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I've been trying to figure out how the angular momentum is preserved. From what I could understand, there needs to be no external torque about the said point. What I could not get into my head is this:

Let's suppose there is a system where Earth orbits The Sun. When referring to the point where The Sun is located, it is understandable that there is no external torque, thus no change in angular momentum. However, although a random point (P) shouldn't have any external torque about it, the angular momentum is somehow not conserved. Even though gravitational forces between The Sun and Earth may cause torque about P, isn't it considered an internal torque, since the system consists of both The Sun and Earth?System

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  • $\begingroup$ S should not be fixed at a point. As diagrammed, S and E should both orbit their combined center of mass - a point which is much closer to S than to E, since S is much bigger, but still not identical to S's location. $\endgroup$
    – g s
    Feb 20, 2022 at 2:04
  • $\begingroup$ When you say: "the angular momentum is somehow not conserved" - can you clarify why you think it's not conserved in this situation? $\endgroup$
    – Carmeister
    Feb 20, 2022 at 16:53

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Torque about some point is equal to the force times the “lever arm”, which is the perpendicular distance from the line of action of the force to the point of interest.

Now, by Newton’s 3rd law the forces on the sun and the earth are equal and opposite. So showing that the torques are equal and opposite reduces to showing that the lever arms are the same. And since the forces share the same line of action, and since the lever arm is the perpendicular distance to that line, it is clear that the lever arms must be the same.

Therefore the torques are equal and opposite and angular momentum is conserved about any point.

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