Two bodies problem in other reference system

In summary, the speaker wants to model the motion of two gravitationally interacting bodies from a separate reference point. They have found a way to calculate the trajectory of one body around the other from the perspective of one of the bodies, but they want to be able to observe the motion from a different reference frame. They are unsure of how to do this and are wondering if they should approach the problem differently using elliptical coordinates.
  • #1
Vrbic
407
18
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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  • #2
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.
 

1. What is the Two Bodies Problem in other reference systems?

The Two Bodies Problem is a classical mechanics problem that involves calculating the motion of two point masses that are influenced only by their mutual gravitational attraction. In other reference systems, the problem refers to solving this motion in non-inertial frames of reference, such as a rotating coordinate system or a non-uniformly accelerating system.

2. Why is the Two Bodies Problem in other reference systems important?

The Two Bodies Problem in other reference systems is important because it allows us to understand the motion of objects in more complex situations, such as planets orbiting around a rotating star or satellites orbiting around a non-uniformly accelerating planet. It also has practical applications in space mission planning and spacecraft navigation.

3. What are the challenges of solving the Two Bodies Problem in other reference systems?

The main challenge of solving the Two Bodies Problem in other reference systems is the complexity of the mathematical equations involved. It requires advanced mathematical techniques, such as differential equations and perturbation theory, to accurately calculate the motion of the two bodies. Additionally, the motion of the two bodies can be affected by external factors, such as the gravitational influence of other nearby objects or the rotation of the reference system itself.

4. How is the Two Bodies Problem in other reference systems solved?

The Two Bodies Problem in other reference systems is typically solved using mathematical models and computer simulations. These methods involve breaking down the problem into smaller, solvable components and using numerical techniques to approximate the solutions. Advanced computer programs and algorithms have been developed to accurately solve the problem for various scenarios and reference systems.

5. What are the real-world applications of the Two Bodies Problem in other reference systems?

The Two Bodies Problem in other reference systems has numerous real-world applications, especially in the fields of astrodynamics and space exploration. It is used to accurately predict and plan the orbits of spacecraft, satellites, and other objects in space. It also has applications in understanding the dynamics of celestial bodies, such as planets and moons, in complex systems such as binary star systems or planetary systems with multiple objects.

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