Trajectories of planets using reduced mass and CM frame

[Soren4]

In planetary motion, the reduced mass of a system \mu is used in order to study the motion of the planet m in the non-inertial frame of the star M. Using \mu the trajectory of m turns out to be a conic. But this is the trajectory of the planet m as seen from the star M, correct?

I read that in the CM frame the trajectories are still conics (ellipses for istance) but that the focus is in the CM. Moreover the Sun (or the star) also follows a conic trajectory with focus in the CM of the system.

Is the trajectory of the planet seen in CM frame different from the one calculated using \mu (and so the one in the M frame)?

 

[drvrm]

In planetary motion, the reduced mass of a system μμ\mu is used in order to study the motion of the planet mmm in the non-inertial frame of the star MMM. Using μμ\mu the trajectory of mmm turns out to be a conic. But this is the trajectory of the planet mmm as seen from the star MMM, correct?

I read that in the CM frame the trajectories are still conics (ellipses for istance) but that the focus is in the CM. Moreover the Sun (or the star) also follows a conic trajectory with focus in the CM of the system.

Is the trajectory of the planet seen in CM frame different from the one calculated using μμ\mu (and so the one in the MMM frame)?

if you see the resources on the net detail plots are there of the orbits when the observer moves from centre of mass frame to one of the bodies.

for example
[PDF]The Two-Body Problem - KSU Math Home
https://www.math.ksu.edu/~dbski/writings/twobody.pdf