The discussion revolves around the gravitational forces and dynamics in a binary star system, particularly focusing on the relationship between the center of mass and the center of rotation. Participants are examining the implications of these concepts on the stability of the system.
The discussion is ongoing, with participants providing insights and questioning the assumptions made in the original statement. Some have offered interpretations of the terms used, such as "moment" and "center of mass," while others are exploring the implications of these definitions on the problem at hand.
There is a noted confusion regarding the definitions of terms like "center of rotation" and "sum of moments about center of mass," which participants are actively trying to clarify. Additionally, the problem involves specific parameters about the stars' masses and their orbital radii, which are central to the discussion.
That's a very odd statement. First, "centre of rotation" implies circular orbits, whereas in general each will follow an elliptical orbit, the common mass centre being at a focus of each. Secondly, if circular, I do not understand how the centres might not coincide.Clara Chung said:
I think the author is referring to angular momentum rather than moments of forces, but I could be wrong.Clara Chung said:
haruspex said:
Clara Chung said:
Ok, I see. The book is using "moment" to refer to the first moment of mass, i.e product of mass and displacement from axis. When the chosen axis is the common mass centre, the sum of the first moments of mass is zero.Clara Chung said: