Gallery (126 different pictures):

Celestial Mechanics

[Galerie (126 images différentes) : Mécanique Céleste]

Jean-François COLONNA
[Contact me]

www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
france telecom, France Telecom R&D

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Celestial Mechanics [Mécanique Céleste]:

Non Chaotical Systems [Systèmes non Chaotiques]	Chaotical Systems [Systèmes Chaotiques]	The Solar System [Le Système Solaire]	Heliocentric Views of the Solar System [Vues Héliocentriques du Système Solaire]	Non Heliocentric Views of the Solar System [Vues non 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]
More Point of View Interpolation in the Solar System [Plus d'Interpolations de Point de Vue dans le Système Solaire]

Celestial Mechanics [Mécanique Céleste]:

[More information about the N-Body Problem]
[More information about the Solar System]
[More information about the Virtual Chaos]

Please, note that due to scale problems, it is almost impossible to visualize simultaneously actual distances and sizes in the Solar System. Then, it is the square root of the distances to the Sun that are displayed; when the Solar System is displayed without such a non linear scaling, the inner planets are "hidden" by the Sun. Moreover, the diameter of each celestial body is multiplied by a huge arbitrary factor.

Each celestial body is colored according to its actual color:

[More information about the Solar System -in french/en français-]

Non Chaotical Systems [Systèmes non Chaotiques]:

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

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 -'heliocentric' point of view, yellow body-.

N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on elliptic trajectories -'geocentric' point of view, green body-.

N-body problem integration (N=5) displaying four planets with symmetrical initial conditions on elliptic trajectories -'heliocentric' point of view, yellow body-.

N-body problem integration (N=5) displaying four planets with symmetrical initial conditions on elliptic trajectories -'geocentric' point of view, green body-.

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

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) -blue body point of view-.

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) -white body point of view-.

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) -orange body point of view-.

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.

The Solar System [Le Système Solaire]:

The actual relative sizes of the Solar System bodies.	The actual relative sizes of the Solar System bodies.	The whole Solar System displayed with arbitrary celestial body radius.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.	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 -the Sun point of view-.

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: {Mercury,Venus,the Earth,Mars}-.	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-.

Detail close-up of the trajectory of the gravity center of the 9 planets of the Solar System.

Hodographs of 5 of the 9 planets of the Solar System during three plutonian years.

Hodographs -with display of a few velocity vectors- of 5 of the 9 planets of the Solar System during three plutonian years.

The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year.

The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years.

The distances Sun-Earth-Jupiter-Saturn-Uranus-Neptune during one neptunian year.

The distances {Sun-Jupiter,Sun-Saturn,Sun-Uranus,Sun-Neptune} during one neptunian year.

Artistic view of the Solar System.

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

From geocentrism to 'Neptune-centrism' -a Tribute to Nicolas Copernic-.

Point of View:	Linear Scales:	Linear Scales:	Non Linear Scales (allowing a better view of the inner Solar System):
The Sun:	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-.
Mercury:	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-.
Venus:	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-.
The Earth:	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-.
Mars:	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-.
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-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Jupiter point of view-.
Saturn:	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-.
Uranus:	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-.
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-.	N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Neptune point of view-.
Pluto:	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-.

A simplified solar system including the Sun, Jupiter and a 'false' Pluto -Sun point of view-.

A simplified solar system including the Sun, Jupiter and a 'false' Pluto -Jupiter point of view-.

From Pluto to the Sun:

From Pluto to the Sun.

Simulation of 'from Pluto to the Sun' with pure uniform circular motions:

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

An extrapolation:

From Pluto to the Sun -extrapolation 2-.

The journey of an Earth-like planet (green) in the Solar System -point of view of the virtual planet-.

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

The Ptolemaic system -without equant- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-.

The Ptolemaic system with equant -grey circle above the Earth- and with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-.

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-.

Artistic view of the Solar System viewed from the Earth.

"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-.

"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-.

"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-.

"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-.

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

More information about Point of View Interpolation and Virtual (or Subjective) Chaos

From Mars to the Sun.

From Mars to the Sun -extrapolation-.

From Pluto to the Sun (non linear scales).

The journey of an Earth-like virtuel planet (green) from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-.

From Pluto to the Sun (linear scales).

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

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

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

The journey of an Earth-like virtuel planet (green) in the Solar System -point of view of the virtual planet-.

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

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

From Pluto to the Sun -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-.

From Pluto to the Sun:

From Pluto to the Sun.

An extrapolation:

From Pluto to the Sun -extrapolation 2-.

The journey of an Earth-like planet (green) in the Solar System -point of view of the virtual planet-.

[More information and visual access to more Celestial Mechanics pictures [Plus d'informations et accès visuel à plus d'images de Mécanique Céleste]]
[See the Celestial Mechanics Slide Show [Visionnez le Diaporama de Mécanique Céleste]]

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Gallery (126 different pictures): Celestial Mechanics [Galerie (126 images différentes) : Mécanique Céleste]

Jean-François COLONNA [Contact me]

www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France france telecom, France Telecom R&D

Celestial Mechanics [Mécanique Céleste]:

Celestial Mechanics [Mécanique Céleste]:

Non Chaotical Systems [Systèmes non Chaotiques]:

Chaotical Systems [Systèmes Chaotiques]:

The Solar System [Le Système Solaire]:

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

Non Heliocentric Views of the Solar System [Vues non 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]:

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

Copyright © Jean-François COLONNA, 2000-2024. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Copyright © Jean-François COLONNA, 2000-2024. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Gallery (126 different pictures):

Celestial Mechanics

[Galerie (126 images différentes) : Mécanique Céleste]

Jean-François COLONNA
[Contact me]

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
france telecom, France Telecom R&D

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.