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I am confused about certain aspects of deriving the planetary orbit equation by considering it as 2-body problem. I will ask my first question now before i get to my other questions. In the David Tong notes on "Dynamics & Relativity" he states that a particle in central force potential obeys

m

**a = -∇**V(r)

He then states that this can be interpreted as 2 particles with separation

**r**interacting through the inter-particle potential V. The origin r = 0 is the centre of mass of the 2 particles. Also m is the reduced mass of the 2 particles.

My question is why is r=0 the centre of mass position ? The vector

**r**starts at one mass and ends at the other one so surely r = 0 corresponds to the position of one of the masses ? Also when calculating gravitational potentials the origin r=0 always seems to be the position of the particle ( or centre of a spherical mass)

Thanks