APPENDIX I

CONCEPT OF TIME1.

Solar and Sidereal TimeAs the earth rotates about its axis in its travel through space, all celestial bodies apparently rotate about the earth (or about its axis) from east to west. Since the earth in its orbit travels about the sun but not about the fixed stars, which are far outside its orbit, once each year the sun apparently encircles the celestial sphere along a path called the

ecliptic, which twice cuts the celestial equator during this interval. The point among the stars where the sun in its apparent travel northward cuts the celestial equator on March 21 of each year is called thevernal equinox. The sun travels rapidly along the ecliptic in a direction opposite to that of the rotation of the celestial sphere.Because the sun is apparently traveling from west to east among the stars, whereas the rotation of the celestial sphere about the earth is apparently from east to west, the angular velocity of the sun about the axis of the celestial sphere is less than that of the fixed stars or the vernal equinox. At a given meridian the hour angle of the sun and of the vernal equinox will agree at some instant on March 21, but thereafter it will be less for the sun than for the vernal equinox. Six months later, on September 22, when the sun has covered one-half of its annual journey, the hour angle of the sun will be 180° or 12

^{h}less than that of the vernal equinox; and 1 year later the angle of the sun will be 360° or 24^{h}less than that of the vernal equinox, and hence hour angles will agree.In the course of a tropical year, as measured by the time taken by the sun apparently to make a complete circuit of the ecliptic, there actually occur 366.2422 rotations of the earth, or apparently a like number of revolutions of the vernal equinox about the earth. For reasons explained, the sun during this interval will have traveled through a total hour angle 360° or 24

^{h}less than that traversed by the vernal equinox; hence, during a tropical year the sun apparently revolves about the earth 365.2422 times.

Solar day, unit of time with which we are all familiar. It is the interval of time occupied by one apparent revolution of the sun about the earth.

Sidereal day, unit of time occupied by one apparent revolution of the vernal equinox.366.2422 sidereal days = 365.2422 solar days.

The sidereal day is shorter than the solar day.

When any celestial body apparently crosses the upper branch of a meridian, it is said to be at

upper transit; when any celestial body crosses the lower branch of the meridian, it is said to be atlower transit.Beginning of a sidereal day at a given place occurs at the instant the vernal equinox is at upper transit.

Beginning of a solar day, or the civil day, occurs at the instant of lower transit of the sun (midnight).

2.

True and Mean SunsBecause of the elliptical shape of the earth's orbit, the apparent angular velocity of the sun that we see, or the

true sun, is not constant; hence, the days as indicated by the apparent travel of the true sun about the earth are not of uniform length. To make our solar day of uniform length, astronomers have invented themean sun, a fictitious body which is imagined to move at a uniform rate along the celestial equator, making a complete circuit from west to east in one year.The time interval as measured by one apparent revolution of the true sun about the earth is called an

apparent solar day. The time interval as measured by one daily revolution of themean sunis called themean solar day, which is the same as thecivil day.3.

Apparent (True) Solar TimeThe "Nautical Almanac" considers the apparent solar day at any place as the time interval between two successive lower transits of the true (apparent) sun for the meridian of that place. The solar day therefore begins at midnight and the

apparent solar timeat any place is given by the hour angle of the true sun plus 12^{h}. Thus, if the hour angle of the sun is 45° 3^{h}at a given place and at a given instant, then the apparent solar time for the place is 3^{h}+ 12^{h}= 15^{h}.Apparent time has the same meaning as apparent solar time. Local apparent time is that for the meridian of the observer. Apparent time for any other meridian is designated by name, for example, Greenwich apparent time.

4.

Civil (Mean Solar) TimeThe "Nautical Almanac" considers the mean solar day at any place to be the time interval between two successive lower transits of the mean sun for the meridian of that place. The mean solar day, therefore, also begins at midnight, and the mean solar time is given by the hour angle of the mean sun plus 12

^{h}. Thus, if the hour angle of the mean sun is -15° = 1^{h}, the mean solar time is 11^{h}. Civil time is the same as mean solar time or mean time. Local civil time is that for the meridian of the observer. Civil time for any other meri dian is designated by name, for example, Greenwich civil time or Greenwich mean time.5.

Equation of TimeWhen the apparent (true) sun is (ahead of/behind) the mean sun, apparent time is (faster/slower) than mean civil time. The difference between apparent and civil time at any instant is called the

equation of time. It is used to convert civil time at any instant to apparent time.In the "Nautical Almanac" the equation of time is given for each day for the hours 00 and 12 Greenwich civil time. The Greenwich civil time at which the true sun crosses the Greenwich meridian is also given. This information is useful in establishing whether the true sun is ahead of or behind the mean sun.

6.

Sidereal TimeThe sidereal time at any place is the hour angle of the vernal equinox at that place; and the beginning of the sidereal day, occurring when the vernal equinox crosses the upper branch of the meridian, is called sidereal noon.

7.

Relationship Between Longitude and TimeAt any instant, the

difference in local timebetween two places, whether the time under consideration is sidereal, mean, or apparent solar, is equal to the difference in longitude between the two places expressed in hours.8.

Standard TimeTo eliminate the confusion in industry attendant upon the use of local time by the public, the United States is divided into belts, each of which occupies a width of approximately 15° 1

^{h}of longitude. In each belt the clocks that control civil affairs all keep the same time, calledStandard Time, which is the local civil time for a meridian near the center of the belt. The time in any belt is a whole number of hours slower than Greenwich civil time, as follows:

Hours Slower than Central Standard Time Greenwich Civil Time MeridianAtlantic 4 60° W Eastern 5 75° W Central 6 90° W Mountain 7 105° W Pacific 8 120° WThe exact boundaries of the time belts are irregular and can be determined only from a map.

Correct standard time can be obtained either from a clock known to be closely regulated or from radio signals.

In certain localities, daylight saving time is used during the summer months. Daylight saving time is 1

^{h}faster than standard time.

Q. E. D.

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