Features:

  1. This is a diagram which is not-to-scale of the Earth-Moon system viewed from the north celestial pole (NCP) side of the celestial sphere.

    Therefore on the diagram, east is counterclockwise and west is clockwise.

    Recall, as usual in astronomy, that east and west are actually angular directions.

  2. The Sun is so far to the right of the diagram that light rays from it are parallel to high accuracy.

  3. The left sides of the Earth and Moon are the night sides.

  4. The Earth rotates eastward (i.e., counterclockwise) daily and the Moon revolves eastward (i.e., counterclockwise) in a lunar month.

  5. Now simple lunar phase questions often seem very difficult to people.

    But once you get the hang of them, they are easy.

  6. They are sort of analogous to a problem in algebra with one equation and THREE VARIABLES.

    You can solve for any ONE variable if you know the other TWO.

    The three "variables" are:

    1. Lunar phase or phase of the Moon.

    2. Location of Moon in the sky: eastern horizon, eastern sky, near the meridian (AKA celestial meridian), western sky, western horizon, and somewhere below the horizon.

      Remember the Moon is always near the ecliptic: i.e., in a day, it will be carried around with the celestial sphere on almost the same arc on the sky as the Sun.

    3. Time of solar day: e.g., sunrise, noon, sunset, and midnight. (Time is also the same as location on the Earth in these problems.) People often find this the hardest one to solve for if it is unknown.

  7. The diagram is a sort of an analog computer that relates the THREE VARIABLES.

    Just identify the two variables you know on the diagram and the third variable is then identifiable.

  8. "You" (AKA the Alien) locates various times of day.

    "Your head" points toward the local meridian.

  9. Recall, the diagram is not-to-scale.

    In particular, the Earth and Earth-Moon are actually small compared to the Earth-Moon distance, but "you" are actually a pinprink on the Earth which looks like an infinite plane to "you".

  10. For example, at face-value, the diagram shows "you" CANNOT see the exact full moon at exact sunset since it is below "your" horizon at that moment.

    And this is actually true for exact lunar opposition. You CANNOT see the center of the Moon rise at exact sunset when the center of the Sun sets.

    But the Earth is relatively small, and Moon and Sun have finite sizes, and so "you" see the Moon rise as the Sun sets or "you" see that so nearly as to make no difference to casual description.

  11. We do NOT usually worry about finicky effects due to the finite sizes of Earth, Moon, and Sun when answering simple lunar phase questions.

  12. Also NOTE that the Moon takes a lunar month = 29.53059 days (mean J2000 to 7 digits) ≅ 29.5 days to go eastward from new moon to new moon and the Earth rotates eastward once per day.

    Thus to 1st order and as a vast SIMPLIFICATION in using the diagram, "you" can take the Moon as fixed on the rotating celestial sphere and fixed in phase for any single day.