One of the oldest quandaries in mathematics and physics is called the three-body problem—the question of how three bodies, mutually attracted by gravity, will move in the future if their current positions and velocities are known
Isaac Newton first posed this problem, along with the simpler “two-body problem.” Later, in the case of three bodies, the question was found to be practically “unsolvable”—it is essentially impossible to find a formula to exactly predict their orbits.
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton’s laws of motion and Newton’s law of universal gravitation
As practically attacked, it consists of the problem of determining the perturbations (disturbances) in the motion of one of the bodies around the principal, or central, body that are produced by the attraction of the third. Examples are the motion of the Moonaround Earth, as disturbed by the actionof the Sun, and of one planet around the Sun, as disturbed by the action of another planet. The problem can be solved for some special cases—for example, those in which the mass of one body, as a spacecraft, can be considered infinitely small; the Lagrangian case, in which the three bodies form an equilateral triangle; and the Eulerian case, in which two bodies are motionless
The three-body problem is a gravitational problem that involves three or more bodies. It’s considered unsolvable because it’s chaotic for most initial conditions.
The three-body problem can be visualized as a combination of the potentials due to the gravity of the two primary bodies along with the centrifugal effect from their rotation. Examples of three-body problems include:
- The motion of the Moon around Earth, as disturbed by the action of the Sun
- The motion of one planet around the Sun, as disturbed by the action of another planet
The three-body problem is extremely unlikely to happen. However, it might be more likely to happen with multiple stars.
In 500 million years, the solar system will complete a full orbit through the Milky Way. There’s no way to predict what will have happened on Earth’s surface by then.
Is our solar system a three-body problem?
The inclusion of solar perturbations of the motion of the Moon results in a “three-body problem” (Earth-Moon-Sun), which is the simplest complication of the completely solvable two-body problem discussed above
How will our solar system likely be destroyed?
The rocky planets’ orbits may go unstable, leading to a potential giant collision between planets. The Sun will become a red giant and swallow the rocky planets. A passing star will trigger a dynamical instability among the remaining planets. A passing star will strip away the final planet
What is an example of three-body problem physics?
Examples are the motion of the Moon around Earth, as disturbed by the action of the Sun, and of one planet around the Sun, as disturbed by the action of another planet
What is the solution to the three-body problem in physics?
There is no general closed-form solution to the three-body problem, meaning there is no general solution that can be expressed in terms of a finite number of standard mathematical operations. Moreover, the motion of three bodies is generally non-repeating, except in special cases
In 2009, a pair of astronomers at the Paris Observatory announced a startling discovery. After building a detailed computational model of our solar system, they ran thousands of numerical simulations, projecting the motions of the planets billions of years into the future. In most of those simulations — which varied Mercury’s starting point over a range of just under 1 meter — everything proceeded as expected. The planets continued to revolve around the sun, tracing out ellipse-shaped orbits that looked more or less the way they have throughout human history
But around 1% of the time, things went sideways — quite literally. The shape of Mercury’s orbit changed significantly. Its elliptical trajectory gradually flattened, until the planet either plummeted into the sun or collided with Venus. Sometimes, as it cut its new path through space, its behavior destabilized other planets as well: Mars, for instance, might be ejected from the solar system, or it might crash into Earth. Venus and Earth could, in a slow, cosmic dance, exchange orbits several times before eventually colliding.
Why is the solar system unstable?
We have understood, within the last two decades, that the orbits of many of the small members of the solar system (asteroids, comets, dust particles), subjected to the combined gravitational perturbations of the major planets, are chaotic and unstable on million-year time scale
What is the most unstable planet in the solar system?
The planet which, with Mercury, has the most unstable orbit is the planet Mars, whose eccentricity can, by this same method reached approximately 0.25 in less than 5 billion of years, while the Earth’s eccentricity barely reached 0.1.26
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