I am confused about the \"two body problem\" To solve this we areusing the centr

Question

I am confused about the "two body problem" To solve this we areusing the centre of mass reference frame.I know that this framemoves with constant velocity, but the lecturer siad that we can useit as an inertial frame, which makes sense, but then also said thatwe can take the velocity to be 0. If it moves with constantvelocity why can we say take the velocity to zero.Body 1 moves witha velocity relative to the centre of mass and body 2 moves with avelocity relative to the centre of mass.,

Using newtons laws for the two bodies we have the force of 1 on 2is equal to the negative of the force of body two on 1. Thereforethe differential becomes m1a1+m2a2=0. By integrating i get m1v1+m2v2=cWhy did the lecturer say that we can make the constantzero, when it is not.

Explanation / Answer

According to Newton's laws of motion, an intertial reference frameis one that moves at a constant velocity, like you mentioned above.When you are in an inertial reference frame, there is no way todetermine that you are moving. Essentially what that means is thatthere is NO physical difference between a stationary inertialreference frame and a reference frame moving at constant velocity.The laws of physics are identical. So, just to simplifycalculations, its easier to assume the velocity of the center ofmass to be zero since it doesn't affect the physics in any way. I hope that helps. Please feel free to message me if you need anyfurther clarification on this.

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