Final answer:
The question appears to confuse history involving Emma with that of King Henry VIII's issues with his marriage to Catherine of Aragon. However, Emma's marriage to King Æthelred was a strategic alliance typical of medieval European courts to secure political and military support.
Step-by-step explanation:
The question "What was the purpose of Emma's marriage to King Aethelred?" seems to be misinformed as the historical context perhaps intends to discuss someone else's marriage. From the provided information, the pertinent history relates to King Henry VIII and his desire to annul his marriage to Catherine of Aragon.
Nonetheless, to clarify, Emma of Normandy was married to King AEthelred the Unready of England in the early 11th century, and later to King Cnut the Great, as a strategic alliance that illustrated the interplay of power, politics, and dynastic affairs in medieval European courts.
Such alliances were common during the time to strengthen claims, secure military support, and establish political links between kingdoms.