B Two-body Kepler problem where the Sun is at rest in a coordinate system orbited by another body

[DrToby]

The two-body Kepler problem where the Sun is at rest in a coordinate system orbited by another body: is the coordinate system an inertial reference system or not? Please no yes/no answers. A bit of elaboration is appreciated towards why and which principles apply.

 

[Ibix]

If the Sun is at rest, you are using the Sun's rest frame. Is the Sun affected by any forces that might make it accelerate?

 

[jtbell]

Suppose the other body has the same mass as the sun, as in e.g. a binary star system. Would you expect either body to be at rest in an inertial coordinate system?

 

[DrToby]

The Sun is orbited by another mass. The origin of a coordinate system is placed at the center of the Sun. The Sun pulls on the mass with a given force. According to Newtons third law the Sun is pulled towards the mass with an equal force. Hence the coordinate system is accelerated and hence it must be a non-inertial coordinate system. An inertial coordinate system is defined as a system for which Newtons 1. law is valid. Is all this reasoning correct?

 

[hutchphd]

An inertial coordinate system

Called the Center Of Mass frame of reference. The same trick is used to reduce many two body problems to modified "one body" ones

 

[Ibix]

Is all this reasoning correct?

Yes.

The barycentre is the point about which both Sun and planet orbit. The barycentric frame is inertial, and the barycentre is one of the foci of the ellipses of both bodies' orbits.

 

[DrToby]

Thank you for confirmation. Nice to find people to discuss stuff with.

 

[hutchphd]

The problem you describe is not what you want . It is an approximation for very disparate masses. The usual exact solution involves reduced mass and relative coordinates, and the sun is not at rest in the chosen coordinate system. It would be good to read carefully all previous answers as well as any good freshman text.