## Time Measurement Systems

Conrad R. Sturch

International Atomic Time, TAI, which is provided by atomic clocks, is the basis for the two time systems used in spacecraft time measurements. Ephemeris Time, ET, which is used in the preparation of ephemerides, is a uniform or "smoothly flowing" time and is related to TAI by

In contrast to ET, Coordinated Universal Time, UTC, uses the TAI second as the fundamental unit, but introduces 1-second steps occasionally to make UTC follow -the nonuniform rotation of the Earth. UTC is necessary for terrestrial navigation and surveying for which the rotational position of the Earth at a given instant is critical. It is this time which is broadcast internationally and is used for tagging spacecraft data and for all civil timekeeping. Finally, sidereal time is a direct measure of the rotational orientation of the Earth relative to the "fixed" stars and, therefore, is used to estimate the position of a spacecraft relative to points on the Earth's surface. The characteristics of the various time systems are summarized in Table J-l.

Any periodic phenomenon may be used as a measure of time. The motion of the Earth, the Moon, and the Sun relative to the fixed stars has traditionally been used for this purpose. However, the need for increasingly accurate time measurements has resulted in the development of several alternative time systems. The requirement for high accuracy comes from the cumulative effect of timing errors. An accuracy of 1 sec/day (1 part in 10s) would appear satisfactory for most scientific or technical purposes. However, an error of this magnitude in an ephemeris of the Earth causes an error of 10,800 km in the position of the Earth

kind of time |
defined by |
fundamental unit |
regularity |
use |

sidereal solar: |
earth*8 rotation relative to stars |
sidereal day. 1 rotation of earth |
irregular |
astronomical observations; determining ut and rotational orientation of earth |

apparent |
earth's rotation relative to true sun |
successive transits of sun |
irregular and annual variations |
sundials |

.mean |
earth's rotation relative to fictitious mean sun |
mean solar day |
irregular |
— |

universal • uto |
observed ut |
mean solar day |
irregular |
study of earth's wandering pole |

ut1 |
corrected uto |
mean solar day |
irregular |
shows seasonal variation of earth's rotation |

uts |
corrected ut1 |
mean solar day |
irregular |
basic rotation of earth |

utc« gmt - z |
atomic second and leap seconds to approximate ot1 |
mean solar day |
uniform except for leap sec« onds |
civil timekeeping;terrestrial navigation and surveying: broadcast time signals |

ephemeris, et |
fraction of tropical year 1900 |
ephemeris second |
uniform |
ephemerides |

atomic, tai |
frequency of 133 ce radiation |
atomic second-ephemeris second |
uniform |
basis of et and utc |

after only 1 year, several orders of magnitude worse than what is acceptable for many unsophisticated measurements. Thus, the generation of accurate ephemerides requires a precise time measurement system.

The diurnal motion of celestial objects is the most obvious timekeeper. Until the Middle Ages "seasonal hours," one-twelfth of daylight or nightime periods, was used. Of course, this unit varies both with the season and with the observer's latitude. A more uniform unit of time is the apparent solar day, defined as the interval between two successive passages of the Sun across the observer's meridian. As discussed below, this interval varies throughout the year due to variations in the Earth's orbital speed and the inclination of the ecliptic. The Earth's orbital motion does not affect the sidereal day, the interval between two succesive meridian passages of a fixed star. However, irregularities in the rotation of the Earth cause both periodic and secular variations in the lengths of the sidereal and solar days.

