#### ( ABOVE: orbits of Jupiter’s** 67 moons**. Jupiter has been referred to as a mini Solar system because of the **thousands** of small bodies under its gravity control. )

**Dynamic stability of the Solar system**

*The origin and formation of the Solar system is one of the oldest unsolved problems in science. It was first separated as a question distinct from the Origin of the Universe in the 17th century, when Copernicus made it meaningful to use the modern phrase “Solar system” and the Sun began to be thought of as one of many stars. — *

**Origin of the Solar system**

*In 1885, King Oscar II of Sweden and Norway offered a prize to anyone who could discover what is responsible for ***the stability of the Solar system.** He wanted to know why it didn’t just fly apart. French mathematician and physicist Henri Poincare won the prize, not by answering the King’s question, but by demonstrating that the stability cannot be mathematically established. He showed that we can say things about bodies rotating about one another and describe and predict their motion, but that the mathematics ultimately suggests **chaotic behavior,** or a sensitivity to initial conditions. This so-called **sensitivity to initial conditions** was publicized in the 1960s and ’70s by mathematician Edward Lorenz, who called it the butterfly effect. It is also known as *chaos theory.* — The Discovery of SuperWaves

**the stability of the Solar system.**He wanted to know why it didn’t just fly apart. French mathematician and physicist Henri Poincare won the prize, not by answering the King’s question, but by demonstrating that the stability cannot be mathematically established. He showed that we can say things about bodies rotating about one another and describe and predict their motion, but that the mathematics ultimately suggests

**chaotic behavior,**or a sensitivity to initial conditions. This so-called

**sensitivity to initial conditions**was publicized in the 1960s and ’70s by mathematician Edward Lorenz, who called it the butterfly effect. It is also known as

*chaos theory.*

* *

*Over the last two decades, there has come about a recognition that chaotic dynamics are pervasive in the solar system. We now understand that the orbits of small members of the solar system—asteroids, comets, and interplanetary dust—are chaotic and undergo large changes on geological time scales. Are the major planets’ orbits also chaotic? The answer is not straightforward, and the subtleties have prompted new questions. Most uncomfortably, the proof that such a scheme “works” for arbitrarily long times has remained elusive. Do the perturbations cause only small changes in the present nearly circular, nearly coplanar orbits of the planets, or might they add up so much over the great age of the solar system that the orbits change greatly, in the past, or future? — *

**Chaos and stability of the solar system**

**Due to the chaotic nature of the Solar System, the question of its long-term stability** can only be answered in a statistical sense. **Destabilization** of the inner planets, leading to close encounters and/or **collisions** can be initiated through a large increase in Mercury’s eccentricity. This poses a dilemma as the physical evolution of the real system – and its probabilistic behavior – cannot depend on the coordinate system or numerical algorithm chosen to describe it. — **Dynamic stability of the Solar System**

HAVE YOU EVER PONDERED DEEPLY ENOUGH WHY THE SOLAR SYSTEM HAS BEEN SO PERFECTLY STABLE OVER SUCH A LONG TIME?

HAVE WE EVER OBSERVED ANY DIRECT OR INDIRECT EFFECTS RESULTING FROM ANY POTENTIAL SOLAR SYSTEM’S INSTABILITIES, LIKE FOR EXAMPLE:

**PLANETS FALLING ONTO THE SUN;****MOONS FALLING ONTO THEIR PLANETS;****PLANETS ESCAPING THE SUN;****MOONS ESCAPING THEIR PLANETS.**

IS THIS PERFECT LONG-TERM STABILITY REALLY THE EXCLUSIVE RESULT OF A **FRAGILE** BALANCE BETWEEN GRAVITATIONAL ATTRACTIONS AND CENTRIPETAL FORCES AMONG THE SUN, THE 8 PLANETS, AND OVER **170** MOONS, NOT INCLUDING PLUTO, ITS **5** MOONS, AND THE **PLANET NINE** so massive that it tilts the entire Solar system by 6 degrees?

COULD THAT HYPOTHESIS OF **FRAGILE** BALANCE BETWEEN GRAVITATIONAL ATTRACTIONS AND CENTRIPETAL FORCES SOMEHOW BE SUBJECTED TO EMPIRICAL VERIFICATION, OR FALSIFICATION? **WHAT WOULD IT TAKE FOR ANY ONE OF THE ABOVE 4 SPECTACULAR INSTABILITIES TO OCCUR IN THE SOLAR SYSTEM?**

Considering that the age of the Solar system (derived from the study of meteorites which are thought to be the oldest accessible material around) is estimated to be close to 5 billion years, have the angular velocities of all the planets and moons been slowing down? Have they been slowing down at the same rate, or at different rates? In either case, **how long will it take before any one of the above 4 spectacular instabilities is going to finally occur? **

### Well, I will not hold by breath, and if none of the above 4 spectacular instabilities had ever happened even once, not to mention that **all of them could have happened more than once,** then it would follow that the present Solar system stability hypothesis of FRAGILE BALANCE BETWEEN GRAVITATIONAL ATTRACTIONS AND CENTRIPETAL FORCES is correct in small part only.

