Work out moon rise and set instantly with clear inputs, formula shown and shareable results.
The Moon rises on average 50 minutes later each day because it moves about 13 degrees eastward daily against the stars. Tracking days since a known new moon gives its age within the 29.53 day synodic month, and the phase then predicts roughly when it rises: new near sunrise, first quarter near midday, full near sunset.
Moon age
age = days since a known new moon, modulo 29.530589
Daily rise lag
about 50 minutes later each day
Because it orbits Earth eastward, so the Earth must turn a little further each day to bring it back to the horizon.
It gives the phase within a day and rise time within an hour or two. Precise times need the Moon's declination and orbital eccentricity.