sidereal right ascensions, 3

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Before continuing, it may be useful to offer an astronomical definition of

the word " sidereal " . The conventional definition is " measured with

reference to (or in the background of) the stars " . My Anchor Dictionary of

Astronomy edited by Valerie Illingworth (New York, 1980) provides this

definition on page 406:

 

" sidereal. Related to or measured or determined with reference to the stars " .

 

This definition is tautological, because it does not explain what " with

reference to the stars " means. A better definition is given further below

(emphasis mine):

 

" sidereal month. The time taken by the moon to complete one revolution

around the Earth, measured with respect to a background star or stellar

group CONSIDERED FIXED IN POSITION " .

 

" sidereal year. The time taken by the Earth to complete one revolution

around the Sun with reference to a background star or stellar group, which

is REGARDED AS FIXED IN POSITION " .

 

In other words, " sidereal " means a fixed stellar reference frame. A

reference frame fixed in space and devoid of motion or rotation is called

" inertial " . Because stars have proper motion, in practice, astronomers use

a " quasi-inertial " frame based on a " fundamental catalog " (such as the

FK5), consisting of reference stars with very well-known proper motions,

and in the last years, for more accuracy a standard set of very distant

radio sources with negligible proper motion instead of fundamental stars

has been used.

 

Astronomers invariably use the stellar or sidereal reference frame to

calculate ephemerides of solar system objects. This is necessary in order

to model as accurately as possible their motion (hence the term " dynamical

reference frame " ). Extreme efforts are taken in order to arrive at the

ideal inertial space, presently defined arbitrarily around the mean equinox

and ecliptic of January 1, 2000 (J2000).

 

Once planetary positions have been calculated for J2000, precession,

nutation, aberration, etc. are applied in order to establish the " of date "

apparent geocentric coordinates which are found in astrological

ephemerides. But the reduction from J2000 to apparent position is made

rigorously, applying precession also to the latitudes and accounting for

the effect of the latitude on the precession in longitude, a factor that is

ignored by sidereal astrologers, who use the tropical positions as source

to convert back to their " quasi-sidereal " reference frame and results in

inaccurate, approximate positions.

 

The use of J2000 to represent positions is equivalent to using the mean

equinox and ecliptic of J2000 instead of A.D. 221 (in the case of the

Fagan/Bradley zodiac) or the time of birth as zero point. The difference is

that it is done rigorously. If one were to take rigorously A.D. 221 as the

zero point of coordinates, the long time-span from then to the present

would result in displaced coordinates when compared with the standard

astrological procedure. In my next post I will illustrate these differences

with an example.

 

Juan