1. When the moon is located between Earth and the sun, the phase of the moon that is seen is called a New Moon. To understand this, you need to know that the moon does not produce its own light but instead reflects sunlight. During a New Moon, the side of the moon that is facing Earth is not illuminated by the sun, making it appear completely dark from our perspective.
2. When the moon is in its first-quarter phase, it is located at a right angle with respect to both Earth and the sun. This means that the sun, Earth, and the moon form a right triangle, with Earth at the right angle. In this position, the sun illuminates exactly half of the moon that is visible from Earth, creating a half-moon shape. The illuminated portion is on the eastern side, giving it the appearance of a right-facing letter "D".
3. The main difference between a waxing crescent and a waning gibbous is the amount of illumination and the shape of the moon. A waxing crescent moon is seen during the waxing phase, which means it is growing in illumination from a New Moon towards a Full Moon. It appears as a small sliver of light on the right side, resembling a crescent shape.
On the other hand, a waning gibbous moon is observed during the waning phase, as the moon is decreasing in illumination from a Full Moon towards a New Moon. It appears as a larger, mostly illuminated moon with a small portion of darkness on the right side, resembling the shape of a gibbous fruit.
4. A similarity between the first-quarter moon and the third-quarter moon is that they both appear as half-moons when viewed from Earth. The first-quarter moon is seen when the moon has completed about one-quarter of its orbit around Earth, whereas the third-quarter moon is observed when the moon has completed about three-quarters of its orbit. In both cases, exactly half of the moon that is facing Earth is illuminated by sunlight, resulting in a half-moon shape. The significant difference is the side of the moon that is illuminated, with the first quarter being illuminated on the right side and the third quarter on the left side.