1. The great constellation Ursa Major at present stretches from the end of July, from its 'egg' (ο) at a location 36 days beyond the solstice (= 128 days beyond the equinox), and perhaps also from the 10th day of the explorers' stay at Hanga Hoonu:

Hanga Hoonu
Ga2-24 (**499) Ga2-25 (*120) Ga2-26 (57) Ga2-27 (*122) Ga2-28 (**31)
Uure Makoi Ira Raparenga Kuukuu
    χ Carinae (120.9) Naos (122.3) Heap of Fuel (123.1)
July 18 (199) 19 8h = 121.7 21 22
p. 24 p. 25 p. 26 p. 27 p. 28
'Cooking Fishes' 'Lifting Turtle'
Ga2-29 (60) Ga3-1 (*125) Ga3-2 Ga3-3
Tegmine (124.3)  Al Tarf (125.3) Bright Fire (126.4) Avior (127.4)
23 24 25 26
Ga3-4 (**36) Ga3-5 Ga3-6 (*130) Ga3-7 Ga3-8 (68)
 ο Ursa Majoris (128.4) θ Cancri (129.2) η Cancri (129.5) π¹ Ursa Majoris and δ Hydrae  (130.6), Al Minhar al Shujā and Museida (130.9), Beehive (131.4) Ascellus Borealis (131.9), η Hydrae (132.0), Ascellus Australis (132.4)
July 27 (208) 28 29 30 31

The 'tip of its tail' is at Benetnash (Alkaid), rising heliacally 7 months beyond the equinox (and precisely 4 lunar months beyond the June solstice, 172 + 4 * 29½ = 290):

77
Ga6-5 (*210) Ga6-6 Ga6-7 (**120) Ga6-8 (149)
Benetnash (209.5)      
October 17 (290) 18 19 14h = 213.1

Thus the extension of Ursa Major is 209.5 - 128.4 = 84 days or 12 weeks. 364 - 84 = 280 (= 40 weeks).