Chapter 3: Earth, Moon, and Sky

3.1 Earth and Sky

3.1.1 Locating Places on the Earth

We define directions on the Earth's surface in terms of the compass points north (N), south (S), east (E), and west(W). North and south are the directions to the north and south poles. East is the direction in which the Earth rotates and west is its opposite.

We define locations on the Earth's surface in terms of latitude and longitude. A meridian is an imaginary circle drawn around the Earth and passing thru the north and south poles. Every position on Earth (except the north and south poles) has a unique meridian passing thru it. The longitude of a location is the angle (E or W) between the meridian thru the location and the meridian thru Greenwich, England. The latitude of a location is the angle between the location and the equator.

3.1.2 Locating Places in the Sky

Position in the sky are measured similarly. Declination is similar to latitude; it is the angle between a position and the celestial equator. (Recall that the celestial equator is the projection of the Earth's equator onto the celestial sphere.) Right ascension (RA) is like longitude except that it is measured with respect to the celestial meridian passing thru the vernal equinox.

3.1.3 The Turning Earth

We now attribute the apparent daily rotation of the celestial sphere to the actual rotation of the Earth. this rotation manifests itself on Earth in a number of phenomena:

3.2 The Seasons

The seasons arise due to the tilt of the Earth's axis to its plane of orbit. The seasons do not result from the Earth, in its yearly orbit, moving closer and further from the Sun. In fact, The Earth is further from the Sun during summer in the northern hemisphere than it is during winter.

Rather seasons arise because during summer in the northern hemisphere, the north pole is tilted toward the sun, giving more hours of daylight -- at the north pole, the Sun stays up 24 hours a day in the summer. And the sunshine is more direct, providing even more heating in the summer.

3.3 Keeping Time

The history of time keeping is a whole lecture unto itself. Here I'll summarize the story.

3.3.1 Length of the Day

Our fundamental measure of time is the day. The same is true in astronomy, but with the complication that from one sunrise to the next, the Earth has moved about one degree around the Sun (1 day/365 days), meaning that the stars appear shifted by about 1 degree when viewed at the same time.

Our normal day is called a solar day, the time for the Earth to rotate once with respect to the Sun. A sidereal day is the time for the Earth to rotate once with respect to the stars. A solar day is about 4 minutes longer than a sidereal day.

3.3.2 Apparent Solar Time

Apparent solar time is determined from the actual position of the Sun at your location. We designate the time before the Sun reaches the meridian (its zenith) as ante meridian or A.M., and the time after as post meridian or P.M. There are several problems with using apparent solar time: it depends on your location, and the "motion" of the Sun is not uniform because the speed of the Earth varies during its orbit about the Sun.

3.3.3 Mean Solar Time and Standard Time

These difficulties are solved by doing two things. First we use mean solar time, based on the average of the solar day over the course of the year.

Second, we establish time zones in which all places keep the same standard time. The continental U.S. is divided into four time zones: eastern, central, mountain, and pacific. Thus, 6:00pm in Detroit is the same as 6:00pm in Miami, N.Y., Washington, D.C., or any other city in the eastern zone. Chicago is in the cental time zone, one hour behind the eastern zone. 6:00pm in Detroit is 5:00pm in Chicago. When flying, you can easily arrive in Chicago at an earlier time than you left Detroit!

Daylight saving time is simply standard time plus one hour. It is implemented, by general agreement, during spring and summer to shift the hours of daylight more in alignment with normal work patterns. It is an economic or political device, not a scientific device.

3.3.4 The International Date Line

Moving westward, you pass into a new time zone about every 15° around the Earth, each an hour earlier than the next. If you go all the way around the Earth, you lose 24 hours in time keeping, or an entire day. Of course, this is ridiculous, since anyone who stayed put didn't lose that day, so your calendars would disagree. This is solved by use of the international date line, an imaginary line running through the Pacific ocean. By agreement, if you travel west across the date line, you gain a day, and if you travel east, you lose a day. This was used to provide the punch line in Around the World in 80 Days.

3.4 The Calendar

3.4.1 The Challenges of the Calendar

The challenge in devising a calendar is that the natural periods of the day, month, and year do not divide evenly into each other. A lunar month is 29.5306 days, and the tropical year (time for the Earth to orbit the Sun) is 365.2422 days.

3.4.2 Early Calendars

As noted in the group discussion of last class, many early civilizations developed calendars. We know of the earliest calendars by ruins of the early civilizations such as Stonehenge in England, and Caracol in Mexico. (Figures 3.11 and 3.12)

The Romans came up with the first known use of a leap year to compensate for the extra fraction of a day in a year. Their calendar had months, but they didn't try to force them to correspond to the lunar cycle. Every fourth year they added an additional day, so that a leap year has 366 days rather than 365.

T3.4.3 he Gregorian Calendar

The Roman (or Julian) calendar still accumulated an "error" of 11 minutes every year. By the year 1582, the 11 minutes added up to 10 days. Additional changes were made to "realign" the calendar and correct so that it would remain aligned in the future. This was done under the auspices of Pope Gregory XIII and is known as the Gregorian calendar.

