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With the 2-body problem relating to planetary orbits i have encountered the following ; the gravitational force on the reduced mass acts towards the large mass(Sun) and since it is a central force it exerts no torque about the fixed centre(Sun) so angular momentum is conserved.

Conservation of angular momentum states that the total angular momentum of an isolated system is always conserved ; so here's my question - the 2-body problem (Sun and orbiting planet) is an isolated system so can i just that its angular momentum must be conserved straight away without having to consider that there is no torque about its centre due to force being central ?

Thanks