Working through this chapter of the study guide will enable you to:

1. Understand how to locate a particular position on the surface of Earth using longitude and latitude.
2. Establish the basis for our current time measurements and relate them to the astronomical processes by which they were originally defined.
3. Show how the seasons of the year are related to the tilt of Earth's axis with respect to its plane of revolution around the Sun and also how the seasons are linked to the vernal equinox.
4. Discuss the precession of Earth's axis and explain what consequences this phenomenon will have for future generations.
5. Explain how the calendar has evolved over the years and how our current calendar adjusts to irregularities in the length of the solar day upon which it is based.

Discussion

The concept of time has evolved, from a vague notion used by prehistoric people for scheduling activities during the available hours of daylight, into a highly precise system of well-defined intervals that can be so short that the human mind can hardly comprehend the units involved. Electronic computers must keep accurate track of time increments measured in nanoseconds (10^-9 seconds), and atomic clocks are now said to be accurate to one part per billion over periods of a year or more.

This chapter shows us the development of the concept of time and helps us to understand the astronomical basis for the original definitions associated with its measurement. Since navigation is important to man, especially on the sea where there are no landmarks to serve as guides, the concept of time has been linked with a system of angular measurement for finding positions on the surface of Earth (longitude and latitude) that can pinpoint a person's location using observations of the Sun or the stars.

Time on a longer scale is also important to us in terms of the seasons of the year and the effects that these yearly changes in climate have on our agricultural activities and even on such things as family vacation plans. These concepts require the use of an accurate and consistent calendar that can be relied upon to keep the months of the year in line with the traditional seasons, as measured with respect to the spring (vernal) equinox.

Of all the material in the textbook, the ideas presented in this chapter are perhaps the most often used in our everyday lives. How many times each day do you look at your watch or think about how long it is until you must be someplace or do something? Even the variations in climate that determine what clothing we wear each day are the result of the seasonal changes in the declination of the Sun and of the duration of daylight, both of which will be discussed in this chapter.


Section  16.1Cartesian Coordinates

Any system used to locate things must make reference to some specific predetermined position. One way to do this is to establish a two- (or three-) dimensional system that involves scales set perpendicular to each other and that all have the same origin, or zero point. Such a system is called a Cartesian coordinate system. When it is extended into spherical coordinates, it can be used to determine the location of things on the surface of Earth or on the celestial sphere.


Section  16.2Latitude and Longitude

Using the North and South Geographic poles of Earth and a plane through the center of Earth that is perpendicular to the rotational axis drawn through these poles, a two-dimensional system can be established that will uniquely locate any specific point on Earth's surface. The intersection of this plane with Earth's surface is called the equator. The equator is a great circle that divides Earth into two equal halves. Any point north or south of the equator can be designated as an angular measurement in degrees north or south. This measurement is called latitude. Circles formed by the intersection of additional planes parallel to the one defining the equator are referred to as parallels. If only the latitude of a place is given, it must be on a specific parallel but could be anywhere on that circle. A latitude reading can be any angle between 0^° (the equator itself) and 90^° N (the North Geographic Pole) or 90^° S (the South Geographic Pole).

To specify exactly where on a parallel a given position is, a second angular coordinate called the longitude must be used. Longitude measures the angular distance either east or west of a reference line called the prime meridian that runs from the North Geographic Pole to the South Geographic Pole through the city of Greenwich, England. Longitude indicates a specific meridian on which the object is located. Such a reading can be anywhere from 0^° to 180^° E or 180^° W, depending on which direction one travels with respect to the Greenwich prime meridian. Once both the longitude and latitude are determined, there is one exact meridian and one exact parallel on which the designated point must lie, and the exact location is the intersection of these two circles.

The position on the celestial sphere is designated in much the same way, with the celestial equator being located directly above Earth's equator. The prime celestial meridian is the meridian that passes through the point on the celestial equator where the ecliptic (the apparent path of the Sun among the fixed stars) crosses the celestial equator as the Sun moves northward. This point is called the spring equinox. The angular distance north or south of the celestial equator is marked + for north and - for south, and is known as the declination. The angular distance around the equator is specified only toward the east for 360^° from the prime celestial meridian. This measurement is called the right ascension. Again, the specification of the two angular measurements, declination and right ascension, gives an exact location on the celestial sphere that can be used to indicate the position of any object in the sky. Further discussion of the use of this system can be found in Chapter 18 in the textbook, where we utilize the celestial sphere for astronomical studies.


