In the Phase Simulator, as you drag the Moon around the Earth, you can observe how the angle between the Sun, Earth, and Moon affects the appearance of the Moon's phase. Here's a general breakdown of how the angle correlates with the Moon phases:
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New Moon (Angle = 0°): When the angle is 0 degrees, the Moon is directly between the Earth and the Sun. The side of the Moon facing the Earth is in shadow, making the Moon appear completely dark.
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Waxing Crescent (Angle 0° < Angle < 90°): As the angle increases, the Moon begins to show a sliver of light. The illuminated part of the Moon starts to become visible from Earth, resembling a crescent shape.
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First Quarter (Angle = 90°): At an angle of 90 degrees, half of the Moon is illuminated (the right side when viewed from the Northern Hemisphere), and it appears as a half Moon.
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Waxing Gibbous (Angle 90° < Angle < 180°): As the angle continues to increase past 90 degrees, more than half of the Moon becomes illuminated. This stage is called waxing gibbous, with the illuminated portion growing larger.
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Full Moon (Angle = 180°): At an angle of 180 degrees, the Earth is between the Sun and the Moon. The entire side of the Moon facing Earth is illuminated, making it appear as a full circle.
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Waning Gibbous (Angle 180° < Angle < 270°): As the angle decreases from 180 degrees, the illuminated portion of the Moon begins to shrink, transitioning from a full Moon to a waning gibbous phase.
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Last Quarter (Angle = 270°): At an angle of 270 degrees, half of the Moon is illuminated again (the left side when viewed from the Northern Hemisphere), resembling a half Moon once more, but in a different orientation than the first quarter.
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Waning Crescent (Angle 270° < Angle < 360°): As the angle approaches 360 degrees, the Moon shows a small crescent shape that decreases until it returns to the new Moon phase.
Overall, the varying angle between the Sun, Earth, and Moon directly correlates with the amount of sunlight reaching the Moon and the portion visible from Earth, thus determining the Moon's phase.