The Iron Pearl of Manoa Lai, known as the Sphere of Manaurai in the European release of the game, is a salvage item found in the first Endless Ocean. This strange sphere is found in the Great Aqua Cave in the White Room (at coordinates E-4 and a depth of eleven meters, or thirty-six feet).
Your footlocker's descriptive text on the Gabbiano notes: "A mysterious metal sphere that was found in an underwater cavern. The surface is carved in ancient writings." Katharine states that she doesn't know how the sphere was made to be so smooth, as it looks ancient, and humans back then presumably didn't have the technology to achieve this level of uniform polishing.