Empty universe except for three indentical planets

[Alan McDougal]

Hi,

I would like you people to approach these problem of an infinite universe, which contains only three identical objects, say planets of equal volume and mass at equal distance from one another:

Scenario 1) They all hover in the sky not moving relative to one another. Are they all stationary moving etc etc............??

Scenario 2) They appear to rise and set relative to one anther at their respective identical time frame. Are they all moving relative to one another or are two moving around one planet or is one planet moving around the other two? etc etc.......??

Scenario 3) They each move in different directions relative the other rising and setting at different times on each planet..........??

Scenario 4) Ahh! the complexity becomes too much for this finite intellect ......?

Famous three body, two body or n-body problem never really solved, but let's just try and use logic and see who far we mere mortal physicists can come towards understanding this enigma.

Regards

Alan

 

[Wallace]

You simply haven't given enough information. It is not enough to know how far apart the objects are but also what initial velocites they have. I have to disagree about the statement about N-body problems. The three body problem can be readily solved numerically to a very high accuracy to answer this question. Again, the result depends on the velocities but is otherwise solved.

 

[Alan McDougal]

WALLACE,

I DELIBERATELY DID NOT GIVE DETAILS ABOUT VELOCITIES THIS EXERCISE SHOULD BE CONSIDERED FROM THE VIEW POINT OF SENTIENT BEING LIVING ON THE PLANETS TRYING TO RESOLVE THE PROBLEM (S). BY OBSERVATION THEY CAN ESTABLISH THE MASS OF EACH PLANET AND HOW THEY RELATE TO ONE ANOTHER
AND BY PROCESS OF LOGIC ASSUMPTION AND ELIMINATION GET SOME IDEA HOW THEY RELATE ONE TO THE OTHER.

The problem should be seen as a challenge

FOR EXAMPLE SCENARIO 1) COULD BE EXPLAINED BY THE THREE PLANETS INTERLOCKED IN A THREE- WAY

" “Y” PATTERN OF EQUAL GRAVITATIONAL PULL AND PUSH."

THE PROBLEM GETS MORE COMPLEX BUT WOULD ISAAC NEWTON GIVE UP IF HE HAD THE SAME LIMITED PARAMETERS AS I GAVE.?

THREE BODY NUMERICAL SOLUTION FOR ONE- DIMENSIONAL THREE BODY PROBLEM

Numerical orbit integrations must be conducted to characterize the types of trajectories in the one-dimensional Newtonian three-body problem with equal masses and positive energy. At positive energies the basic types of motions are binary + single particle and ionization , and when time goes from – to + all possible transitions between these states can take place.

The basic motion types exist at all positive energies, but the binary + single particle configuration is obtained only in a narrow region of initial values if the total energy is large. At very large energies the equations of motion can be solved approximately, and this asymptotic result, exact in the limit of infinite energy, is presented.

This is just a first approach to solving three body problem.But let's at this stage of the thread keep it simple and confined to planetary orbits

Alan

 

[Borek]

It doesn't make sense. In the universe where only three planets exists there is no source of light, so you can't see them

Then, from what I have read, and from what I have seen playing with several simulation programs, the real three body system is stable only if two bodies are close (ie they form a binary system) and third is far from them. In other cases (especially purely symmetrical one, with all objects circling around system mass center) slightest perturbation makes the system unstable and either one of the objects is shot out, or after some time they settle as binary plus sattelite.

 

[Alan McDougal]

Borek,

Then, from what I have read, and from what I have seen playing with several simulation programs, the real three body system is stable only if two bodies are close (ie they form a binary system) and third is far from them. In other cases (especially purely symmetrical one, with all objects circling around system mass center) slightest perturbation makes the system unstable and either one of the objects is shot out, or after some time they settle as binary plus sattelite

A sort of three-dimensional figure eight?

Alan

 

[junglist]

if only one of the planets is initially moving then the others will have to move due to changing gravitational acceleration as distances between the stationary/moving planets vary.

 

[Borek]

A sort of three-dimensional figure eight?

Sorry, can't see it. Please elaborate.

 

[junglist]

Borek,



A sort of three-dimensional figure eight?

Alan

if you mean two orbiting each other and then one performing a figure 8 by passing through the gravitational centre of the first 2, then no.

borek means 2 in close orbit and the third in a much wider orbit almost as though it is orbiting a single object of double the mass.

see alpha-centauri (AB) and proxima centauri for a similar orbit that exists in reality, though with objects of non-identical mass.