Remember that annoying physics question back in high school that nobody could solve and find the answer to? Well, in real life that question is the three-body problem. And yes, it’s a real pain in the butt. It started with the great Sir Isaac Newton in the 1600s and has been passed down from generations until today.
In essence, the three-body problem is mathematical in nature. It involves three bodies interacting with each other through a mutual force (such as gravity). This interaction causes the bodies to move in certain ways that are interconnected with each other. But when we apply the principles of physics to evaluate the motion(s), we can’t come to a solution. Making the problem unsolvable.
Important disclaimer: The problem isn’t fully unsolvable. It just doesn’t have a natural solution in the form of a formula like most problems in physics. Computer simulations can find approximate solutions to specific three-body problems, but there is no “one size fits all” formula that works for all three-body problems.
Three body problem in real life
The best way to explain the three-body problem in real life without referring to physics is through relationships. Let’s say you are married or in a long and fulfilling relationship with your partner. You love each other, care for each other, and do things together. A perfect example of a happy couple.
This is an example of a two-body problem in physics. It’s natural, easy to understand, and well, stable.
Now bring in a third person in your relationship. Your partner begins cheating on you with someone else. Let’s say you find out this in the worst possible way like catching them with their pants down – literally.
Now, the relationship just got a lot more difficult.
People process emotions differently. You may cuss at him, cry your heart out, or throw a bottle in their direction. The simple, harmonious relationship has now devolved into a chaotic and messy one.
This is the three-body problem.
The Earth, the Moon, and the Sun – A classical three-body problem
It’s interesting that the Moon and the Sun, the two biggest celestial bodies dominating our sky are in a turbulent relationship with Earth. This was first discovered in the 1600s by Isaac Newton when he applied his laws of motion and universal law of gravitation to the Earth, Moon and the Sun.
As in real life, let’s first try to understand what a two-body problem looks like in physics.
A good example of a two-body problem is the Earth-Moon system. The two celestial bodies interact with each other through a mutual gravitational force. The Earth attracts the Moon and the Moon reciprocates, attracting the Earth with an equal and opposite force.
Since gravity is the only force between the bodies, we apply Newton’s law of universal gravitation and laws of motion to the system. This results in a beautiful system of mathematical equations whose solutions tell us all about the motion. Such as
- The motion of the Moon around the Earth is elliptical in nature. This means the Moon’s velocity varies throughout its path around the Earth.
- The Earth and the Moon system actually orbit their common centres of mass, which due to the Earth’s large mass, lies within the Earth’s surface
This is a system that is easy to understand and neatly fits the laws of physics like a glove.
Now introduce a third problem – the Sun
The Earth-Moon system is an ideal scenario. In reality, there is are other planets and the Sun in that relationship. So, obviously, we shouldn’t expect it to be perfect.
The elephant in the room is clearly the Sun. Unlike the other planets, the Sun’s huge gravitational influence affects both the Earth and the Moon, altering their mutual relationship with each other.
This is a classical three-body problem. Newton ran into this hurdle when he tried to apply his newly found laws of motion and gravity to the Earth-Moon-Sun system.
Like the two-body problem described earlier, we apply Newton’s law of gravitation and laws of motion to determine the motion of the bodies. Unlike the previous two-body problem, however, the resulting equations seem not to have natural solutions.
Despite efforts by prominent mathematicians and physicists over the centuries, the best that we can do is to find approximations to those equations.
The three-body problem today
It may be hard to understand how a 400+ years old problem is still unsolvable today despite advancements in science, mathematics, and technology. One result suggests it may be by design. There is actually a finding that implies we can never know all the solutions to the three-body problem at a level of detail remotely approaching Newton’s complete solution to the two-body problem.
Still, the three-body problem is still a subject of interest for many leading mathematicians today. One such mathematician working on the problem is Richard Montgomery, who wrote a nice article about his work in Scientific American.
You may be wondering how difficult it is for an ordinary person to understand the three-body problem in its fullness. Well, you don’t need me to tell you that its not easy becoming a self-taught physicist. You’ll need at least a firm understanding of calculus to tackle such problems. I’m talking of an undergrad physics major or a highly motivated high school physics major student. It’s not
