The tenth millennium of the Gregorian calendar will begin on January 1, 9001, and end on December 31, 10000. It will be the tenth millennium in the Anno Domini or Common Era.
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Astronomical events
All these dates are in a uniform time scale such as Terrestrial Time. When converted to our ordinary solar time or Universal Time, which is decidedly non-uniform, via ΔT, the dates would be a couple of days earlier. Furthermore, they are only astronomical dates, so they are given in the astronomical format of Year Month Day, which allows them to be ordered.
Year 10,000 problem
Software that encodes the CE / AD calendar year of a date as a four-character binary-coded decimal will no longer be able to encode the contemporaneous date.
References
10th millennium Wikipedia(Text) CC BY-SA