is it possible to derive exact orbital equation of motion of planet by using gravitational relative mass of planet?

is it possible to derive exact orbital equation of motion of planet by using gravitational relative mass of planet?

 

No, for three reasons.

 

1. What you wrote doesn't quite make sense. What, exactly do you mean by "gravitational relative mass"?

 

2. Granting for the sake of argument that this could be wrangled into something make sense, the answer is still no for the simple reason that there are multiple planets. They interact. This is the N-body problem. Yes, a solution theoretically exists, but there's no practical way to find it or to use it.

 

3. Granting for the sake of argument that a solution could be formulated, it's still not possible. An exact solution requires exact knowledge of position and momentum. That is something we *know* cannot exist.

 

An exact solution requires exact knowledge of position and momentum. That is something we *know* cannot exist.

 

Have you tried to put figures on this uncertainty at the scale of planets? Any reasonable person would qualify by "exact" a solution that would neglect this uncertainty.

The N-body problem is chaotic, which means that even a quantum level of uncertainty will eventually lead to instability. The original post said "exact" and I took that at its word. Sans perfect information, there is no "exact" solution to the N-body problem.

The N-body problem is badly known. Few decades ago, all books still told "unstable" because Poincaré claimed it a century before, but recently planets have been observed around double stars, and around one star of a double system - both being unexpected from common belief. Old triple stars are known also.

 

So presently, people are extremely coutious about the choas or stability of N-bodies. Looks like Poincaré botched it and everyone followed him for a century.

What are you talking about? "All" books? Name one. Nobody that knows orbital dynamics claimed that binary stars cannot have planets, which is apparently what you are claiming. Perhaps you are confusing "chaotic" with "unstable". They are not the same.

I would not presume to argue with D.H. about orbital dynamics, but multi-body problems can be solved to arbitrary accuracy ( not however, exactly ) by using approximate mathematical tools like perturbation methods. It all depends on the complexity of the math you are willing to tackle.

multi-body problems can be solved to arbitrary accuracy ( not however, exactly ) by using approximate mathematical tools like perturbation methods.

That's true only if the initial conditions, the relevant physical constants, and the underlying differential equations are all perfectly known. Initial conditions and physical constants are limited by our ability to measure things. Regarding the differential equations, Newton's law of gravitation is but an approximation, and the same is most likely true for general relativity. Integrate too far into the future and that arbitrary accuracy prediction will be 100% pure fiction.

 

Have you tried to put figures on this uncertainty at the scale of planets? Any reasonable person would qualify by "exact" a solution that would neglect this uncertainty.

I may not know well about those complicated things may be when I get in to astrophysics but i got this link which may add fuel to this hot discussion

http://www.sciencedaily.com/releases/2013/05/130529191041.htm?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+sciencedaily%2Fmatter_energy%2Fphysics+%28ScienceDaily%3A+Matter+%26+Energy+News+--+Physics%29

BTW I really like the discussion!!!

Edited May 31, 201312 yr by daniton

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Moderator Note

 

daniton

 

great post but very off-topic. Everyone - can we not discuss new concepts regarding Heisenberg in this thread on orbital mechanics

 

I will be opening a new thread in science news based on Danitons post