### No orbit in the Solar system is perfect, like a **spinning roulette,** and since **chaotic dynamics are pervasive** in the Solar system, whatever the reasons of its** billion-years** stability, they cannot be fragile, and in order to be able to compensate for the variety of these chaotic dynamics, they need to be appropriately robust.

* “ Scientific discovery consists of seeing what everybody has seen, and thinking what nobody else has thought. **Scientific d**iscovery must be, by definition, at variance with existing knowledge. During my lifetime, I made two. Both were rejected offhand by the Popes of that field of science.”*** **

**— Nobel Prize Laureate, 1937**

**STABILITY**

In the following video, the magnetic device composed of one big central magnet, and six smaller “flipped” (or “inverted”) magnets is clearly capable of magnetic **attraction and repulsion at the same time. **Just because the large magnet attracts, and small magnets repel, it does not follow that these two opposing effects cancel each other out and become nonexistent. From this stems the unexpected and particularly important “side-effect” : **STABILITY.**

Let’s imagine what could happen between the Sun and the Earth, when Sun is gravitationally attracting Earth, but Earth is both gravitationaly attracting and repelling the Sun at the same time. **Would it be possible that Earth could have a stable orbit around the Sun as a result of such “side-effect” ?**

### This could, in principle, explain the **stability of the entire Solar system,** including all the moons of all the planets.

Patrick Blackett (1897–1974) was a prominent British astronomer who noticed a correlation between the rotation rates, the gravitational fields, and the magnetic fields of the Sun, Earth, and Jupiter. In a paper in the British journal *Nature,* Blackett presented an empirical equation relating these quantities. He went on to suggest that there might be a previously unsuspected principle of nature by which magnetic fields are generated directly in massive electrically neutral rotating bodies like the Earth. A few years later, a science-fact article in John W. Campbell’s *Astounding Science** **Fiction* described Blackett’s work as the possible discovery of a new law of nature. The author of that article suggested that **if gravity and spin could produce magnetism, then spin and magnetism might produce gravity, and even antigravity.**

### Gravitomagnetism is produced by stars and planets when they spin. *“It’s similar in form to the magnetic field produced by a spinning ball of charge,”* explains physicist Clifford Will of Washington University (St. Louis). Replace charge with mass, and magnetism becomes gravitomagnetism.

Written out in full glory, the equations of General Relativity are intensely complicated. Indeed, they have been solved in only a few special cases. One of them is the case of weak gravity, like we experience here on Earth.

In the “weak field limit,” Einstein’s equations reduce to a form remarkably like Maxwell’s equations of electromagnetism. Terms appear that are analogous to the electric field caused by charges and the magnetic field produced by the flow of charge. The **“electric terms”** correspond simply to the gravity that keeps our feet on the ground. The **“magnetic terms”** are wholly unfamiliar; we don’t sense them in everyday life.

### The **“spin”** (angular momentum) **+ **the** “electric terms**” **+** the **“magnetic terms” = ** Quantum gravity

* Temptations of Theory, Strategies of Evidence: P. M. S. Blackett and the Earth’s Magnetism, 1947-52.* By Mary Jo Nye, The British Journal for the History of Science, Vol. 32, No. 1 (Mar., 1999), pp. 69-92. Published by

*Cambridge University Press*on behalf of The British Society for the History of Science. Stable URL:

**http://www.jstor.org/stable/4027970**

The great physicist, father of quantum mechanics, Niels Bohr proposed to model the atom after the Solar system. I propose to do it the other way around. It is not to say that the Solar system is exactly like an atom, but that it is structured according to **similar** principles.

**Electron vs Earth Orbits**

In the following drawings, some circular orbits of satellites around the earth are compared with the electron orbits within the hydrogen atom. In all cases equilibrium orbits are shown in which the centripetal acceleration is equal to the gravity or electrical force pulling the satellite or electron toward the center. Both illustrations are drawn to the scales of the earth and the Bohr radius. Despite the great difference in size, approximately 20 orders of magnitude, these orbits are identical in their mathematical descriptions.