The annual motions of celestial objects provide a measurement of time which is independent of the irregular variations in the rotation of the Earth. The tropical year, upon which our calendar is based, is defined as the interval of time from one vernal equinox to the next. The ephemeris second is defined as 1/31556925.9747 of the tropical year for 1900. Because of the precession of the equinoxes (Section 2.2.2), the tropica] year is about 20 minutes shorter than the orbital period of the Earth relative to the fixed stars. This latter period is known as the sidereal year. Due to secular Variations in the orbit and rate of precession of the Earth, .the lengths of both types of year (in units of se, the ephemeris second) vary to first order according to the relations:

Tropical year=31556925.9747 -.5307

Sidereal year=31558149.540 +.0107

where T is the time in units of Julian Centuries of 36525 days from 1900.0 [Newcomb, 1898],

The first satisfactory alternative to celestial observations for the measurement of time was the pendulum clock. The period of a pendulum is a function of the effective acceleration of gravity, which varies with geography and the position of the Sun and the Moon. The resonance frequency of quartz crystals has recently been employed in clocks; this frequency depends on the dimensions and cut of the crystal and its age, temperature, and ambient pressure. Atomic clocks are based on the frequency of microwave, emission from certain atoms. An accuracy of 10"14 (fractional standard deviation) may be achieved with atomic clocks; corresponding accuracies for quartz and pendulum clocks are 2X10"13 and 10~6, respectively. For an extended discussion of time systems, see Woolard and Clemence [1966], the Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac [H.M. Nautical Almanac Office, 1961] and Miller and Jappel [1977].

Solar Time. The celestial meridian is the great circle passing through the celestial poles and the observer's zenith. As shown in Fig. J-l, the hour angle, HA, is the azimuthal orientation of an object measured westward from the celestial meridian. As the Earth rotates eastward, a celestial object appears to move westward and its HA increases with time. It takes 24 hours for an object to move completely around the celestial sphere or 1 hour to move 15 deg in HA; thus, 1 deg of HA corresponds to 4 minutes of time.

The apparent solar time is equal to the local HA of the Sun, expressed in hours, plus 12 hours. Apparent solar time can be measured with a simple sundial constructed by driving a long nail perpendicularly through a flat piece of wood. If the nail is then pointed toward the celestial pole, the plane of the wood is parallel to the equatorial plane, and the shadow of the nail cast by the Sun onto the wood is a measure of the HA.

Due to the Earth's orbital motion, the Sun appears to move eastward along the ecliptic throughout the year. Because the Earth travels in an elliptical orbit, it moves faster when near the Sun and slower when it is more distant; therefore, the length of the solar day varies. Even if the Earth were in a circular orbit with a constant speed, the azimuthal component of the Sun's motion (parallel to the celestial equator) would vary due to the inclination of the ecliptic relative to the equator. To illustrate this, consider a satellite in a nearly polar orbit, as shown in Fig. J-2. The satellite changes azimuth slowly while near the equator and rapidly while near the poles. Although the variation in the length of the day due to the

Fig. J-2. Variation in Azimuthal Rate for a Satellite Moving Uniformly in its Orbit. A1.A2 AS are azimuthal projections of the orbital points 1,2,...5 and are equally spaced in time.

Fig. J-2. Variation in Azimuthal Rate for a Satellite Moving Uniformly in its Orbit. A1.A2 AS are azimuthal projections of the orbital points 1,2,...5 and are equally spaced in time.

eccentricity and inclination of the Earth's orbit is small, the cumulative variation reaches a maximum of 16 minutes in November.

To provide more uniform time than the real Sun, a fictitious mean Sun, which moves along the equator at a constant rate equal to the average annual rate of the Sun, has been introduced. Mean solar time is defined by the HA of the mean Sun. The difference between the mean and apparent solar times is called the equation of time.

Standard Time. Mean solar time is impractical for communication and transportation because it varies continuously with longitude. Therefore, the world has been divided into 24 time zones of approximately 15 deg each. Normally, these zones are centered on standard meridians which are multiples of 15 deg in longitude. The uniform time throughout each zone is referred to as Standard Time, and usually differs by an integral number of hours from the mean solar time at 0 deg longitude, or Universal Time, as discussed below. Table J-2 lists the standard meridians for time zones in the continental United States. The apparent solar time is converted to Standard Time by adding the equation of time for the date and subtracting the algebraic difference (expressed in units of time) between the observer's longitude and the standard meridian.

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