Determining Longitude by the Equation of Time of the Moon (Professor Robert Cribbs)
The inconsistent motion was first discovered by Jia Kui in the Eastern Han period (25-200 AD) (Research of Ng Say Tiong and Helmer Aslaksen).
After the moon’s motion was found to be inconsistent, a method of calculating the moon’s future orbit ( the equation of time of the moon) was achieved by Liu Zhou (544-610) which was then improved upon in the Yuan dynasty by Guo Shoujing using a third degree formula of interpretation (Helmer Aslaksen and Ng Say Tiong).
Professor Cribbs has taken this research further. By using Starry night he was able to plot out the difference from average time of the moon crossing the local meridian (Beijing) for each day of the year (graph 1- “Equation of Time – Moon 2006”). By measuring the angle between the moon crossing the local meridian and a selected star longitude may be calculated – only a sextant is required and no time measuring device is needed. In Appendix 1 are results for 30th, 31st July 2006 for Beijing and for Sacramento California showing the moon on the local meridian and the position of Jupiter. The difference in Jupiter’s position between the sightings from Beijing and Sacramento equals the difference in longitude between Beijing and Sacramento.
The implication are that since the Yuan dynasty the Chinese were capable of calculating future positions of the moon, making ephemeris tables and using these and a sextant to determine longitude at sea without the need for time measuring devices.
