Gallery :

Celestial Mechanics

[Galerie : Mécanique Céleste]

• Non Chaotical Systems [Systèmes non Chaotiques] :
• Chaotical Systems [Systèmes Chaotiques] :
• Heliocentric Views of the Solar System [Vues Héliocentriques du Système Solaire] :
• Geocentric Views of the Solar System [Vues Géocentriques du Système Solaire] :
• "Jupiter-centric" -on the plane of Pluto- Views of the Solar System [le Système Solaire vu depuis le plan de Pluton à une distance égale à celle de Jupiter] :
• "Neptune-centric" -on the plane of Pluto- Views of the Solar System [le Système Solaire vu depuis le plan de Pluton à une distance égale à celle de Neptune] :
• "Pluto-centric" Views of the Solar System [le Système Solaire vu depuis Pluton] :
• "Nine Planets Gravity Center" Views of the Solar System [le Système Solaire vu depuis le Centre de Gravité des neuf planètes] :
• Point of View Interpolation in the Solar System [Interpolations de Point de Vue dans le Système Solaire] :

Celestial Mechanics [Mécanique Céleste] :

The non linear transformation of the coordinates in the Solar System

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year as it is -without non linear scaling-

the Sun (bright yellow),
Mercury (orange),
Venus (orange),
the Earth (dark blue),
Mars (red),
Jupiter (orange),
Saturn (yellow),
Uranus (cyan),
Neptune (light blue),
Pluto (grey).

Non Chaotical Systems [Systèmes non Chaotiques] :

N-body problem integration (N=2) displaying a perfect Keplerian orbit.

display of the inclination of two elliptic trajectories.




Chaotical Systems [Systèmes Chaotiques] :

N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on circular trajectories.

N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on elliptic trajectories.

N-body problem integration (N=3) with one yellow star and two planets (the red one being very heavy and the blue one being light).

N-body problem integration (N=4) with one yellow star and two planets (the red one being very heavy and the blue one and its white satellite being light).

N-body problem integration (N=4 : one star, one heavy planet and one light planet with a satellite) -sensitivity to initial conditions-.

N-body problem integration (N=4 : one star, one heavy planet and one light planet with a satellite) computed on three different computers (the Red one, the Green one and the Blue one : sensitivity to rounding-off errors).

N-body problem integration (N=4 : one star, one heavy planet and one light planet with a satellite) computed with 2 different optimization options on the same computer (sensitivity to rounding-off errors).

N-body problem integration (N=9) with a simultaneous 2.pi rotation of the observer.

16 earth-like planets initially on the same keplerian trajectory.




Heliocentric Views of the Solar System [Vues Héliocentriques du Système Solaire] :

N-body problem integration (N=10) displaying the actual Solar System with its simultaneous 2.pi rotation.	N-body problem integration (N=10) displaying the actual Solar System.	N-body problem integration (N=10) displaying the actual Solar System during one marsian year -Sun point of view and zoom on the four first planets-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the Sun point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the Sun point of view-.
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the green eleventh body being the gravity center of the 9 planets-.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the green eleventh body being the gravity center of the 9 planets-.

Close-up detail of the trajectory of the gravity center of the 9 planets of the Solar System.

Hodograph of the velocity vectors of the 9 planets of the Solar System during one plutonian year.

Artistic view of the Solar System.




Geocentric Views of the Solar System [Vues Géocentriques du Système Solaire] :

N-body problem integration (N=10) displaying the actual Solar System with its simultaneous 2.pi rotation, our Earth being at the origin of the coordinates.	N-body problem integration (N=10) displaying the actual Solar System, our Earth being at the origin of the coordinates.	N-body problem integration (N=10) displaying the actual Solar System during one marsian year -Earth point of view and zoom on the four first planets-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the Earth point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the Earth point of view-.
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Earth point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Earth point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Earth point of view-.




"Jupiter-centric" -on the plane of Pluto- Views of the Solar System [le Système Solaire vu depuis le plan de Pluton à une distance égale à celle de Jupiter] :

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Jupiter point of view-.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Jupiter point of view-.




"Neptune-centric" -on the plane of Pluto- Views of the Solar System [le Système Solaire vu depuis le plan de Pluton à une distance égale à celle de Neptune] :

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Neptune point of view-.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Neptune point of view-.




"Pluto-centric" Views of the Solar System [le Système Solaire vu depuis Pluton] :

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Pluto point of view-.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Pluto point of view-.




"Nine Planets Gravity Center" Views of the Solar System [le Système Solaire vu depuis le Centre de Gravité des neuf planètes] :

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -gravity center of the 9 planets point of view-.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -gravity center of the 9 planets point of view-.




Point of View Interpolation in the Solar System [Interpolations de Point de Vue dans le Système Solaire] :

[more information about Point of View Interpolation and Virtual (or Subjective) Chaos]



From the Sun to Mars.

From the Sun to Mars -extrapolation-.

From the Sun to Pluto (non linear scales).

From the Sun to Pluto (linear scales).

Simulation of 'from the Sun to Pluto' with pure uniform circular motions (linear scales).

From the Sun to Pluto -extrapolation 1- (non linear scales).

Artistic view of the Solar System in motion viewed from a virtual planet.

Artistic view of the Solar System viewed from a virtual planet.

From the Sun to Pluto -extrapolation 2- (non linear scales).

The Solar System with a dark blue virtual planet -virtual planet point of view-.

The Solar System with a dark blue virtual planet -virtual planet point of view-.

The Solar System with a dark blue virtual planet -virtual planet point of view-.

The Solar System with a dark blue virtual planet -virtual planet point of view-.

Artistic view of the Solar System viewed from a virtual planet -a Tribute to Isaac Newton-.

Simulation of 'from the Sun to Pluto -extrapolation 2-' with pure uniform circular motions (non linear scales).

From the Sun to Pluto -extrapolation 3- (linear scales).	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.
A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.	A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view-.

Artistic view of the Solar System viewed from the Earth.

Artistic view of the Solar System viewed from the Earth.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.	the Sun,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Mercury point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Mercury point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Mercury point of view-.	Mercury,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Venus point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Venus point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Venus point of view-.	Venus,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Earth point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Earth point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Earth point of view-.	the Earth,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Mars point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Mars point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Mars point of view-.	Mars,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Jupiter point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Jupiter point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Jupiter point of view-.	Jupiter,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Saturn point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Saturn point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Saturn point of view-.	Saturn,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Uranus point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Uranus point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Uranus point of view-.	Uranus,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Neptune point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Neptune point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Neptune point of view-.	Neptune,
N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Pluto point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Pluto point of view-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Pluto point of view-.	Pluto.

From the Sun to Pluto.	From the Sun to Pluto.	From the Sun to Pluto,
From the Sun to Pluto -extrapolation 2-.	From the Sun to Pluto -extrapolation 2-.	An extrapolation.

Copyright (c) Jean-François Colonna, 2000-2013.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2013.