In his famous undergraduate physics course, the Nobel Prize in physics Richard Feynman showed from the first year how it was possible, with elementary numerical calculation means already on simple computers from the very beginning of the 1960s, to describe and predict the movements of N material points modeling planets moving under the action of universal attraction. This is typically what is called a many-body problem which is known to be very difficult to solve analytically, whether with planets, stars in a galaxy, or electron gas in a solid. .

In fact, there is a whole theory largely constituted initially by the works of Lagrange, Laplace, Gauss but also of Hamilton, Siméon Denis Poisson and Sophus Lie (all mathematicians) of the XVIII^{e} in the 19th^{e} century, which makes it possible to calculate analytically and numerically up to a certain point the movements of at least three bodies, not punctual, in celestial mechanics. Modern forms of this theory, with corrections coming from Einstein’s theory of gravitation and which introduces so-called non-Newtonian terms into the equations, are used to understand in particular the formation and evolution of the Solar System but also exoplanetary systems.

We can get an idea of all these theories developed for more than two centuries now with well-known works such as those of Goldstein (a great classic of mechanics giving tools to understand quantum and relativistic mechanics as a bonus) and Fitzpatrick.

They had already enabled not only Leverrier to discover Neptune because of its influence on the movements of Uranus, but also Milutin Milankovitch, Serbian mathematician, geophysicist, astronomer and climatologist, to discover the origin of the glacial cycles as evidenced by the geological archives. of the quaternary of our Blue Planet.

What are Milankovitch cycles? This video explains it to us. © The Official Sorcerer’s Spirit

## From Milankovitch to exobiology

We know from Kepler that the orbits of the planets of the Solar System are more or less eccentric ellipses, sometimes very close to a circle or on the contrary very elongated as in the case of other celestial bodies on periodic orbits, certain comets. There are in fact several parameters which are used to characterize the movements of the Earth, not only the values of the semi-major axis and the eccentricity of the Earth’s orbit but also the inclination of its axis with respect to its orbital plane. around the Sun.

These parameters play on the sunshine of the Earth’s surface, the energy it receives from the Sun and therefore *ultimately* on the existence of the seasons and as we said of the glacial cycles (see video above). Milutin Milankovitch showed that these were initially due to periodic changes in the eccentricity of the Earth’s orbit and the obliquity of its axis of rotation.

He demonstrated that they are the consequence of the gravitational attraction of the other planets of the Solar System, in particular Jupiter and Saturn, because of their large mass, but also Venus or Mars because of their proximity. As eccentricity and obliquity govern insolation and the seasons on Earth, these modifications change the climate and influence the habitability of the Earth, that is to say its capacity to maintain liquid water over the long term. its surface.

We know that the question of habitability is in fact a complex question because it is also necessary to take into account the existence of an atmosphere capable of creating a greenhouse effect, which can also make a planet *a priori* too cold because ultimately too far from its sun, welcoming to life, by raising its average temperature or, on the contrary, transforming it into a Venusian hell.

Still, both for the long-term evolution of the habitability of the Earth or of certain exoplanets, it is potentially useful to study the influence of gravitational disturbances on the orbital and rotational parameters of the Earth. or other exoplanets to specify the past, present or future habitability of the latter.

## The future of the solar system?

A group of American and Australian astronomers have again addressed these questions by doing complex N-body calculations and taking into account general relativity in which they have varied the eccentricity of Jupiter’s orbit but not the value of its semi-major axis, giving an estimate of Jupiter’s distance from the Sun.

As they explain in an article published in *Astronomical Journal* and freely available on arXiv, these researchers discovered that this would in turn induce big changes in the shape of the Earth’s orbit.

” *If Jupiter’s position remained the same, but the shape of its orbit changed, it could actually increase the habitability of this planet.* “Summarizes in one sentence the astronomer Pam Vervoort, lead author of the study and stationed at the University of Riverside in California.

In the press release from this University, it states that “ *many are convinced that Earth is the epitome of a habitable planet and that any change in Jupiter’s orbit, being the massive planet that it is, could only be bad for Earth. We show that both hypotheses are false.* “.

The researchers’ new calculations show that the eccentricity of Earth’s orbit would change so that it would be a little warmer on average and that the polar regions would have correspondingly less ice cover, which would therefore increase, according to them, the habitability of our Blue Planet.

On the other hand, if in addition to a more eccentric orbit, Jupiter had a shorter semi-major axis, then it would be the obliquity of the Earth which would be changed, that is to say the inclination of its axis of rotation relative to that of its orbital plane and this would result in greater inclination and larger regions that would be covered in ice.

All of these conclusions would potentially also apply to another exoplanet system with an exo-earth. Let’s also remember that our Solar System is subject to a certain chaotic instability, so the researchers’ scenario could perhaps become the reality of tomorrow.

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