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5 X-ray Pulsar-Based Navigation: Theories and Experiments
circle. The great circle where the Earth’s orbit around the Sun is intersected with
the celestial sphere is called ecliptic, and the angle between the ecliptic plane and
the equatorial plane is called obliquity of the ecliptic (ε), which is approximately
23.5°. Two points where a straight line passing through the center of the celestial
sphere and perpendicular to the ecliptic plane is intersected with the celestial sphere
are called ecliptic poles, in which the intersection point near the north celestial
pole is called north ecliptic pole (Π n ), and that near the south celestial pole called
south ecliptic pole (Π s ). When the Sun moves on the ecliptic from the southern
hemisphere to northern hemispheres, the intersection of the ecliptic and the celestial
equator is called vernal equinox (). Similarly, when the Sun moves on the ecliptic
from the northern to southern hemispheres, the corresponding intersection is called
the autumnal equinox. The vernal equinox and the celestial equatorial plane are,
respectively, the reference point and plane to establish the celestial reference system.
Time is the objective form of existence and movement of matter, and the time
system is established by the reference to the movement of matter. According to
the different forms of material movement, the commonly used time systems can be
divided into three categories, as shown Fig. 5.2. One is the universal time system,
which is based on the Earth’s rotation movement, being also the earliest time metering
system established by human beings; the other is the ephemeris time system, which
is based on the orbital revolution of the Earth around the Sun; the third is the atomic
time system, which is based on the movement characteristics of the atoms in the
matter. According to the different space reference points selected for observing the
Earth’s rotation, the universal time system is divided into sidereal time, apparent solar
time, mean solar time and universal time. According to the different definitions and
application scenarios, the atomic time system is divided into International Atomic
Time (TAI), Coordinated Universal Time (UTC) and navigation satellite time. The
classifications of these commomly used time sytems are further shown in Fig. 5.3.
5.3.2.1 Sidereal Time
The sidereal time refers to a timescale that is the time measured by the apparent
motion about the Earth, of the distant, so-called fixed points, such as the vernal
equinox and stars. The time interval between two successive passages of the local
meridian circle (the upper culmination) at the vernal equinox is called a sidereal
day, which is subdivided into 24 sidereal hours, 1,440 sidereal minutes and 86,400
sidereal seconds. The sidereal time is numerically equal to the hour angle of the vernal
equinox relative to the local meridian circle, and the hour angle of the vernal equinox
is equal to the sum of the hour angle of any star and its right ascension. For the same
moment, the sidereal time gotten at different observation stations is different. That is
to say, the sidereal time is with locality, and the local sidereal time at a moment can
be obtained by observing the stars. Due to the influence of the axial-precession and
nutation, the direction of the Earth’s rotation axis in space is constantly changing,
so that the position of the vernal equinox on the celestial sphere is not fixed. For the
same epoch, the north celestial pole can be divided into the apparent north celestial
5 X-ray Pulsar-Based Navigation: Theories and Experiments
circle. The great circle where the Earth’s orbit around the Sun is intersected with
the celestial sphere is called ecliptic, and the angle between the ecliptic plane and
the equatorial plane is called obliquity of the ecliptic (ε), which is approximately
23.5°. Two points where a straight line passing through the center of the celestial
sphere and perpendicular to the ecliptic plane is intersected with the celestial sphere
are called ecliptic poles, in which the intersection point near the north celestial
pole is called north ecliptic pole (Π n ), and that near the south celestial pole called
south ecliptic pole (Π s ). When the Sun moves on the ecliptic from the southern
hemisphere to northern hemispheres, the intersection of the ecliptic and the celestial
equator is called vernal equinox (). Similarly, when the Sun moves on the ecliptic
from the northern to southern hemispheres, the corresponding intersection is called
the autumnal equinox. The vernal equinox and the celestial equatorial plane are,
respectively, the reference point and plane to establish the celestial reference system.
Time is the objective form of existence and movement of matter, and the time
system is established by the reference to the movement of matter. According to
the different forms of material movement, the commonly used time systems can be
divided into three categories, as shown Fig. 5.2. One is the universal time system,
which is based on the Earth’s rotation movement, being also the earliest time metering
system established by human beings; the other is the ephemeris time system, which
is based on the orbital revolution of the Earth around the Sun; the third is the atomic
time system, which is based on the movement characteristics of the atoms in the
matter. According to the different space reference points selected for observing the
Earth’s rotation, the universal time system is divided into sidereal time, apparent solar
time, mean solar time and universal time. According to the different definitions and
application scenarios, the atomic time system is divided into International Atomic
Time (TAI), Coordinated Universal Time (UTC) and navigation satellite time. The
classifications of these commomly used time sytems are further shown in Fig. 5.3.
5.3.2.1 Sidereal Time
The sidereal time refers to a timescale that is the time measured by the apparent
motion about the Earth, of the distant, so-called fixed points, such as the vernal
equinox and stars. The time interval between two successive passages of the local
meridian circle (the upper culmination) at the vernal equinox is called a sidereal
day, which is subdivided into 24 sidereal hours, 1,440 sidereal minutes and 86,400
sidereal seconds. The sidereal time is numerically equal to the hour angle of the vernal
equinox relative to the local meridian circle, and the hour angle of the vernal equinox
is equal to the sum of the hour angle of any star and its right ascension. For the same
moment, the sidereal time gotten at different observation stations is different. That is
to say, the sidereal time is with locality, and the local sidereal time at a moment can
be obtained by observing the stars. Due to the influence of the axial-precession and
nutation, the direction of the Earth’s rotation axis in space is constantly changing,
so that the position of the vernal equinox on the celestial sphere is not fixed. For the
same epoch, the north celestial pole can be divided into the apparent north celestial