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If you regularly read about astronomy and space related articles, you might have heard about something called the three body problem. But do you know what this problem, that has stumped scientists for centuries, actually is? This post explains what it exactly is and what is so problematic about this problem.
An Introduction To The Two Body Problem
The Two Body Problem, is not exactly a problem, as it has a solution, but is closely related to the Three Body Problem.
So, to understand the Two Body Problem, lets consider 2 celestial bodies, Earth and the Moon. In this system, you might think that the Moon orbits the Earth right?
It actually doesn't. Because the Moon also has significant mass, its gravity affects Earth too. Due to this, the Moon and Earth actually orbit a common centre of mass located a few kilometres inside Earth's crust. This animation should help you understand better. The '+' is the centre of mass.
Credit: Wikipedia
Now, in this case, the movements of the two bodies can be accurately predicted for any point in time using the equations of gravity given by Sir Isaac Newton
The Three Body Problem
Just like the Two Body Problem, let us now consider 3 bodies with similar masses. When you add a third body to the Two Body system, it starts pulling on both of the bodies, pushing or pulling them out of their regular, stable orbits.
Credit: Wikipedia
This completely destabilises the orbits of all the bodies in the system, making their future positions completely unpredictable. What makes it even more difficult is that the motion of every Three Body System is completely random.
What Affects Such Situations?
The movements of such situations with 3 or more bodies are affected by the mass, velocity and positions of all of the objects. Even a slight change in any of these values leads to drastic changes in the entire system.
For example, in the Alpha Centauri star system, which has 3 stars, even a slight change in the postion (say, 1mm), velocity (say, 1m/s) or mass (say, 1g), of one of the stars, could lead to one of the stars being ejected out of the system, or colliding with another.
Credit: Wikipedia
Why Do We Care?
The example given above shows the scale of the Three Body Problem. This problem is a very important component of future interstellar space missions.
Consider that we found a habitable planet orbiting the star Alpha A in the Alpha Centauri system, and we plan to go there. Even with the latest technology, it will take us at least a few years to get there. However, because of the Three Body Problem, we will not know what the positions of the stars and the planet will be by the time we get there.
It could be possible that the planet is still in a stable condition, or we could have a situation where the planet has been pulled inside Alpha A, in which case the mission would become pointless!
Hence, this problem greatly affects the future of mankind and space exploration.
n Body Problem?
The situations I have given above all contain 3 bodies. So, you might be wondering what happens when you have more than 3 bodies. The answer is, as the number of bodies increase, the complexity in predicting their movements and the erraticness increases exponentially.
Such cases can be seen in star clusters like the Pleiades, the Beehive Cluster, etc, where there are hundreds, if not thousands, of closely packed stars, pulling and pushing on each other with gravity.
Credit: Wikipedia
Hence, there can be 'n' number of bodies in this problem and starting with 3, it becomes unsolveable.
Is There A Three Body Problem Involving Earth?
You might wonder why Earth, the Moon and the Sun are not part of a Three Body Problem. The answer is quite simple. The Sun is so far away from Earth and the Moon, that the gravity of Earth and Moon appear to be the gravity of only one object. This converts this Three Body Problem into a Two Body Problem, which has a stable solution.
Hence, the Moon and Earth are happily sitting in their (relatively)stable positions.
Are There Any Solutions?
Quite a few solutions of this problem have been calculated, but most of them can come true only in ideal conditions.
One such solution is that if all the 3 bodies have an equal mass, in ideal conditions, they could move around each other in a figure-eight pattern. However, such situations are almost impossible, due to which this solution is not very probable.
Credit: Brittanica
This is only one of the many theorised solutions. Countless others also exist, but are not very applicable in actual scenarios.
That is all for this post on the enigmatic Three Body Problem. Stay tuned for more posts on astrophysics, and in the meantime, check out a some of my other posts!
Clear skies,
Aarav Iyer
This post is OP. Never knew about it, but op nonetheless
ReplyDeleteThanks a lot AIML_304
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