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$$\vec{r_{a}}$$ and $$\vec{r_{b}}$$ is calculated from an inertial frame of reference.

then for any two objects (named a and b) in a system of more than two objects,

Is this the newton's third law,

$$\frac{d^{2}}{dt^{2}}m_{a}\vec{r_{a}}=-\frac{d^{2}}{dt^{2}}m_{b}\vec{r_{b}}$$

i think this cant be right because then this implies

$$\frac{d^{2}}{dt^{2}}m_{i}\vec{r_{i}}=0$$ for every object in that system.

so i think i have misunderstood the law, so my question is can anyone state the law in terms of above variables for n-body system ?

Edit 1 (fix)

fixed a embarrassing mistake d/dt -> d^2/dt^2

thank you

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# Newton's third law in terms of inertial position vectors for n-body system

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