Final answer:
Science cannot precisely predict the date when the sun will burn out, because it is a far-future event that is beyond the realm of empirical science and current methodologies.
Step-by-step explanation:
The question which science cannot answer is 'What will be the date when the sun burns out?' While science can make predictions based on current understanding of stellar lifecycles, the precise date of such a far-future event remains speculative and falls more into the realm of philosophical inquiry than empirical science. The other questions listed can be answered using the scientific method and our current understanding of astronomy and biology.