Dr. SaMeH S. Ahmed

Civil and Environmental Engineering Department

Sun's apparent mot


Sun's apparent motion


The motions as described above are simplifications. Due to the movement of the Earth around the Earth-Moon barycenter, the apparent path of the Sun wobbles slightly, with a period of about one month; due to perturbations by the other planets of the Solar System, the Earth-Moon barycenter wobbles slightly around a mean position in a complex fashion. Theecliptic is actually the apparent path of the Sun throughout the course of a year. Also, the Earth does not actually orbit the Sun, but the Solar System barycenter, therefore an alternate definition of the ecliptic is the mean plane of the orbit of Earth-Moon barycenter around the Solar System barycenter.[1][2]

As the Earth takes one year to make a complete revolution around the Sun, the apparent position of the Sun also takes the same length of time to make a complete circuit of the ecliptic. With slightly more than 365 days in one year, the Sun moves a little less than 1° eastward[3] every day. This small difference in the Sun's position against the stars causes any particular spot on the Earth's surface to catch up with (and stand directly north or south of) the Sun about 4 minutes later each day than it would if the Earth did not orbit; our day is 24 hours long rather than the approximately 23 hour 56 minute sidereal day. Again, this is a simplification, based on a hypothetical Earth which revolves at uniform speed around the Sun. The actual speed with which the Earth orbits the Sun varies slightly during the year, so the speed with which the Sun seems to move along the ecliptic also varies. For example, the Sun is north of the celestial equator for about 185 days of each year, and south of it for about 180 days.[4] The variation of orbital speed accounts for part of the equation of time.[5]

[edit]
Relationship to the celestial equator

The plane of the Earth's orbit projected in all directions forms the reference plane known as the ecliptic. Here, it is shown projected outward (gray) to the celestial sphere, along with the Earth's equatorand polar axis (green). The plane of the ecliptic intersects the celestial sphere along a great circle(black), the same circle on which the Sun seems to move as the Earth orbits it. The intersections of the ecliptic and the equator on the celestial sphere are the vernal and autumnal equinoxes (red), where the Sun seems to cross the celestial equator.

As the rotational axis of the Earth is not perpendicular to its orbital plane, the Earth's equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23°.4, which is known as the obliquity of the ecliptic.[6] If the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as theequinoxes. The Sun, in its apparent motion along the ecliptic, crosses the celestial equator at these points, one from south to north, the other from north to south.[3] The crossing from south to north is known as the vernal equinox, also known as the first point of Aries and the ascending node of the ecliptic on the celestial equator.[7] The crossing from north to south is the autumnal equinox or descending node.

The orientation of the Earth's axis and equator are not fixed in space, but rotate about the poles of the ecliptic with a period of about 26,000 years, a process known as lunisolar precession, as it is due mostly to the gravitational effect of the Moon and Sun on theEarth's equatorial bulge. Likewise, the ecliptic itself is not fixed. The gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of the Earth's orbit, and hence of the ecliptic, known as planetary precession. The combined action of these two motions is called general precession, and changes the position of the equinoxes by about 50 arc seconds (about 0°.014) per year.[8]

Once again, this is a simplification. Periodic motions of the Moon and apparent periodic motions of the Sun (actually of the Earth in its orbit) cause short-term small-amplitude periodic oscillations of the axis of the Earth, and hence the celestial equator, known asnutation.[9] This adds a periodic component to the position of the equinoxes; the positions of the celestial equator and (vernal) equinox with fully updated with precession and nutation are called the true equator and equinox; the positions without nutation are the mean equator and equinox.[10]

[edit]
Obliquity of the ecliptic

Obliquity of the ecliptic is a name used by astronomers for the inclination of Earth's equator to the ecliptic, or of Earth's rotation axis to a perpendicular to the ecliptic. Currently about 23°.4, it varies slightly due to motion of the plane of the Earth's orbit, and hence the ecliptic, with planetary precession.[11]

The angular value of the obliquity is found by observation of the motions of the Earth and planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived.

Obliquity of the ecliptic for 20,000 years, from Laskar (1986).[12] Note that the obliquity varies only from 24°.2 to 22°.5 during this time. The red point represents the year 2000.

Until 1983, the angular value of the obliquity for any date was calculated based on the work of Newcomb, who analyzed positions of the planets until about 1895:

ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T2 + 0″.00181 T3

where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.[13]

From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:

ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T2 + 0″.00181 T3

where hereafter T is Julian centuries from J2000.0.[14]

JPL's fundamental ephemerides have been continually updated. For instance, the Astronomical Almanac for 2010 specifies:[15]

ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T2 + 0″.00200340 T3 − 0″.576×10−6 T4 − 4″.34×10−8 T5

These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps ± several centuries.[16] J. Laskar computed an expression to order T10 good to 0″.04/1000 years over 10,000 years.[12]

All of these expressions are for the mean obliquity, that is, without the nutation of the equator included. The true or instantaneous obliquity includes the nutation.[17]


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