Why dont the equations/properties and numbers offered by sites (including wiki) ever match up right?

Things like orbital periods and mean motion are averages over some period. By changing the averaging period, you can get slightly different values. 27.321582 days (+/- 0.0000005 days) = 27 days, 7 hours, 43.07808 minutes (+/- 0.00072 minutes). If you need accuracy better than 2 seconds, then you need to recognize that there are variations from one period to another. For example, during 2011 the difference between the shortest and longest orbit is more than 10 hours. Compared to that, 2 seconds is very small. NASA contracts out orbital calculations to the Jet Propulsion Laboratory (Cal Tech). JPL gives the orbit period as 27.321582 days; that period is an average over a few 100 years. Their value for the mean motion is 13.17635836 deg/day. I don't see how you could observe an mean motion to 12 significant digits. In any case, mean motion is averaged over anomalistic months, while orbital period is averaged over tropical months.

Nature is not that mathematical precised, you can calculate to the the nth digits the orbital period of an object, but a moment a comet comes by, it will change.

Nothing is static in space. Everything depends upon what you are measuring it relative to. All of your answers are correct. I think you are relying on general sources, you need to get more detailed information about the technicalities of orbital motions. There are four commonly recognised ways of computing the orbital period of the moon : Synodic month, which is from new moon to the next new moon - 29.53059 days Sidereal month, which is from fixed star to the same fixed star - 27.32166 days Anomalistic month, from apse to apse (nearest point to earth) - 27.55455 days (this is the one you derived from the mean daily motion). Tropical month, equinox to equinox (this refers the moon's path to the ecliptic - the apparent path of the sun) - 27.32158 days (this is obviously the one used in the Wikipedia article). Draconic month, from node to node (where the moon crosses the plane of the Earth's orbit, north to south or south to north) - 27.21222 There is no single "correct" answer to a question like this. It all depends upon how you measure it (and what purpose you want it for ).

Nothing is static in space. Everything depends upon what you are measuring it relative to. All of your answers are correct. I think you are relying on general sources, you need to get more detailed information about the technicalities of orbital motions. There are four commonly recognised ways of computing the orbital period of the moon : Synodic month, which is from new moon to the next new moon - 29.53059 days Sidereal month, which is from fixed star to the same fixed star - 27.32166 days Anomalistic month, from apse to apse (nearest point to earth) - 27.55455 days (this is the one you derived from the mean daily motion). Tropical month, equinox to equinox (this refers the moon's path to the ecliptic - the apparent path of the sun) - 27.32158 days (this is obviously the one used in the Wikipedia article). Draconic month, from node to node (where the moon crosses the plane of the Earth's orbit, north to south or south to north) - 27.21222 There is no single "correct" answer to a question like this. It all depends upon how you measure it (and what purpose you want it for ).

Nature is not that mathematical precised, you can calculate to the the nth digits the orbital period of an object, but a moment a comet comes by, it will change.