Chapter 22.2: The Earth-Moon-Sun System Notes

Motions of Earth

The two main motions of Earth are rotation and revolution.
Precession is a third and very slow motion of Earth’s axis.

Rotation

Rotation is the turning, or spinning, of a body on its axis.
Two measurements for rotation:
- Apparent solar day: The time interval from one noon to the next, about 24 hours.
- Sidereal day: The time it takes for Earth to make one complete rotation ( $360^{\circ}$ ) with respect to a star other than the sun—23 hours, 56 minutes, 4 seconds.
- The difference between apparent solar day and sidereal day comes from the fact that the direction to distant stars barely changes from day to day because of Earth's revolution around the sun.
- The direction to the sun from one day to the next changes by almost 1 degree.

Earth's Day Measurements:

Apparent Solar Day:
- The most familiar measurement of a day.
- The time interval from one noon to the next, approximately 24 hours.
- Noon is when the sun has reached its highest point in the sky.
Sidereal Day:
- The time it takes for Earth to make one complete rotation with respect to a star other than the sun.
- A period of 23 hours, 56 minutes, and 4 seconds.

Why Use Mean Solar Day Instead of Sidereal Day?

In sidereal time, noon occurs 4 minutes earlier each day, so after 6 months, noon would occur at midnight.
Sidereal time is more useful to astronomers because stars appear in the same position every 24 sidereal hours.

Revolution of Earth

Earth orbits the sun in an elliptical path, maintaining an average velocity of 107,000 kilometers per hour.
The average distance from the sun is approximately 150 million kilometers, but the elliptical nature of Earth's orbit leads to variations in its distance from the sun.
Revolution is the motion of a body, such as a planet or moon, along a path around some point in space.
Earth revolves around the sun in an elliptical orbit.
- Perihelion: Earth is closest to the sun (approximately 147 million km) on January 3rd. Earth receives the most sunlight and experiences its shortest distance from the sun.
- Aphelion: Earth is farthest from the sun (approximately 152 million km) on July 4th. Earth is farthest from the sun and receives less sunlight.
Because of Earth's annual movement around the sun, each day the sun appears to move among the constellations. The apparent annual path of the sun against the backdrop of the celestial sphere is called the ecliptic.

The Ecliptic

The ecliptic is the apparent path that the sun takes through the sky as observed from Earth.
It is an imaginary line that represents the plane of Earth's orbit around the sun.
The ecliptic is tilted at an angle of approximately $23.5$ degrees relative to Earth's equatorial plane, which is why we have seasons.
Throughout the year, the sun appears to move along the ecliptic, crossing through different zodiac constellations.
This path is important for astronomers and astrologers alike, as it helps determine the position of celestial objects in the sky.

Earth’s Axis and Seasons

The plane of the ecliptic is an imaginary plane that connects Earth’s orbit with the celestial sphere.
Earth's axis of rotation is tilted about $23.5$ degrees toward the plane of the ecliptic.
Because of the inclination of Earth’s axis to the plane of the ecliptic, Earth has its yearly cycle of seasons.
When the position of the sun is plotted on the celestial sphere over a period of a year's time, its path intersects the celestial equator at two points; spring equinox (March 19 or 20) and autumnal equinox (September 22 or 23) from a Northern Hemisphere point of view.
On June 20 or 21, the date of the summer solstice, the sun appears $23.5$ degrees north of the celestial equator. Six months later, on December 21 or 22, the date of the winter solstice, the sun appears $23.5$ degrees south of the celestial equator.

Precession

Precession is the slow movement of Earth.
Earth's axis varies in tilt between $21.5^{\circ}$ and $24.5^{\circ}$ with a repeating period of 41,000 years. This shifting axis is important in affecting climate change.
In addition, the direction in which the axis points continually changes. This movement is very similar to the wobble of a spinning top.

Reference Points for Mean Solar Day and Sidereal Day

Mean Solar Day:
- Measured using the sun as a reference point.
- The time it takes for the sun to return to its highest point in the sky (noon).
- Aligns with our daily cycle of light and darkness.
Sidereal Day:
- Measured using a star other than the sun as a reference point.
- The time it takes for the Earth to complete one full rotation on its axis relative to the distant stars.

Why These Reference Points Give Different Results:

Distant Star: The direction from Earth to a distant star barely changes over time because of the vast distance between Earth and the star.
Sun: The direction from Earth to the sun changes each day. Earth revolves about one degree in its orbit around the sun every day, causing a noticeable change in its direction.

