From Newsgroup: sci.physics.research

Animation
https://www.geogebra.org/classic/mzf3e87b

Two identical planets rotate around a common center of mass.

The center of rotation and the center of mass coincide.

There's no doubt about that.

Then choose to have different masses using the appropriate button.

In this case, are the center of rotation and the center of mass still coinciding, or are they disjoint, as in the animation?

In other words, is the center of mass of two different planets
stationary, or does it also rotate around the center of rotation C?

Luigi Fortunati

[[Mod. note -- We can use conservation of momentum to answer Luigi's
question. If the center of rotation were anywhere other than the center
of mass, that would mean that the center of mass would oscillate in
position, which would mean that the total linear momentum of the
two-planet system would be time-dependent. Since there are (we assume)
no external forces on the two-planet system, that (time-dependent total
linear momentum) can't happen. This proves that the center of mass
must be stationary, i.e., that the center of rotation must coincide
with the center of mass.
-- jt]]
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From Newsgroup: sci.physics.research

Il 07/02/2026 03:00, Luigi Fortunati ha scritto:

Animation
https://www.geogebra.org/classic/mzf3e87b

Two identical planets rotate around a common center of mass.

The center of rotation and the center of mass coincide.

There's no doubt about that.

Then choose to have different masses using the appropriate button.

In this case, are the center of rotation and the center of mass still coinciding, or are they disjoint, as in the animation?

In other words, is the center of mass of two different planets
stationary, or does it also rotate around the center of rotation C?

Luigi Fortunati

[[Mod. note -- We can use conservation of momentum to answer Luigi's question. If the center of rotation were anywhere other than the center
of mass, that would mean that the center of mass would oscillate in
position, which would mean that the total linear momentum of the
two-planet system would be time-dependent. Since there are (we assume)
no external forces on the two-planet system, that (time-dependent total linear momentum) can't happen. This proves that the center of mass
must be stationary, i.e., that the center of rotation must coincide
with the center of mass.
-- jt]]

The "perihelion precession" demonstrates that the center of mass is not stationary at all.

Luigi Fortunati


[[Mod. note --
No, perhelion precession doesn't demonstrate that.
1. The usual meaning of "perihelion precession" refers to a
general-relativity effect; here we're discussing Newtonian mechanics.
2. Perihelion precession also occurs in Newtonian mechanics... but only
if there are 3 or more planets; here we're discussing the case where
there are only 2 planets.
3. In Newtonian mechanics, perihelion precession doesn't imply any
movement of the center of mass. There's an easy proof of this, given
in
https://en.wikipedia.org/wiki/Two-body_problem
in the section "Center of mass motion (1st one-body problem)".
-- jt]]
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