[SolidRedState]

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The definition of a second has nothing to do with the rotation of the Earth:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

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So we have only been measuring seconds since we were able to figure out the transition in cesium 133 atoms?

I did not know that.

[dr_lew]

Before atomic clocks there was no way to keep time more accurately than astronomical standards allowed.

According to the website, Astronomical Time Keeping, it was realized around 1930 that the earth's rotation rate varied somewhat. The earth's solar orbit is more stable, and was made the basis for the second in 1957. This standard was called Ephemeris Time, but it was very difficult to use because its calibration depended on observations of the stars and planets spread over years.

The article also points out that even atomic clocks are affected by the motion and gravitation of the earth, so it's impossible to entirely remove astronomical considerations from a standard time scale.

[DManA]

The definition changed as we were able to isolate phenomena that weren’t affected by gravity etc. It’s called progress.