the three body problem
In: 5
How does the solar system stay stable enough for us to keep living?
You want equations to give you the position and velocity of 3 planets orbiting each other
But the three planets’ gravities influence each other’s movement in dynamic ways too complex for basic equations to represent
Thus approximate simulations are needed instead of truly-perfect equations
How does the solar system stay stable enough for us to keep living?
You want equations to give you the position and velocity of 3 planets orbiting each other
But the three planets’ gravities influence each other’s movement in dynamic ways too complex for basic equations to represent
Thus approximate simulations are needed instead of truly-perfect equations
You want equations to give you the position and velocity of 3 planets orbiting each other
But the three planets’ gravities influence each other’s movement in dynamic ways too complex for basic equations to represent
Thus approximate simulations are needed instead of truly-perfect equations
The actual difficulty for a three-body problem is that at this moment you can’t define a function f(t) for any three-body system in which it outputs the status of the system at time t, without having to iterate from f(0) all the way up to t, not to mention the granularity or resolution of t also affects the results.
If you want to perfectly simulate a three-body system, the resulotion has to be infinitely fine, meaning you will have to perform an infinite number of iterations from f(0) to get to the point of any t.
This isn’t a practicality problem in most of the situations, you can get reasonably fine resolution and perform many iterations very fast using modern computers, but it will be a tradeoff of computation workload and accuracy, no perfect solution exists.
The actual difficulty for a three-body problem is that at this moment you can’t define a function f(t) for any three-body system in which it outputs the status of the system at time t, without having to iterate from f(0) all the way up to t, not to mention the granularity or resolution of t also affects the results.
If you want to perfectly simulate a three-body system, the resulotion has to be infinitely fine, meaning you will have to perform an infinite number of iterations from f(0) to get to the point of any t.
This isn’t a practicality problem in most of the situations, you can get reasonably fine resolution and perform many iterations very fast using modern computers, but it will be a tradeoff of computation workload and accuracy, no perfect solution exists.
The actual difficulty for a three-body problem is that at this moment you can’t define a function f(t) for any three-body system in which it outputs the status of the system at time t, without having to iterate from f(0) all the way up to t, not to mention the granularity or resolution of t also affects the results.
If you want to perfectly simulate a three-body system, the resulotion has to be infinitely fine, meaning you will have to perform an infinite number of iterations from f(0) to get to the point of any t.
This isn’t a practicality problem in most of the situations, you can get reasonably fine resolution and perform many iterations very fast using modern computers, but it will be a tradeoff of computation workload and accuracy, no perfect solution exists.
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