupart de ces orbites ne soient pas stables face à de petites perturbations de la masse, de la position ou de la vitesse. Cependant, certains cas stables particuliers ont été identifiés, notamment une orbite en forme de huit sur un plan occupée par trois corps en mouvement. Des études ultérieures ont révélé que des orbites non planes sont également possibles, notamment une impliquant 12 masses se déplaçant dans 4 orbites approximativement circulaires et imbriquées, topologiquement équivalentes aux arêtes d'un cubo-octaèdre.

On considère qu'il est extrêmement improbable de trouver de telles orbites se produisant naturellement dans l'univers, en raison de l'improbabilité que les conditions requises surviennent par hasard.

### Draft ###

### 1. Query Decomposition

"excentricités des orbites planétaires" → planetary orbital eccentricities
"rester constantes" → remain constant  
"sans subir aucune variation" → without experiencing any variation
"dans le futur" → in the future

User asking: Can planetary eccentricities stay fixed over time?

Translation clear. No semantic ambiguity. ●

### 2. Domain Context

Celestial mechanics. Solar System dynamics. Long-term orbital stability.

Timeframe: Future epochs (millions+ years).
Knowledge required: Perturbation theory, gravitational physics, orbital mechanics.

### 3. Physical Constraints Analysis

**Fundamental constraint:** Solar System ≠ isolated system.

External perturbations:
- Galactic tidal forces
- Planetary interactions  
- Yarkovsky effect
- Solar wind effects

**Key insight:** Eccentricity variations are observed phenomena, not future predictions.

Current eccentricities (approximate):
- Mercury: 0.21  
- Venus: 0.01
- Earth: 0.02
- Mars: 0.09
- Jupiter: 0.05
- Saturn: 0.06
- Uranus: 0.05
- Neptune: 0.01

### 4. Stability Analysis

**Milanković cycles:** ~100k to ~400k year eccentricity variations. ●

**Aitken cratering record:** Evidence of past perturbations. ●

**Long-term stability:** Chaotic behavior over Gyr timescales. ◐

∴ Eccentricities will NOT remain constant. Physical impossibility.

### 5. Mathematical Framework

Orbital elements (including eccentricity) follow Keplerian laws but...

Perturbation equations:
```
d²r/dt² = -(GM/r²) + Σ(mᵢ/rᵢ² × (r - rᵢ)/|r - rᵢ|³)
```

Solutions: Chaotic over long timescales. ●

**Hamiltonian chaos:** Even small perturbations → large eccentricity changes.

### 6. Counter-Evidence to "Constancy Assumption"

**Historical record:** 
- Venus eccentricity: Currently ~0.01, but variations documented
- Mercury: Always highly eccentric (current 0.21)
- Earth: Some stability but periodic variations

**Observational evidence:** 
- Asteroid belt eccentricity variations
- Kuiper belt object perturbations
- Past mass extinctions correlated with orbital changes

### 7. Physical Realism Check

**Yarkovsky effect:** Thermal momentum transfer → orbital decay
**Tidal forces:** Moon-Earth, Jupiter-Io interactions
**Planetary collisions:** Rare but significant perturbations

All → eccentricity changes inevitable. ●

### 8. Synthesis

User's assumption: ✗ False premise

Reality: Eccentricities are inherently variable
Evidence: Historical records, current observations, physical theory
Mechanism: Gravitational perturbations, external forces, chaotic dynamics

**Answer trajectory:** Explain why constancy impossible → provide physical evidence → conclude with current understanding of orbital evolution.

∴ Planetary eccentricities cannot remain constant due to fundamental physics and observational constraints.

### Answer###
La question de la stabilité des excentricités orbitales planétaires est complexe et touche aux lois fondamentales de la mécanique céleste. 

Actuellement, les planètes du système solaire présentent des excentricités orbitales variables : Mercure a l'orbite la plus excentrique, suivie par Mars, tandis que Vénus et Neptune ont les plus petites excentricités orbitales. Ces différences reflètent l'influence mutuelle des perturbations gravitationnelles entre les corps célestes.

Il est important de noter que les excentricités orbitales des planètes varient effectivement au fil du temps. Ce phénomène est inhérent au comportement dynamique des systèmes planétaires soumis aux interactions gravitationnelles continues.

Concernant la possibilité de maintenir ces excentricités constantes, cela nécessiterait un équilibre parfait entre toutes les forces gravitationnelles et l'absence totale de perturbations externes. Cependant, les orbites planétaires sont sujettes à des perturbations mutuelles constantes qui en modifient périodiquement les éléments, y compris l'excentricité.

La question de la stabilité orbitale à long terme est un domaine d'étude complexe qui dépend de nombreux facteurs comme la masse des corps, leurs positions relatives et leurs vitesses. Même si certains arrangements orbitaux peuvent théoriquement rester stables sur des périodes prolongées, l'histoire du système solaire montre que les configurations évoluent constamment sous l'influence des perturbations gravitationnelles.

L'avenir des excentricités planétaires reste donc soumis à ces variations naturelles plutôt qu'à une constance stable.