This article reports the discovery in the Bamboo Annals of verifiable accounts of the general conjunctions of planets witnessed by Shang and Zhou dynasty observers, which occurred in 1576 and 1059 B.C. Besides exploring the connections between the planetary phenomena and mythologized accounts of the same events in Zhou and Han texts, the significance of these astronomical dates is discussed in reference to the events surrounding the Zhou Conquest of Shang and the founding of the Shang dynasty. The investigation proposes that the Shang and Zhou astrologers were astute observers of the motions of the planets and that there are a number of Zhou traditions, such as those concerning visitations of the Phoenix, which are intimately associated with certain planetary periods. In addition, it is suggested that the concept of the Mandate of Heaven as a physical manifestation of Heaven's will and that of its transfer to virtuous rulers at 500 year intervals both derive from the period of the so-called Triple Conjunctions accurately recorded in the Bamboo Annals.