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If two particle are neither approaching towards nor receding away from other then their relative velocity is non zero.

How is this possible??

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Turning my comment into an answer ...

The velocity can be non-zero because velocity is represented by a vector, so the vector changes when the direction changes, even if the magnitude ("speed" in this case) remains constant.

For example, consider the case of two objects in circular orbits around the barycenter. If I am riding on top of one of them their separation is constant, but the direction to the other one is changing, describing a circle. The direction changes, so velocity is not constant.

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If your two objects are not subject to external forces, then gravity would accelerate them toward each other. They can do this with a fixed separation only if they are orbiting each other with both velocity vectors changing direction as a function of time.

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The answer lies in your question itself. The two particles neither approach each other i.e. their separation isn't decreasing, nor are they moving apart i.e. their separation isn't increasing In other words with respect to both the particles, the separation between them is not changing. Relative velocity is given as the rate of change in relative separation (with respect to the particle) with respect to time, and as the relative separation is a constant, it's rate of change is zero i.e. the relative velocity is zero. Note only their relative separation matters, if both the first particle moves 5 meters in a second and so does the second particle, then their separation hasn't changed, thus the two particles could be moving, but with respect to each other the relative velocity is zero.

Edit: I didn't read the question properly, as it asks how there is a relative velocity between two objects, even though their separation is neither increasing nor decreasing. Well Velocity is a vector, so it can have both magnitude and direction, so it is possible that the separation doesn't change but their direction does change continuously, for example, two objects in circular motion, their relative velocity at every instant is non zero, despite their relative speed being zero

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    $\begingroup$ Is that a standard definition of relative velocity? I would have thought it would be the rate of change of the relative position vector in which case the separation could remain constant while their relative velocity is changing. $\endgroup$
    – garyp
    Commented Jul 26, 2020 at 16:33
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    $\begingroup$ Velocity is a vector, so direction is just as important as distance change. $\endgroup$
    – Bill N
    Commented Jul 26, 2020 at 20:00

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