Hello,
Supposing that the stars S1 and S2 orbit around their barycenter and S1 is two or three times much heavier than S2. Say the average distance between these stars is about 100 Mkm so that there is no mass transfer among them.
A body ( like a telluric planet) orbits at a distance about 200+ Mkm, in the plane generated by the orbit of S1 and S2.
Then the gravitational field could vary depending on the configuration of the stars and the planet.
Questions :
- how is the trajectory influenced by the position of the stars?
- is this trajectory a conic?
- periodicity and stabilty ?
I think the 3-bodies problem could cover this case. Are there recent articles on this topic?
In Newtonian mechanics, the two stars move in the conic orbits. The orbits could be bounded, so periodic and stable. They could be unbounded, ie., hyperbolic curves.
In General Relativity, the orbits are nearly conic, as long as the two stars are far away from each other. For example, Mercury orbits around the Sun, and its orbit is not an eclipse but one whose perigee also orbits around the Sun very slowly.
Thank you Shaoqi, I was more questioning about the third objet in my question.
Gabriel
This system is dynamically near the so called restricted three-body problem. There are a few special orbits that can be called stable,
but in general the third body orbits are chaotic and/or unstable.
Mathematically it has been proved that it is IMPOSSIBLE to predict the
motion (for longer than a bit).
Anyway, generally three-body problems (with any masses of the bodies)
is mathematically unsolvable. Meaning that there does not exist
any formula telling the motion. Only numerical computation,
which proceeds in short steps, can tell how the system moves.
For special systems it is sometimes possible to construct
approximate solutions that are practically valid over some longer,
but finite time. Our Solar System is one such many-body system.
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