Final answer:
The Portuguese captain who circumnavigated the Earth for Spain was Ferdinand Magellan, and it took his crew three years to complete the journey from 1520 to 1525, confirming the Earth's roundness and necessitating the creation of the International Date Line.
Step-by-step explanation:
The Portuguese captain and his crew, at the service of Spain, who is mentioned for proving that the earth was round by circumnavigating it, is none other than Ferdinand Magellan. It took Magellan's fleet an incredible three years to complete their journey around the globe.
They embarked on their expedition in 1520 and completed it in 1525. Although Magellan died mid-voyage, his fleet's achievement significantly advanced European geographical knowledge and played a pivotal role in the history of exploration.
The voyage also had an enormous human cost, and out of the original 237 men and five ships that set out on the journey, only 18 men and one ship survived to return to Spain.
Not only did Magellan's journey prove the roundness of the Earth, but it also helped to establish the need for an International Date Line due to the discrepancy in the date recorded by the sailors upon their return to Europe.
This exploration also reinforced political and economic rivalry between Spain and Portugal. The two kingdoms had divided the world into two spheres of influence through the Treaty of Tordesillas; however, Magellan's circumnavigation further strained relations, which was later addressed by the Treaty of Zaragosa.