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Today, Oct. 1, 2024, the moon is 28 days old and is in the New Moon phase of its lunar cycle. It is 1% illuminated. 

The phases of the moon are a consequence of its motion around Earth in relation to the geometry assumed with respect to the sun. To better understand how it works, let us, first of all, remember that the moon does not emit its own light but reflects that of the sun and partly that reflected by the Earth–phenomenon of ashen light.

Of the moon, we always see a hemisphere and a little more because its rotation is synchronous and blocked by the tide. This means that one lunar rotation on its axis corresponds to the time of revolution around Earth, equal to 29.5 days. On a daily basis, the moon appears to move eastward in the sky by 12°, and this determines different angles of its illumination by the sun. As it orbits Earth, the moon will show different illuminated parts based on the angle to the sun and hence the phases of a lunation. Although these lighting variations are gradual, traditionally, only four moments are identified, which are also useful for regulating the ancient calendars.

They are in order, New Moon, First Quarter, Full Moon, and  Last Quarter.

The substantial difference is in the illumination percentage of the side facing the Earth. In the new moon phase, this percentage is 0% and becomes 100% at Full moon, about 14 days later. Thanks to the regular repetition of these moments, since ancient times, the lunar phases have been the basis of the lunisolar calendar.

However, it was difficult to establish the exact moment of the new moon, therefore, many ancient civilizations started the lunar month with the appearance of the first crescent after sunset. However, this is a very simplified description since the lunar motion is actually very complex, and the perspective with which we see the near side constantly changes, getting to see almost 60% of the lunar surface thanks to the phenomenon called libration.

The production of the phases depends on the Earth-moon-sun geometry and on the revolution motion of the moon around the Earth. Moving towards the east, our satellite rises later every day, and this is the reason why we see it in different positions at the same time. Approximately every day the moon delays its rising (and setting) by about 50 minutes, and this explains why the waxing becomes better visible a few days after the new moon as the elongation from the sun increases and further and further eastward.

According to this reasoning, the maximum delay is at the new moon (24 hours) but also the minimum (0 hours) with the start of a new cycle.

Tides are periodic changes in sea level known since ancient times. The phenomenon was explained satisfactorily by Isaac Newton, attributing it to the gravitational attraction exerted by the moon and the sun. We can consider the gravitational attraction exerted by the other planets to be negligible, therefore the greatest effects on the Earth will be those produced by the sun and the moon. These three bodies attract each other, however, the greatest effect is in the Earth-moon interaction.

Both the moon and the Earth undergo a deformation along the line joining them,  however, it is the fluid masses of the oceans that undergo the most significant deformations with the formation of a swelling.

In addition to the swelling along the joining line, a diametrically opposite one on the other side of the Earth is formed due to the centrifugal force. The bulges move with the rotation of the moon around the Earth. An observer on the Earth’s surface as the bulge approaches will see the sea level rise and then fall after it is exceeded. This observed phenomenon is called a tide. When the sea level is minimum, it is called low tide, while when it is maximum, it is a phase of high tide.

The difference in height between the height of high tide and low tide is defined as a tidal range. The behavior of the tides is influenced by the orography and shape of the basins, size, and depth. Two to four tides can occur in one day. If there is one high and one low tide, we speak of diurnal tides, while if there are two high and two low tides, these are called semi-diurnal tides. During diurnal tides, the excursion is minimal, while for diurnal tides, the difference in level can also be considerable. It also depends on the height of the moon above the equator as a result of its inclined orbit. The sun also affects the tides, albeit less so than the moon, by attracting masses of water. The solar role is additive to the lunar one therefore, the respective geometry also influences the tides.

When the moon is New or Full, the tides are maximum because the attraction forces of the sun and the moon add up. When the moon is in the First or Last Quarter, forming a 90° angle with the sun and the Earth, the tides are minimal because the attractive forces of the sun and moon oppose each other. To predict the magnitude of the tide we will also consider the position of the sun.