question: why you can see the moon for so long during the day when the sun is fully in the sky?
comment: The full moon is 180 degrees opposite the sun and will only be in the sky directly across from the sun for brief periods at dawn and dusk. The other phases of the moon are closer to the sun, until you get to the barely visible new moon phase where they're together but the moon is dark. As the moon approaches the sun, you'll see less illumination on the surface but it will be visible for more daylight hours. Thin crescent moons are mostly visible in daylight and only briefly at night.
passages: A full moon is often thought of as an event of a full night's duration. This is somewhat misleading because its phase seen from Earth continuously waxes or wanes (though much too slowly to notice in real time with the naked eye). By definition, its maximum illumination occurs at the moment waxing stops. For any given location, about half of these maximum full moons may be visible, while the other half occurs during the day, when the full moon is below the horizon.
   At a major lunar standstill, the Moon's range of declination, and consequently its range of azimuth at moonrise and moonset, reaches a maximum. As a result, viewed from the middle latitudes, the Moon's altitude at upper culmination (the daily moment when the object appears to contact the observer's meridian) changes in just two weeks – from highest to lowest above the horizon due north or south, depending on the observer's hemisphere. Similarly, its azimuth at moonrise changes from northeast to southeast and at moonset from northwest to southwest. Solar eclipses at ascending node occurs in March, solar eclipses at descending node occurs in September. Lunar eclipses at descending node occurs in March, lunar eclipses at ascending node occurs in September.
   Section::::Visual presentation.:The Moon.
  
  Earth's Moon is a grey disc in the sky with cratering visible to the naked eye. It spans, depending on its exact location, 29-33 arcminutes - which is about the size of a thumbnail at arm's length, and is readily identified. Over 27.3 days, the moon goes through a full cycle of lunar phases. People can generally identify phases within a few days by looking at the moon. Unlike stars and most planets, the light reflected from the moon is bright enough to be seen during the day. (Venus can sometimes be seen even after sunrise.)
   The Moon's highest altitude at culmination varies by its phase and time of year. The full moon is highest in the sky during winter (for each hemisphere). The 18.61-year nodal cycle has an influence on lunar standstill. When the ascending node of the lunar orbit is in the vernal equinox, the lunar declination can reach up to plus or minus 28° each month. This means the Moon can pass overhead if viewed from latitudes up to 28° north or south (of the Equator), instead of only 18°. The orientation of the Moon's crescent also depends on the latitude of the viewing location; an observer in the tropics can see a smile-shaped crescent Moon. The Moon is visible for two weeks every 27.3 days at the North and South Poles. Zooplankton in the Arctic use moonlight when the Sun is below the horizon for months on end.
   Because of the inclination of the Moon's orbit with respect to the Earth's equator, the Moon is above the horizon at the North and South Pole for almost two weeks every month, even though the Sun is below the horizon for six months at a time. The period from moonrise to moonrise at the poles is a tropical month, about 27.3 days, quite close to the sidereal period. When the Sun is the furthest below the horizon (winter solstice), the Moon will be full when it is at its highest point. When the Moon is in Gemini it will be above the horizon at the North Pole, and when it is in Sagittarius it will be up at the South Pole.
   Atmospheric refraction – the bending of the light from the Moon as it passes through the Earth's atmosphere – alters the observed declination of the Moon, more so at low elevation, where the atmosphere is thicker (deeper).
  
  Not all the maxima are observable from all places in the world – the Moon may be below the horizon at a particular observing site during the maximum, and by the time it rises, it may have a lower declination than an observable maximum at some other date.
  
  Section::::2006 standstill.
   At higher latitudes, there will be a period of at least one day each month when the Moon does not rise, but there will also be a period of at least one day each month when the Moon does not set. This is similar to the seasonal behaviour of the Sun, but with a period of 27.2 days instead of 365 days. Note that a point on the Moon can actually be visible when it is about 34 arc minutes below the horizon, due to atmospheric refraction.
   Moonlight
  
  Moonlight consists of mostly sunlight (with little earthlight) reflected from the parts of the Moon's surface where the Sun's light strikes.
  
