Revisiting Riccioli's free fall calculations

TL;DR

This paper reexamines Riccioli's 1651 measurements of gravity using Huygens' pendulum formula, revealing a 15% systematic error likely due to historical measurement challenges with the Roman foot.

Contribution

It provides a novel analysis of Riccioli's data by applying Huygens' formula, uncovering systematic errors in early gravity measurements.

Findings

A 15% systematic error in Riccioli's pendulum length data

Difficulty in subdividing the Roman foot affected measurement accuracy

Reassessment of early gravity experiments using modern formulas

Abstract

In 1651 Giovanni Riccioli reported the earliest accurate measurements the acceleration due to gravity, g, from pendulum-timed free fall experiments. The use of Huygens' pendulum formula (published 1673) allows one to deduce the pendulum length from this data, free from assumptions about the conversion to modern units, and independent of the actual value of g. When this length is compared to the reported pendulum length, a 15% systematic error is revealed. This could perhaps be attributed to the difficulty Riccioli faced in subdividing the contemporary unit of length (the Roman foot) to the requisite millimeter accuracy.