You do not need a clock to determine longitude. In fact, a sextant can be used, as long as you have the appropriate tables that map various celestial angles to the correct date and time. These tables were originally overseen by Nevil Maskelyne, one of Harrison's rivals to the longitude prize. The two methods are an early instance of the closed-tech vs open-tech argument we're so used to now. Maskelyne argued that mariners should not depend on Harrison's (closed) bespoke clocks. Instead, he said that open information (the Royal Observatory's tables) should be used with open tech (the sextant) to solve the problem. But Harrison's clocks were so easy to use that his solution won the prize. Sound familiar? Do read Dava Sobel's excellent book on the subject; it's excellent.

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