When the moon is full, fully lit by the sun, will it appear full everywhere on the planet?
E.g. if I where to set the date for the next three full moons for say: Sweden, Bali and Seattle how different would those dates be?
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[This is intended to supplement @userLTK's answer and reaches the same conclusion.]
By definition, the Moon is full when its ecliptic longitude is exactly 180 degrees greater than the Sun's ecliptic longitude for a theoretical geocentric observer (first paragraph of https://en.wikipedia.org/wiki/Full_moon and definition of "full moon" at http://www.ncsm.city.nagoya.jp/astro/astrotool/glossary.html but couldn't find a 100% reliable resource).
By this definition, your location on Earth doesn't matter, since the full moon is defined by a theoretical observer.
Realistically, the moon's position for an observer on the surface of the Earth can differ by as much as a degree from the geocentric position. (This is the arctangent of 1/60, since the moon's distance is about 60 times the Earth's radius.)
Since the moon circles the ecliptic once every 27.321662 days or so (its "sidereal period"), its ecliptic longitude increases by about 0.55 degrees per hour.
Thus, roughly speaking, the "full moon" at a given point on Earth can differ by as much as ±1.8 hours from the true full moon. By this token, it takes the "full moon" about 3.6 hours to cross the Earth.
Of course, all of this refers to the moon's geometric position. If you allow for refraction, the results could be slightly different, especially since both the sun and moon experience over 0.5 degree refraction when rising/setting and the full moon rises right about when the sun sets and vice versa.
As others have said, the full moon (date and time) is set by when the center of the Moon passes over or under a line that passes from the center of the sun through the center of the Earth. That gives the full moon a precise time, to the minute, that's the same everywhere on earth, provided you adjust for timezone.
The "over or under" is important, cause mostly the Moon doesn't orbit in the same plane as the Earth's orbit, so it's usually above or below that line drawn from the sun through the center of the Earth. If it's near the Spring or Fall Equinox and they are more lined up, and the Moon passes very close to the line, then it passes through the Earth's shadow. In the sense of being a full circle in the sky, the Moon is never that, because that would require the Moon be in the Earth's shadow. That's why full moon's often appear wider than they are tall. A full moon often appears like a squashed ball, not a circle. Because by definition, a full Moon is full East to West, but not North to South. It remains within about 6 degrees of full North to South all the time, so that's generally ignored.
But, unlike the new-years countdown, which happens one hour later for every timezone, the full moon moment happens the same time everywhere on Earth, day or night and whether the moon is visible in the sky or not.
Unlike sunsets, most of us see the full moon as lasting the entire night and perhaps, even back to back nights. The specific minute of the full moon doesn't strike most of us as particularly relevant. "The moon is full tonight" is still a perfectly good thing to say, and "The moon was full 10 minutes ago, dang we missed it", would frankly be a strange thing to say, unless you wanted to catch it at Moonrise or Moonset - which can make for some great low to the horizon moon watching.
But, if we look at the full moon as the night when it's fullest, then you have up to a 12 hour difference, depending on longitude, because night begins 12 hours later on one side of the globe, than on the other. (And the moon moves across the sky, so this takes a bit longer than 12 hours, but lets not get into that).
Now, if you wanted to get silly-fussy and you wanted to know when the Moon would appears fullest to you. That's not an official fullest time, but that does change slightly depending on your longitude. It takes about 3 1/2 hours for the Moon to cross the Earth's diameter, so when it appears fullest varies by about that much time, depending on where you are on the earth and if the moon is visible. Our eyes can't detect a change in fullness that occurs over a 3.5 hour period. It's too small, so this is kind of an irrelevant point and not astronomically relevant, but if you wanted to define the moment when the Moon is visually fullest, not just the moment when it passes over or under the line through the center of the Earth, that would give you about 3.5 hours of variation from one side of the Earth to the other. I've never heard of anyone who felt that distinction was of particular use.
The correct answer is that the astronomical full moon happens the same time everywhere on Earth. The point of view answer can give you variations of up to 12 hours if you consider full moon starting on the rise of the full moon during the night of the full-moon, or 3.5 hours if you fuss over the precise longitude of Earth as the measuring point of when the Moon appears 100% fullest. But those are point of view answers and not astronomical answers. Officially The Moon is full everywhere on Earth at the same precise minute.
The moon phase is corresponding to the position of the moon round the earth. The peak of full moon is the same time. At this time, one side of the world that can see the peak of full moon and another side not.
As the phase change is much slower than earth rotation, another side of the world can see near full moon at the moon-set or at the moon-rise, a few hours before or after the peak of full moon, depending on location. While it is not at the peak, by comparing to previous and next day, it is still perceived as full moon on this day.
Therefore, whether Sweden, Bali and Seattle can see this peak at the same time, it varies on each full moon. But their longitude varies too much, it is impossible for three places to see this peak at the same time. At least one of them is facing away from the moon at the peak of full moon.
The points in time where the Moon is new/1st quarter/full/last quarter are defined to be from a geocentric point of view.
The plane defined by Sun, Earth/Moon barycenter, Moon separates those that can see a full Moon - i.e., the ones on that plane and the ones closer to the Sun - from those who have to wait a little.