Astronomy Principles and Practice Fourth Edition.pdf

Chapter 9
The celestial sphere: timekeeping systems
9.1 Introduction
Primitive people based their sense of the passage of time on the growth of hunger or thirst and on
impersonal phenomena such as the changing altitude of the Sun during a day, the successive phases
of the Moon and the changing seasons. By about 2000 BC civilizations kept records and systematized
the impersonal phenomena into the day, the month and the year. We have seen that emphasis was
given to the year as a unit of time by their observation that the Sun made one revolution of the stellar
background in that period of time.
Since everyday life is geared to daylight, the Sun became the body to which the system of
timekeeping used by day was bound. The apparent solar day was then the time between successive
passages of the Sun over the observer’s meridian or the time during which the Sun’s hour angle
increased by 24 h (360 ◦ ). In a practical way the Sun was noted to be on the meridian when the shadow
cast by a vertical pillar was shortest.
However, the apparent diurnal rotation of the heavens provided another system of timekeeping
called sidereal time, based on the rotation of the Earth on its axis. The interval between two successive
passages of a star across the observer’s meridian was then called a sidereal day. Early on in the history
of astronomy it was realized that the difference between the two systems of timekeeping—solar and
stellar—was caused by the orbital motion of the Sun relative to Earth. Thus, in figure 9.1, if two
successive passages of the star over the observer’s meridian define a sidereal day (the star being taken
to be at an infinite distance effectively from the Earth), the Earth will have rotated the observer O
through 360 ◦ from O 1 to O 2 . In order that one apparent solar day will have elapsed, however, the
Earth will have to rotate until the observer is at O 3 when the Sun will again be on the meridian. Since
the Earth’s radius vector SE sweeps out about 1 ◦ per day and the Earth rotates at an angular velocity
of about 1 ◦ per 4 minutes, the sidereal day is consequently about 4 minutes shorter than the average
solar day.
We will now consider these systems in greater detail.
9.2 Sidereal time
We have seen that the First Point of Aries (Vernal Equinox ) is the reference point chosen on the
rotating celestial sphere to define the sidereal day. The time between successive passages of the vernal
equinox across the observer’s meridian is one sidereal day. So the hour angle of the vernal equinox
increases from 0 h to 24 h and the local sidereal time (LST) is defined as the hour angle of the vernal
equinox (HA). The LST, as its name implies, depends upon the observer’s longitude on the Earth’s
surface.
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