K.M. Borkowski, Centre
for Astronomy, Nicolaus Copernicus University, Torun, Poland
|It is rigorously demonstrated that the much talked about December solstice of 2012, from an astronomical point of view, will be in no way exceptional. It is claimed that the closest approach to the galactic plane has occured already in 1997 or 1994, and the solstice closest to the galactic centre will happen only in 2228.|
With the approach of the year 2012 the Internet and other media are being flooded with various predictions, many of them fearful. Most of them are based on messages from unseen beings and are frequently justified by (in addition to the end of certain cycles in the Mayan calendar) alleged exceptional configurations of the Earth and Sun on December 21, 2012. In particular, we are being told that on the December solstice of 2012 the Earth and Sun will be crossing the galactic equator, or that these bodies will be then in a position which is closest to the galactic centre so that the Earth, the Sun and the galactic centre will be aligned. This text presents the factual configuration of the Sun and Earth and demonstrates that both these claims are false.
From the point of view of a common citizen, the solstice is when during the year the Sun at local noon reaches highest or lowest altitude (the angular height above the horizon). Such events happen twice each year, on June 20 or 21 and on December 21 or 22 and correspond to the extreme declinations of the Sun (angles between the direction to the Sun and the plane of the celestial equator, a coordinate on the sky very much akin to the geographical latitude). At these extreme declinations, the right ascension (the spherical coordinate analogous to geographical longitude) is equal to 90° (or, equivalently, 6 hours), exactly, in June, and 270° (18 hours) in December. These round angles are exactly the same when measured as the ecliptic longitude, along the ecliptic, i.e. along mean apparent path of the Sun on the sky as it moves annually relative to stars. Thus the December solstices occur when the ecliptic longitude of the Sun is equal to 270°, exactly.
It is a matter of simple computations to find the time (hours and minutes) of a solstice (by iterative probing the ecliptic longitude near the expected date to pinpoint the exact moment when the longitude is equal to e.g. 270°). Depending on desired accuracy, one chooses for the purpose one of existing algorithms for ephemeris of the Sun (or rather the Earth, for movements of the Sun are but a reflection of those of the Earth). Having found the time, in the process one has had already found also the ecliptic latitude of the Sun (which is a small quantity since deviations of the actual path of the Sun from the ecliptic are small; they are the result of varying gravitational pull of the Moon and planets exerted on the Earth whose orbit would otherwise be a perfect ellipse, the Sun being located in one of its foci).
The ecliptic coordinates can easily be converted into galactic coordinates, the longitude and latitude, which refer positions on the sky to fixed galactic equator and to direction to galactic centre (the direction lies on the equator and is the origin of the galactic longitude, like Greenwich meridian is for the geographical longitude). For the present purpose I have used the algorithm by P. Bretagnon, J.L. Simon and J. Laskar (J. Hist. Astron., 17 (1986), 39-50) which allows computing the ecliptic longitude of the Sun to 2" accuracy. The results, the positions of the Sun at the exact moments of December solstices are plotted in the galactic coordinates in Fig. 1. and Fig. 2. Looking at them one quickly finds that neither the claim of galactic equator crossing nor the closest approach to the galactic centre can be attributed to the 2012 year.
|Fig. 1: Positions of the Sun on the sky on December solstices in the years 1990 through 2250. These positions also mark approximate path that the Sun traces in our times each year (in the direction towards increasing longitude, from left to right) in about four days around December 21. The dashed lines show directions to galactic centre at three solstices. It is clear that the Sun will be closest to the centre only during the solstice of December 21, 2228 and was closest to the galactic equator on the solstice of December 21, 1997 (consult also higher resolution plot in Fig. 2.). The year 2012 appears to be as usual as thousands of other common years in the 26 000 year precession cycle.|
|Fig. 2: Portion of Fig. 1 showing in higher resolution positions of the Sun in the galactic coordinates at the moments of December solstice. The blue line represents an average path of the Sun (the ecliptic), which can be considered stationary with respect to stars (and thus also to our Galaxy and its conventional spherical coordinates). The spacing between the orange dots, about 50", in this plot reflect the precessional rotation of the Earth axis of diurnal rotation which amounts to a full, 360° rotation in about 26 000 years.|
Also, it should be remembered that the Sun crosses the galactic equator twice every year near the points where the ecliptic intersects the equator. Anyway, even though the crossing that occurred in December 1997 was very close to galactic equator it wasn't really exceptional in any physically or otherwise significant way. Further, during the solstice of 2228, which will be closest to the galactic centre, the Sun will be still as far as 5.5 degrees away from it (in 1997 the distance was 6.4 degrees).
Recent astronomical observations suggest that the actual centre of our Milky Way galaxy resides a few arc minutes away from the nominal position defined by astronomers in 1958. It coincides with the radio source Sagittarius A* (and a supermassive black hole). Moving the origin of galactic coordinate system by this small angle wouldn't appreciably change the results presented in this report. The solstice closest to this new galactic plane (166" below the present position) would shift from 1997 to 1994, but the one closest to the centre would remain in 2228.
Someone may argue that it is the physical Sun, and not projection of it on the celestial sphere, that is crossing the galactic equatorial plane in 2012. This is also impossible, because, according to estimates, our Sun is located 24 ± 6 pc (1 pc = 3.086×1016 m) above the galactic plane and its velocity, relative to nearby stars, is only 19.7 km/s, or about 24 pc per million years, at an angle (about 33°) to but away from the plane.
To conclude, if we are to believe in messages speaking of a galactic
'alignment' of 21 December, 2012, we cannot directly connect it with the
dynamics of our Solar System and Galaxy as we know them in this 3D
(some would rather say: 3rd dimension) reality.
Posted July 4, 2011