the earth is just barely blocking the sun from hitting the moon
No; it comes after. In order, the phases are: New Moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third (or last) quarter, then the waning crescent.
After the first quarter, the sunlit portion is still increasing, but now it is more than half, so it is waxing gibbous. After the full moon (maximum illumination), the light continually decreases. So the waning gibbous phase occurs next.
During the weekend 27th-28th April 2013 the moon's phase was Waning Gibbous.
April 17, 2014 featured a waning gibbous moon. This phase occurs after the full moon and before the last quarter phase, where more than half but less than fully illuminated.
Waxing, as opposed to waning, is when the moon is getting bigger, going towards full. Gibbous is the phase when it's between half and full. So waxing gibbous is when it's nearly full.
Waning Gibbous, Third Quarter and Waning Crescent.
The moon is in its waning (shrinking) gibbous phase for roughly the week after the Full Moon.
Third quarter phase
It is "waning gibbous".
The Phases of the moon are Full moon,Waxing Gibbous,Waning Gibbous, Waxing Cresent, Waning Cresent and New Moon.
Waning gibbous, Third Quarter and Waning Crescent are the 'waning' moon phases.
Two weeks after the waning gibbous phase of the moon you will see a new moon.
Third Quarter.
It is a point in the waxing gibbous phase and can also a point in the waning gibbous phase, but not in the first quarter.
All of them do, if you go back far enough in the records. The last named phase immediately before the waning gibbous is the Full Moon.
(Restating the question as "What phase of the Moon follows 'waning gibbous'?) The phase of the Moon which follows 'Waning Gibbous' is 'Last Quarter'. The Gibbous phases are the periods when the Moon is more than 50% illuminated. Waxing being the period when it is approaching Full, and Waning being the period after Full, but before 'Last Quarter'. See Wikipedia entry for "Lunar Phase"
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