It is established in the inertial frame. For the non-inertial frame, the moment of the inertial force is added.

For the definition of angular momentum and moment, there is moment and angular momentum for any reference point, but both must be for the same fixed reference point.

The moment of gravity on an object is equivalent to the moment of gravity when the mass is concentrated at the center of mass

The premise needs to be met: if the object is in a uniform gravity field

Forces that are equal in magnitude and opposite in direction and act on different particles are called force couples

Analogy to previous work: The work effect of a pair of internal forces has nothing to do with the selection of the reference system (for convenience of calculation, one of them is generally selected as the reference system)

If this question only considers cannonballs, the momentum of the system is not conserved.

Key to solving the problem:

Determining the orbital characteristics of stars based on system energy

Select the inertial frame and further discuss the motion of the two bodies.

Choose the center of mass system of the two, there is no external force, the center of mass system is the inertial system

Use translational non-inertial mass center system

Final Results