The Moon's Movement. Eclipses. Calendars Revision Notes

In these revision notes for The Moon's Movement. Eclipses. Calendars, we cover the following key points:

• How does the Moon move?
• What is tropical and synodic month? How do they differ from each other?
• What are the Moon phases? When do they occur?
• What are eclipses? How many eclipses are there?
• How calendars are designed? How many calendars are there?
• What factors are considered when designing a calendar?
• How to calculate the alignment period between two planets?

The Moon's Movement. Eclipses. Calendars Revision Notes

The Moon is the only natural satellite of the Earth and its closest celestial body. It is a rocky celestial body with many craters on its surface formed by asteroid strikes. The Moon was formed about 4.5 billion years ago.

Gravitational forces, like in all the other celestial bodies, are the main factors that determine the movement of the Moon. There are two different gravitational forces that determine the trajectory of the Moon: gravitational force exerted by the Sun and that exerted by the Earth on the Moon. As a result, the Moon revolves around the Earth showing always the same face to it.

The Moon makes one complete cycle around the Earth in an elliptic-shape trajectory in a similar fashion to planetary motion around the Sun, where the Earth is located in one of the ellipse foci. This cycle lasts for 27.32 days (tropical month) when the (unmoveable) stars are taken as a reference frame and 29.53 days (synodic month) when the Sun is taken as a reference frame.

Aphelion (the longest distance) of the Moon's orbit around the Earth is 407 000 km while perihelion (the shortest distance) is 356 000 km.

The different view of the Moon obtained from the Earth in different times of lunar (synodic) month determines the Moon's phases. The names of the eight phases of the Moon are, in order, new Moon (M₁), waxing crescent (M₂), first quarter (M₃), waxing gibbous (M₄), full Moon (M₅), waning gibbous (M₆), third quarter (M₇) and waning crescent (M₈).

In addition to its' orbital revolution the Moon rotates around its own axis as well. This rotation occurs at the same period as the period of revolution around the Earth (in one synodic month). This is the reason why the Moon always shows the same face to the Earth.

An eclipse is an obscuring of the light from one celestial body by the passage of another between it and the observer or between it and its source of illumination. The orbital plane of the Moon forms an angle of 5° 9' on average to that of the Earth. This small angle is the reason why eclipses occur.

There are two types of eclipses that occur on the Earths surface. They are the solar and lunar eclipses. In total solar eclipse, the Moon lays between the Sun and the Earth and therefore, it prevents almost entirely the sunlight from reaching the Earth. As a result the view is obscured. Partial solar eclipses occur when the Sun is partially blocked by the Moon, causing a partial obscuration of the view.

Lunar eclipse occur when the Earth is between the sun and the Moon. In total lunar eclipse all sunlight is blocked from reaching the Moon and as a result, it looks red when viewed from the Earth. On the other hand, in partial lunar eclipse this phenomenon occurs only partially.

Humans have invented calendars for the purpose of orientation in time. All calendars are based on the three major cycles that are visible from Earth:

1. Solar day (24.00 h) related to the self-rotation of the Earth around its axis. This cycle involves the continuous alteration of day and night.
2. Synodic month (29.53 days) related to the orbital revolution of Moon. This cycle lasts between two identical phases of Moon.
3. Solar year (365.2422 days) - otherwise known as the tropical year - which is related to the orbital revolution of the Earth around the Sun. This cycle appears through the continuous alteration of seasons.

The calendar used by majority of countries (and officially by all countries) in the world is the "Gregorian calendar". It has 365 days except the years divisible by 4, which have 366 days. This rule excludes full-century years the first two digits of which are not divisible by 4.

Years that have 366 days are known as leap years. The additional days corresponds to February 29 (regular years have 28 days on February).

Prior to Gregorian calendar introduction in 1582, a similar calendar (Julian calendar) was used in most of the world. The main difference between Julian and Gregorian calendars is that an average year in Julian calendar is 365.25 days while an average year in Gregorian calendar is 365.2422 days.

Muslim countries on the other hand, use the lunar calendar in their religious practices. This calendar based on Moon's phases is about 11 days shorter than solar ones Therefore, the duration of lunar months is 29 or 30 days, unlike in solar calendars in which a month is 30 or 31 days long (except February).

The common feature all calendars in use share is the number of months (12).

The synodic period θ (the period of two consecutive alignments with Earth) of an outer planet (from Mars to Neptune) is calculated by

and that of an inner planet (Mercury or Venus) is

where T_E and T_p are the stellar (sidereal) periods of the Earth and planet revolution respectively.