On the face of it, the solution to the equation above is clear: 0359 local time. That, says a research paper in the latest Geographical Journal, published by the Royal Geographical Society, is where the first dawn of the new millennium will be seen, according to the equation for calculating sunrise times published in the US Navy and Royal Observatory Astronomical Alamanac (1994 edition).
And the place: the 177-metre summit of Mount Hakepa, on the tiny Pitt Island - presently, home to just 55 people - 680 miles east of New Zealand.
But rather than being a definitive answer, this could be just the latest round in a vicious battle being fought in the South Pacific to win tourist business from travellers wanting to witness the authentic first dawn of the next 1000 years.
A number of islands have been planning lucrative millennium tours, promising visitors they will be the first to see in the year 2000. Last year, the Tongan government was considering introducing daylight saving time so that it could pip New Zealand to the millennium post. But all seem to have been beaten by the Republic of Kiribati, whose Ministry of Foreign Affairs declared in January 1995 that all the islands in its jurisdiction would take the same day of the week.
Though outwardly reasonable, this decision unilaterally put a huge, 1000- mile eastward bulge into the International Date Line - and, coincidentally, brought Caroline Island, an uninhabited atoll previously on the extreme eastern side of the line (and so at the end of every solar day) over to the western side - and thus the start of each day.
That seems to have dismayed a team at the Millennium Adventure Company, based in New Zealand. They returned to their maps, consulted tables of sunrise calculation times to determine that the first sunrise would, after all, be seen off Pitt Island.
They are dismissive of Kiribati's tactics. "The arbitrary and unilateral moving of time zones or the international date line does not give rise to any level of credibility in the international navigation community," they write. "Any claim on the first millennium sunrise from a place geographically quite removed from the traditional dateline lacks sensibility, as any country in the world could do the same."
HOW TO FIND THE MILLENNIUM DAWN
T = 0.99727 (a - l+ cos-1(-tanf tand) - (GMST at 0000 UT)
Where T=time of sunrise; a=right ascension of Sun; l=east longitude; f=latitude; d=declination of sun; GMST=Greenwich Mean Standard Time; UT=Universal TimeReuse content