Motions of the Moon-Earth System

Moon's Orbit

Because the moon's orbit is elliptical, its distance to Earth varies.
- Perigee: The moon is closest to Earth.
- Apogee: The moon is farthest from Earth.
The terms perigee and apogee are also used to describe the closest and farthest orbital points of artificial satellites orbiting Earth.

Phases of the Moon

On a monthly basis, we observe the phases of the moon as a change in the amount of the moon that appears lit.
The phases of the moon are the progression of changes in the moon’s appearance during the month.
Lunar phases are a result of the motion of the moon and the sunlight that is reflected from its surface.
About two days after the new moon, a thin sliver (crescent phase) appears at the right side of the moon, low in the western sky just after sunset.
During the following week, the lighted portion of the moon visible from Earth increases (waxing) to a half circle (first-quarter phase) and is visible from noon to midnight.
A week later, the full disk (full-moon phase) can be seen rising in the east as the sun is sinking in the west.
During the next two weeks, the percentage of the moon that can be seen decreases (waning), until the moon disappears altogether (new-moon phase).
The cycle begins again with the reappearance of the crescent moon.
Lunar phases are caused by the changes in how much of the sunlit side of the moon faces Earth.

Lunar Motions

The synodic month is based on the cycle of the moon’s phases. It lasts $29 \frac{1}{2}$ days.
The sidereal month is the true period of the moon’s revolution around Earth. It lasts $27 \frac{1}{3}$ days.
The cycle from new moon to full moon and back to new moon takes about 29 days, or one synodic month.
However, a synodic month is the apparent period of the moon's revolution around Earth. The true period which takes only $27 \frac{1}{3}$ days, is known as the sidereal month.
*Note that as the moon orbits Earth, the Earth-moon system also revolves in an orbit around the sun. Even after the moon has made a complete revolution around Earth, it is not yet directly between Earth and the sun. It takes another two days for the moon to reach its starting position (relative to the sun).

Moon Rotation

The same side of the moon constantly faces Earth.
It takes the moon the same amount of time to rotate (spin) on its axis as it does to revolve around Earth.
Both motions (moon rotation and the moon revolution) take 27 days. So, as the moon revolves around Earth, the same side of the moon is always facing Earth.
Humans had their first views of the far (or back) side of the moon only when artificial satellites with cameras orbited the moon and took the first pictures of the far side.
The far side of the moon appears to have many more craters than the side we see. One reason for this is that the far side is constantly pointed toward space.

Daylight Period on the Moon:

The length of one daylight period on the moon is two Earth weeks.
Since the moon rotates on its axis only once every $27 \frac{1}{3}$ days, any spot on the moon's surface has two weeks of daylight followed by two weeks of night.
This partially accounts for the high temperature of $127^{\circ}C$ on the day side of the moon and the low temperature of $-173^{\circ}C$ on its night side.

Eclipses

Solar eclipses: Occur when the moon moves in a line directly between Earth and the sun, casting a shadow on Earth. This situation occurs during new-moon phases.
Lunar eclipses: Occur when the moon passes through Earth’s shadow. This situation occurs during full-moon phases.

Why Eclipses Don't Occur Every Month

If the orbit of the moon lay exactly along the plane of Earth's orbit around the sun, then we would have one solar and lunar eclipse each month.
However, the moon's orbit is inclined about 5 degrees to the plane that contains Earth and the sun.
During most new-moon phases, the shadow of the moon misses Earth (passes above or below).
Similarly, during most full-moon phases, the shadow of Earth misses the moon.
During a new-moon or full-moon phase, the moon's orbit must cross the plane of the ecliptic for an eclipse to take place.
Because these conditions are normally met only twice a year, the usual number of eclipses is four. These occur as a set of one solar and one lunar eclipse, followed six months later with another set.

Total Lunar Eclipse

During a total lunar eclipse, Earth's circular shadow can be seen moving slowly across the disc of the full moon.
When totally eclipsed, the moon is completely within Earth's shadow but is still visible as a coppery disk. This happens because Earth’s atmosphere bends and transmits some light into its shadow.
A total eclipse of the moon can last up to four hours and is visible to anyone on the side of Earth facing the moon.

Total Solar Eclipse

During a total solar eclipse, the moon casts a circular shadow that is never wider than 275 kilometers.
Anyone observing within this region will see the moon slowly and completely block the sun from view, and the sky darken. The temperature sharply drops a few degrees.
The solar disk is completely blocked for seven minutes at the most. The reason for the short duration of a solar eclipse is that the diameter of the moon's shadow is so small.
Then one edge of the solar disk reappears, and the moon continues moving until it no longer covers any part of the sun.