  Section::::Illumination.
  
  The intensity of moonlight varies greatly depending on its phase, but even the full Moon typically provides only about 0.05–0.1 lux illumination. When the full Moon is at perigee and viewed around upper culmination from the tropics, the illuminance can reach up to 0.32 lux. From Earth, the apparent magnitude of the full Moon is only about that of the Sun.
   The Moon's average orbital distance is , or 1.28 light-seconds. This is about thirty times the diameter of Earth. The Moon's apparent size in the sky is almost the same as that of the Sun, since the star is about 400 times the lunar distance and diameter. Therefore, the Moon covers the Sun nearly precisely during a total solar eclipse. This matching of apparent visual size will not continue in the far future because the Moon's distance from Earth is gradually increasing.
   In effect, this means that the "tropical year" on the Moon is only 347 days long. This is called the draconic year or eclipse year. The "seasons" on the Moon fit into this period. For about half of this draconic year, the Sun is north of the lunar equator (but at most 1.543°), and for the other half, it is south of the lunar equator. Obviously, the effect of these seasons is minor compared to the difference between lunar night and lunar day. At the lunar poles, instead of usual lunar days and nights of about 15 Earth days, the Sun will be "up" for 173 days as it will be "down"; polar sunrise and sunset takes 18 days each year. "Up" here means that the centre of the Sun is above the horizon. Lunar polar sunrises and sunsets occur around the time of eclipses (solar or lunar). For example, at the Solar eclipse of March 9, 2016, the Moon was near its descending node, and the Sun was near the point in the sky where the equator of the Moon crosses the ecliptic. When the Sun reaches that point, the centre of the Sun sets at the lunar north pole and rises at the lunar south pole.
   Typically, a number of high ridges undergoing sunrise or sunset can view it. Although the Moon is in Earth's umbra, both the Sun and an eclipsed Moon can be simultaneously seen because atmospheric refraction causes each body to appear higher in the sky than their true geometric positions.
  
  Section::::Danjon scale.
  
  The following scale (the Danjon scale) was devised by André Danjon for rating the overall darkness of lunar eclipses:
  
  Section::::Lunar versus solar eclipse.
   Sunrise occurs at the prime meridian when the Lunar phase reaches First Quarter, after one fourth of a lunar day. At this location the selenographic colongitude at sunrise is defined as 0°. Thus, by the time of the Full Moon the colongitude increases to 90°; at Last Quarter it is 180°, and at the New Moon the colongitude reaches 270°. Note that the Moon is nearly invisible from the Earth at New Moon phase except during a solar eclipse.
   Finally, the Moon's perigee is moving forwards or precessing in its orbit and makes a complete circuit in 8.85 years. The time between one perigee and the next is slightly longer than the sidereal month and known as the anomalistic month.
   For example, after taking refraction and parallax into account, the observed maximum on 15 September in Sydney, Australia was several hours earlier, and then occurred in daylight. The table on the right shows the major standstills that were actually visible (i.e. not in full daylight, and with the Moon above the horizon) from both London, UK, or Sydney, Australia.
   Another interesting phenomenon visible with the naked eye is Earthshine. Best visible shortly before or after new a moon (during the waning and waxing crescent phases respectively), Earthshine is the faint glow of the non-illuminated (night) side of the Moon caused by sunlight reflecting off the surface of Earth (which would appear nearly full to an observer situated on the Moon at this time) and onto the night side of the Moon. By the time the Moon reaches first its quarter however, the sunlight illuminated portion of the Moon becomes far too bright for Earthshine to be seen with the naked eye, however it can still be observed telescopically.
   The Moon is a very commonly observed astronomical object, especially by amateur astronomers and skygazers. This is due to several reasons: the Moon is the brightest object in the night sky, the Moon is the largest object in the night sky, and the Moon has long been significant in many cultures, such as being the basis for many calendars. The Moon also does not require any kind of telescope or binoculars to see effectively, making it extremely convenient and common for people to observe.
   Because the Moon is relatively close to the Earth, lunar parallax alters declination up to 0.95° when observed from Earth's surface versus geocentric declination, the declination of the Moon from the center of the Earth. Geocentric declination may be up to about 0.95° different from the observed declination. The amount of this parallax varies with latitude, hence the observed maximum of each standstill cycle varies according to position of observation.
   All full moons rise around the time of sunset. Since the Moon moves eastward among the stars faster than the Sun, lunar culmination is delayed by about 50.47 minutes (on average) each day, thus causing moonrise to occur later each day.
   Among the most prominent features of the Moon's sky is Earth. Earth's angular diameter (1.9°) is four times the Moon's as seen from Earth, although because the Moon's orbit is eccentric, Earth's apparent size in the sky varies by about 5% either way (ranging between 1.8° and 2.0° in diameter). Earth shows phases, just like the Moon does for terrestrial observers. The phases, however, are opposite; when the terrestrial observer sees the full Moon, the lunar observer sees a "new Earth", and vice versa. Earth's albedo is three times as high as that of the Moon (due in part to its whitish cloud cover), and coupled with the wider area, the full Earth glows over 50 times brighter than the full Moon at zenith does for the terrestrial observer. This Earth light reflected on the Moon's un-sunlit half is bright enough to be visible from Earth, even to the unaided eye – a phenomenon known as earthshine.
   Many almanacs list full moons not only by date, but also by their exact time, usually in Coordinated Universal Time (UTC). Typical monthly calendars that include lunar phases may be offset by one day when prepared for a different time zone.
  
