Scientists measure the Moon's rotation period by observing its synchronous rotation with Earth, where a lunar day matches a lunar month at approximately 27.3 days. This synchronization is due to tidal friction, which has gradually slowed the Moon's rotation until it is locked to Earth. To calculate the lunar month, observers can track the time it takes for the Moon to cross a bright star and note the interval until it crosses again, roughly 28 days later. For measuring the lunar day, one can assess the angle of craters' edges relative to the Moon's surface. Resources on these methods can be found in astronomical literature and studies on lunar dynamics.