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Systematic errors in Galileo's astronomical observations and alleged anomalies in the position of Neptune

In 1980 Kowal and Drake found that in December 1612 and January 1613 Galileo observed the planet Neptune. At that time, according to these authors, Galileo was able to measure angular separations with an accuracy of about 10 seconds of arc. However, as noticed by Kowal and Drake, the position of Neptune reported by Galileo is wrong with respect to the position computed with the modern ephemeris of about 1 minute of arc. This led Kowal and Drake to speculate on the possible errors of modern ephemeris of Neptune and sparked some debate about Neptune's ephemeris and/or possible errors in Galileo's measures. Until today this anomaly has remained without a conclusive answer. Here we show that, in addition to the random errors, there are other significant measurement errors present in Galileo's observations. These errors may help clarify the origin of the alleged anomalies in the position of Neptune.