  Full moon is generally a suboptimal time for astronomical observation of the Moon because shadows vanish. It is a poor time for other observations because the bright sunlight reflected by the Moon, amplified by the opposition surge, then outshines many stars.
   The arc path of the full Moon generally reaches its widest in midwinter and its narrowest in midsummer. The widest arc path of the new Moon (when it near the Sun in the sky) is in the summer, as for the Sun.
   Contrary to popular belief, the Moon should ideally not be viewed at its full phase. During a full moon, rays of sunlight are hitting the visible portion of the Moon perpendicular to the surface. As a result, there is less surface detail visible during a full moon than during other phases (such as the quarter and crescent phases) when sunlight hits the Moon at a much shallower angle. The brightness of a full moon as compared to a phase where a smaller percentage of the surface is illuminated tends to wash out substantial amounts of detail and can actually leave an afterimage on an observer's eye that can persist for several minutes. First quarter (six to nine days past new moon) is generally considered the best time to observe the Moon for the average stargazer. Shadows and detail are most pronounced along the "terminator", the dividing line between the illuminated (day side) and dark (night side) of the Moon.
   BULLET::::- The full moon covers only about 0.2 deg of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly 0.5 deg), so the moon's disk covers a circular area of:  × (), or 0.2 square degrees.
  
  BULLET::::- Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only 0.2 deg as well.
  
  BULLET::::- It would take times the full moon (or the Sun) to cover the entire celestial sphere.
   However, because the 18.6-year cycle of standstills is so much longer than the Moon's orbital period (about 27.3 days) that the change in the declination range over periods as short as half an orbit is very small. The period of the lunar nodes precessing in space is slightly shorter than the lunar standstill interval due to Earth's axial precession, altering Earth's axial tilt over a very long period relative to the direction of lunar nodal precession. Simply, the standstill cycle results from the combination of the two inclinations.
  
  Section::::Apparent position of the Moon during standstill.
   The distance between the Moon and Earth varies from around to at perigee (closest) and apogee (farthest), respectively. On 14 November 2016, it was closer to Earth when at full phase than it has been since 1948, 14% closer than its farthest position in apogee. Reported as a "supermoon", this closest point coincided within an hour of a full moon, and it was 30% more luminous than when at its greatest distance because its angular diameter is 14% greater and formula_1. At lower levels, the human perception of reduced brightness as a percentage is provided by the following formula:
  