Section  16.3Time

Time must be measured in reference to some periodic or repeated motion or event. The rotation of Earth on its axis is such a periodic motion and we use it to define the concept of the solar day. The fluctuations in the phases of the Moon define the basic length of the month, and the annual revolution of Earth around the Sun and the changes of the seasons define the year. Such long units of time probably were good enough for our early ancestors, but increased complexity of people's daily schedules soon required smaller, more precise units. The day was, therefore, subdivided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds. This gives us a basic definition for the primary unit of time, the second. The length of each day is not the same throughout an entire year, however, so an average or mean solar day must be used in this definition.

As discussed earlier in Chapter 1, our current time standard is established using the natural frequency of radiation given off by an atom of cesium-133. The second is now officially defined as the time required for a little less than 9.2 billion cycles of cesium-133 radiation. Such an exact definition makes it possible to deal with time intervals as short as picoseconds (10^-12 s). Many types of clocks have been used over the years, including sundials, water clocks, banded candles, and mechanical timepieces, but the atomic clock, which uses cesium-133 radiation as a reference, is currently our ultimate timepiece.

Everyday time measurement still refers to the position of the Sun with respect to the observer. When the Sun is on the observer's overhead meridian, it is 12 noon local solar time. Twelve hours later, when the Sun is on the exact opposite side of Earth, it is 12 midnight local solar time. The hours in between are designated A.M. (before noon) and P.M. (after noon) on any given day.

With today's high-speed modes of travel it would be very inconvenient if the time changed continuously as we traveled east or west around the world, so a system of standard time zones has been established. The standard time over an east-west distance of about 900 nautical miles (at the equator) will be the same as it is at the central 15^° meridian for that time zone. This is true because Earth takes about one hour to turn through 15^° in its daily rotation. Anywhere within a given time zone, the time remains the same, but if a time zone boundary is crossed, the standard time changes by a one-hour increment. It should also be noted that the local solar time changes by four minutes for each one degree of east-west travel, even though the standard time does not change unless a time zone boundary is crossed. Standard time, or Daylight Saving Time (a shift of 1 hour from standard time to provide another hour of daylight in the evening during summer months), is normally used to record and plan our daily activities. Only when precise navigational calculations or astronomical observations are being made must local solar time be considered; otherwise, our daily lives run on standard time.


Section  16.4The Seasons

The axis of rotation of Earth is not perpendicular to the ecliptic plane in which Earth orbits the Sun. Because of this, the Sun shines more directly on the Northern Hemisphere during June, July, and August, and more directly on the Southern Hemisphere during December, January, and February. This leads to periodic seasonal variations in the weather over most parts of Earth. Since the tilt of Earth's axis is 23.5^°, these variations are quite noticeable and greatly affect the growing seasons and average temperatures in most temperate areas both north and south of the equator.

The Sun appears to move north of the equator during what we in the Northern Hemisphere call the summer months and south of the equator during what we consider winter. This apparent change in position is called the Sun's declination. The Sun appears to be farthest north of the equator on June 21. This in known as the summer solstice. The Sun appears farthest south of the equator on December 22, the winter solstice. The Sun is directly over the equator on March 21 and again on September 22, at which time all locations on Earth experience 12 hours of daylight and 12 hours of darkness. These dates are called the vernal (or spring) equinox and the autumnal (or fall) equinox, respectively. During the summer months, the Northern Hemisphere experiences longer days and shorter nights, and during the winter, fewer hours of daylight and more hours of darkness. For the Southern Hemisphere the duration of daylight is reversed, and the seasonal variations in climate are also switched around.


Section  16.5Precession of Earth's Axis

Although today the North Geographic Pole of Earth points to a spot in the sky very close to Polaris (the North Star), this has not always been the case. The direction in which the poles of Earth point changes over about a 26,000-year cycle, so that the rotational axis of Earth does not always point toward the same fixed stars. This process is called precession. Because of this, the stars visible at midnight will not always be the same for a given season of the year. About 13,000 years from now, the stars we now see in the night sky during the summer will have progressed around until they are behind the Sun and not visible during this season of the year, and those that are behind the Sun today will be overhead at midnight in July.


Section  16.6The Calendar

To keep the seasons of the year, and also the religious and secular holidays, occurring on the same dates, it was decided that the spring equinox will always occur on or about the same day of the year, March 21. Since the sidereal year does not contain an exact whole number of days, it occasionally is necessary to adjust our calendar to keep in step. This necessitates a leap year every four years, during which one more day than usual is added to the month of February.

Our calendar is set up with 12 months, each of about 30 days, corresponding roughly to the cycle of the phases of the Moon. Known as the Gregorian calendar, our current calendar requires some other corrections for fine tuning, but in its corrected form, it is accurate to within 1 day in 3300 years.

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