Discussion Overview
The discussion revolves around the two-body Kepler problem with the Sun at rest in a coordinate system orbited by another body. Participants explore whether this coordinate system can be considered inertial and the implications of the forces acting on the Sun and the other body involved.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant questions if the coordinate system is inertial, seeking elaboration on the principles involved.
- Another participant notes that if the Sun is at rest, the coordinate system is based on the Sun's rest frame and asks if the Sun experiences any forces that could cause it to accelerate.
- A hypothetical scenario is presented where the other body has the same mass as the Sun, prompting a discussion on whether either body would be at rest in an inertial coordinate system.
- One participant argues that since the Sun is pulled by the other mass with an equal force, the coordinate system must be non-inertial, referencing Newton's third law and the definition of inertial systems.
- Another participant introduces the concept of the Center of Mass frame of reference, suggesting it can simplify the two-body problem.
- A later reply confirms the reasoning about the barycentre being an inertial frame and its relation to the orbits of both bodies.
- One participant expresses gratitude for the confirmation and the opportunity to discuss the topic.
- Another participant critiques the initial framing of the problem, stating that it is an approximation for disparate masses and emphasizes the importance of using reduced mass and relative coordinates.
Areas of Agreement / Disagreement
Participants express differing views on the nature of the coordinate system, with some asserting it is non-inertial while others suggest the barycentric frame is inertial. The discussion remains unresolved regarding the implications of these perspectives.
Contextual Notes
There are limitations in the assumptions made regarding the masses involved and the applicability of the inertial frame definitions. The discussion also highlights the complexity of the two-body problem and the need for careful consideration of the forces at play.