Question

assuming that average sun rises at 6:00 A.M , crosses the meridian at noon , and sets at 6:00 P.M, what are the average times for the moon's rising , crossing the meridian , and setting for each of the lunar phases [ new moon , waxing crescent , first quarter , waxing gibbous , full moon , waning gibbous , third quarter and waning crescent ] , assume that each of phases is 45 degree apart in elongation ?

Answer 1

Since it gives you the average sun rise and set, you can figure that either a new moon or full moon will be up at the top of the clock (noon).

Since at noon time, the sun is going to in the sky, this means that it wouldn't be possible to see a full moon. This tells you that a new moon then would be the phase.

So now that we know a new moon would rise around 6 am, peak at noon, and then set around 6 pm, we can establish all of the other rise/set times by simply moving symmetrically around the clock.

Full moon would be opposite, so that would be rise at 6 pm, peak at midnight, set at 6 am.

Half moons would be rise at noon, peak at 6 pm, set at midnight or rise at midnight, peak at 6 am, set at noon.

The others (gibbous and crescent) are just in between. For example, a waxing crescent would be something like: rise 9 am, peak 3 pm, set 9 pm.