Two bodies problem in other reference system

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SUMMARY

The discussion focuses on modeling the motion of two gravitationally interacting bodies from a reference frame where the observer is static, as opposed to being at one of the bodies' foci. The user successfully applies Binet's formula to determine trajectories from one body's perspective but seeks guidance on transforming these results to a different reference frame. The conversation emphasizes the importance of understanding elliptical coordinates and their transformation into rectangular coordinates while maintaining the relative positions of the origins.

PREREQUISITES
  • Understanding of gravitational interactions and orbital mechanics
  • Familiarity with Binet's formula for orbital trajectories
  • Knowledge of coordinate transformations, specifically from elliptical to rectangular coordinates
  • Basic principles of reference frames in physics
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  • Research coordinate transformations in celestial mechanics
  • Study advanced applications of Binet's formula in multi-body systems
  • Explore the concept of inertial and non-inertial reference frames
  • Learn about numerical methods for simulating gravitational interactions
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Physicists, astrophysicists, and students studying celestial mechanics who are interested in modeling gravitational interactions from various reference frames.

Vrbic
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Hello,
I would like to try to "model" motion of two gravitationally interacting bodies. But from some "separated" point. I can find the trajectory of mass point to orbits around some other mass point from point of view one of them (using binets formula). But in this reference frame I am sitting in focus (on that point). But I would like to observe moving of these bodies from other reference system, where I am "static" (or sitting at infinity) and the bodies are orbiting each other.
I am thinking it should be possible to transform result where I am in the focus to some other frame, but I don't know how.
Or is it better look at this problem in other way from start? How?
 
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If your "local" model uses elliptical coordinates you should be able to transform those to your rectangular system. You just have to keep track of the relative locations of the origins.
 

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