Final answer:
The military goal that the Panama Canal would facilitate, according to Roosevelt, was the quick movement of the U.S. Navy between the Atlantic and Pacific, showcasing American power and protecting interests. This need was highlighted by the lengthy journey of the U.S.S. Oregon during the Spanish-American War.
Step-by-step explanation:
According to President Theodore Roosevelt, the primary military goal that the Panama Canal would facilitate was the rapid deployment and movement of the United States Navy between the Atlantic and Pacific Oceans. This strategic advantage was crucial for projecting American strength, protecting American interests both domestically and abroad, and ensuring the security of new trade routes. The experience of the battleship U.S.S. Oregon during the Spanish-American War, which took two months to travel around South America to reach Cuba, underscored the critical need for a shortcut, validating Roosevelt's pursuit of a canal in Central America.
The construction of the canal was also intertwined with Roosevelt's foreign policy principles, encapsulated in the Roosevelt Corollary to the Monroe Doctrine, which asserted the United States' right to intervene in Latin American countries to maintain stability and prevent European colonization. Roosevelt's actions in facilitating Panama's independence from Colombia and in negotiating the Hay-Bunau-Varilla Treaty, which granted the United States control over the Canal Zone, were directly linked to these broader military and strategic goals.