Of the Center of the Solar System

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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Many centuries ago, the Earth was the center of everything. But unfortunately, the perfect God's order was disturbed with the retrogradations of Mars as can be seen on this simulation of the Solar System, the Earth -the dark blue body- being as the origin of the coordinates.

Please, note that due to scale problems, it is impossible to visualize actual distances and sizes in the Solar System. Then, after computations using actual astronomical measures, it is the square root of distances to the Sun that are displayed; moreover, the diameter of each celestial body is multiplied by a huge arbitrary factor.

As can be seen at the end of this simulation, each celestial body (with the exception of the Sun -the big yellow body-) seems to follow a complex trajectory that can be understood approximatively as the superposition of circular motions.

Since the work of Nicolas Copernic (De revolutionibus orbium caelestium libri VI, 1543) it is known that in fact the Sun is the center of the Solar System.

In the year 1609, Johannes Kepler (Astronomia Nova) described the planet trajectories as ellipses whose focus is the Sun.

Finally, in the year 1687, Sir Isaac Newton published his famous Philosophiae Naturalis Principia Mathematica, where the laws of the classical mechanics can be found.

Then, each body of the Solar System is subject to the following acceleration:

                    
                      2 ---->    i=N
                     d   OC     -----       M
                           k    \            i     ----->
                    --------- = /     G ----------- C C
                         2      -----            3   k i
                       dt        i=1     |----->|
                                (i#k)    | C C  |
                                            k i

This allows us to display the motion of the 9 planets.

Now, let's try to visualize the epistemological revolution that led us from geocentrism to heliocentrism. To do that, let's start with a 3-body system:
- the Sun (yellow),
- Mars (red),
- and a virtual planet dubbed "the Earth" (blue).
The Earth is moved from the Sun -top right- to Mars -bottom left-. Each of the displayed trajectories has a duration equals to one martian year and the Sun is the origin of the coordinates.

Now, let's display the same computation using the Earth as the origin of the coordinates.

Very interesting experiments can be conducted from there. For example, it is possible to study what happens if the plane of the Earth is chosen to be perpendicular to the one of Mars.

Now, we will use the following 11-body system:
- the Sun (yellow),
- the 9 planets,
- and a virtual planet dubbed "the Wanderer" (dark blue).
The Wanderer is moved from Pluto -bottom left- to the Sun -top right-. Each of the displayed trajectories has a duration equals to one plutonian year and belongs to the plane of Pluto. The Sun is used as the origin of the coordinates.

Now, let's display the same computation using the Wanderer as the origin of the coordinates.

All trajectories look non periodical and even chaotic (at the exception of the ones of Pluto and of the Sun). Do not forget that the trajectories of the Wanderer and of the Earth do not belong to the same plane (the plane of Pluto for the former and the ecliptic plane for the latter).

Here again, very interesting experiments can be conducted from there. For example, it is possible to study what happens if the plane of the Wanderer is 2.pi rotated and to display an artistic view of this motion.

In such a non regular context, it is then highly probable that Science (and Astronomy in particular) would have followed a very different way than the one we know (and the same would apply certainly to the religions). But this chaos is only apparent; it suffices to change the point of view (using the Sun) to obtain the magnificent order we all know.

Copyright © Jean-François COLONNA, 1996-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 1996-2024.

Of the Center of the Solar System

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

Copyright © Jean-François COLONNA, 1996-2024. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 1996-2024.

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, 1996-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 1996-2024.