In Catholic countries, the day following Oct 4, 1582 became Oct. 15, 1582! Furthermore, the year of a century would no longer be a leap year, unles that year is divisible by 400. Therefore 1600 and 2000 were leap years, while 1700, 1800, and 1900 were not.

England and America, didn't adopt the Gregorian calendar until 1752. Then, Sept. 2, 1752 was followed by Sept. 14, 1752. The intervening 12 dates simply don't exist.

Russia didn't adopt the Gregorian calendar until the revolution (1917), by which time they had to omit 13 days. Little effects are still with us to this day. Orthodox Russian Christmas and New Year are celebrated 2 weeks later than the "traditional" dates.

3.5 Phases and Motions of the Moon

The Moon is the second brightest object in the sky. The Moon doesn't produce its own light; none of the planets, moons, or asteroids produce their own light. The light we see is sunlight reflected off the Moon.

During a period of about a month, the Moon goes through a cycle from new moon, to first quarter, to full moon, to third quarter, and back to new moon. As the Moon changes from full to new, we say that it is waning, and as it goes from new to full we say it is waxing. What causes these changes? Is it the shadow of the Earth? Why does the cycle take a month?

3.5.1 Lunar Phases

The phases of the Moon are due to the relative position of the Sun, Earth, and Moon. See Figure 3.13. When the Moon is new, it lies between the Earth and the Sun. The illuminated side of the Moon faces away from the Earth and we see nothing.

When the Moon is full, it lies on the opposite side of the Earth from the Sun. It's illuminated half is facing us so that we can see it fully.

At other points in its orbit around the Earth we see some fraction of the illuminated side of the Moon. The Moon takes about a month (29 days) to orbit the Earth, hence the cycle takes about a month, and then repeats.

3.5.2 The Moon's Revolution and Rotation

The sidereal period (measured relative to the stars) of the Moon is 27 days. The period for the Moon to go from full to full is about 29 days. The difference is due to the motion of the Earth.

The Moon rotates in exactly the same period as it revolves around the Earth. The result is that the same side of the Moon always faces the Earth. That is, for as long as we've been looking, humans have seen the same part of the Moon.

The side of the Moon that faces away from us, and hence was not observed until spacecraft circled the Moon, is sometimes called the dark side of the Moon. This doesn't mean that the side is always in shadow, but rather that it is unknown to us.

3.6 Ocean Tides and the Moon

The tides are primarily due to the motion of the Moon, with some lesser influence from the Sun. A full understanding of tides requires Newton's law of gravity.

3.6.1 The Pull of the Moon on the Earth

All the points on Earth are not equally distant from the Moon, and therefore they feel the pull of the Moon's gravity to different degrees [Figure 3.15]. The side of the Earth facing the Moon feels more pull than the side away from the Moon, and the equator feels more pull than the poles.

3.6.2 The Formation of Tides

These differences in pull produce horizontal forces on the surface. While these forces are not significant enough to move rocks and people, they are enough to push water around and raise tides.

Each day there are two high tides and two low tides. Why is that?

This happens because there is a high tide on the side of the Earth facing the Moon (where the Moon's gravity exerts the most force) and on the side opposite the Moon (where the Moon's gravity exerts the least force). The low tides occur about half way between the high tides. The precise times of high and low tides also depend on other factors.

The Sun influences the tides to a lesser extent. When the Sun, Earth, and Moon line up, the tides will be particularly high, and are called spring tides. When the Sun, Earth, and Moon form a right angle, the tides are lower than usual, and are called neap tides.

3.7 Eclipses of the Sun and Moon

An eclipse occurs when one object passes between the Sun and another object, blocking the light from the Sun. During a solar eclipse the Moon moves between the Earth and the Sun, casting a shadow over part of the Earth. The results on Earth are rather dramatic because the apparent size of the Moon and the Sun are nearly identical, and the Moon will totally obscure the Sun. During a lunar eclipse the Earth moves between the Moon and the Sun, casting a shadow on the Moon. Lunar eclipses are visible from anyplace on the night side of Earth.

3.7.1 Eclipses of the Sun

The geometry of a solar eclipse is shown in Figure 3.20. Notice that the full shadow (umbra) of the Moon is cast on just a small area of the Earth. A larger region lies in partial shadow (penumbra). A total eclipse lasts from just a minute up to about 7 minutes, depending on what part of the shadow you are in.

3.7.2 Appearance of a Total Eclipse

Total eclipses, besides being rather spectacular events in themselves, are one of the few chances for astronomers to study the Sun's corona. The corona is the Sun's outer atmosphere.

3.7.3 Eclipses of the Moon

Lunar eclipses occur when the Moon enters the Earth's shadow. As discussed earlier, the Earth casts a round shadow onto the Moon, a fact known to the ancient Greeks and evidence that the Earth is spherical.

Lunar eclipses occur only during a full Moon.

© Robert Harr 2004