On which day of the year is the Earth closest to the Sun?

Jan 1   1997      23:00 UT         0.983267 AU
Jan 4   1998      21:00 UT         0.983300 AU
Jan 3   1999      13:00            0.983281
Jan 3   2000       5:00            0.983321
Jan 4   2001       9:00            0.983286
Jan 2   2002      14:00            0.983290
Jan 4   2003       5:00            0.983320
Jan 4   2004      18:00            0.983265
You can also visit the Artimus web site and fill in their form for a series of days. They calculate the Earth-Sun distance in terms of the Astronomical Unit.
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