What is the reason for the date of the Georgia runoff elections for the US Senate?
Law.
Georgia Code Title 21. Elections § 21-2-501
(3) In the case of a runoff from a general election for a federal office or a runoff from a special primary or special election for a federal office held in conjunction with a general election, the runoff shall be held on the Tuesday of the ninth week following such general election.
November 3, 2020 to January 5, 2021 (a Tuesday) is nine weeks.
One of the runoffs is from a "general election for a federal office". The other is from a "special election for a federal office held in conjunction with a general election".
Background leading to the "ninth week" choice
In 2009, Congress approved the Military and Overseas Voter Empowerment (MOVE) Act as an amendment to the National Defense Authorization Act for Fiscal Year 2010. One of the provisions of the MOVE act is a 45-day period to allow certain voters to receive and return ballots for elections.
States are required to transmit a validly requested absentee ballot to an absent
uniformed services voter or overseas voter no later than 45 days before an
election if the request is received at least 45 days before the election. A state can
seek a hardship waiver from the requirement under certain circumstances.
The Uniformed and Overseas Citizens Absentee Voting Act: Overview and Issues
While states, including Georgia, passed legislation to come into compliance regarding the time between primaries and elections, Georgia did not change its law regarding runoffs, which were less than 45 days. In 2012, the Department of Justice sued Georgia.
The United States of America ("United States") and the State of Georgia ("Georgia") now disagree as to how federal law should be interpreted and applied to Georgia's efforts with regard to the timing and methodology of Georgia's runoff absentee voting scheme.
The disagreement was over the meaning of "election" as it relates to a "runoff" in the context of the MOVE Act. The United States prevailed at District Court. Georgia appealed. The Appeals Courts upheld the District Court. Georgia changed its law.
At the time of the suit, Georgia was using 21 days for primary and special elections, with 28 days for general elections, to set the date of a runoff. Under the rules of the MOVE Act, Georgia could use any date at least 45 days after any election. For a runoff to occur on Tuesday and using seven weeks after the general election would mean that the runoff could occur on Christmas Day; eight weeks could be New Years Day. Nine weeks was chosen.
Georgia could have complied with the MOVE Act by changing to plurality rather than majority to decide the election, that would have eliminated the runoff.