What is the definition of sunrise/sunset and moonrise/moonset, especially regarding the exact times of day when they occur?
Sunset occurs when the upper edge of the Sun — called the upper limb — sinks just under the horizon; sunrise occurs when the upper limb rises just above the horizon. The same is true for the Moon. These events can happen earlier or later than expected because the atmosphere bends the light rays near the horizon in such a manner that the Sun and Moon can appear to be above the horizon when they are already (or still, in the case of sunrise and moonrise) beneath it.
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