Consider a small area ΔA that is sweep out when an orbiting body moves through a small differential area Δθ.

We divide by the small time interval Δt to find the average rate of change in the area with time.

If we now take the limit as Δt approaches zero the area of the triangle becomes equal to the area swept out and we get the instantaneous rate of change of the area.

This can we written in terms of the conservation of angular momentum.

Since L is constant then the rate of change (i.e. the derivative ) of the area sweep out dA/dt will be equal to zero. Thus you can see that the conservation of angular momentum implies Kepler’s second law.

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