Astronomers have little confidence in orbital forcing calculations on time scales beyond ten million years. They are confident that the fundamental frequencies of the planetary orbits remain nearly constant on time scales of hundreds of millions of years. Small variations in these frequencies and chaotic behavior of certain resonance relationships, however, can introduce large uncertainty regarding the exact orientation of planetary orbits on time scales of tens to hundreds of millions of years. We introduce a simple trigonometric series expression for eccentricity in order to evaluate effects that arise from imposing specified displacements in orientation of planetary orbits. The resulting changes in the character of the calculated eccentricity time series should be a guide to stratigraphers seeking to relate orbital forcing to stratigraphic time series throughout the Phanerozoic. This geologic calibration of eccentricity time series in relatively old stratigraphic sequences may provide astronomers with clues to further refinement of their calculations.

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