Please see the work below.
Work Step by Step
We know that the earth's rotation on its axis is not a uniform motion. It is sometimes an accelerated motion and sometimes decelerated motion. Hence, the interval to cover a specific distance changes. Let's say that we measure a particular distance and fix the interval for it as second, but when we repeat the experiments, we will have a different distance traveled. Thus, the definition of second cannot be fixed if using the earth's rotation to define it.