Object coordinates are usually given in the equatorial , sytem.
The zodiacal light is given in terms of ecliptic coordinates
with the zero point of
in the Sun.
Description of a line of sight by elongation and inclination
i also is common. For the relation between these two sets
of coordinates see Fig. 2 (click here)
and Sect. 3.5 (click here) below.
Integrated starlight is naturally presented in galactic coordinates l,b.
For estimates of the diffuse background brightness at a given position, transformation between these three systems is necessary. Figures 3 (click here)-7 (click here) provide a simple way to do so graphically with about one-degree accuracy, which is sufficient for many applications. The underlying transformation equations are summarised below for ease of access.
Airglow, extinction and scattering are best described in the local horizontal system A, z (azimuth, zenith distance). The transformation to the other systems depends on time and on the observer's geographic coordinates. For the horizontal system, only the equations for the transformation to the equatorial system are given.
The obliquity of the ecliptic is essentially constant, = 23.446 for equinox 1950, respectively = 23.439 for equinox 2000.
The precession of the vernal equinox along the ecliptic
is p0 = 50.3 ''/year. Hence
The north ecliptic pole is at = 18 h, .
The north celestial pole is at , .
Both and are counted eastward
from the vernal equinox.
Apart from the minimal change in , the transformation
equations then are the same for 1950 and 2000:
By IAU decision, for equinox 1950 the north galactic pole (NGP) is at = 12 h 49.0 m, = 27.4 and the celestial pole at l = 123.0, b = 27 24.0'. Hence the ascending node of the galactic equator is at = 18 h 49.0 m = 282.25, = 33.0. For equinox 2000, the coordinates of the north galactic pole are = 12 h 51.42 m, = 27 07.8', and we have = 282.86, = 32.93. The inclination of the galactic equator with respect to the ecliptic is . As and , l is also counted eastwards.
With these parameters, the transformations are as follows:
In ecliptic coordinates, for equinox 1950 the north galactic pole is at = 179.32, = 29.81, and the ascending node of the galactic equator at = 269.32, l1 = 6.38. For equinox 2000, the coordinates of the north galactic pole are = 180.02, = 29.81, and we have = 270.02, l1 = 6.38. The inclination of the galactic equator with respect to the ecliptic is . As already mentioned, l is counted eastwards. With these parameters, the transformations are as follows:
The transformation depends on local sidereal time and on geographical latitude . Instead of elevation, zenith distance z = will be used. The zenith distance of the celestial pole is . Both, azimuth A and hour angle are counted from the meridian through west.
Instead of also
a sun-centered polar coordinate system is used. Its coordinates are the angular
distance from the sun, called elongation , and a position
angle i, counted from the ecliptic counterclockwise,called inclination.
The relation between the two sets of coordinates,
when describing the position of a field-of-view with respect to the sun,
is shown in Fig. 2 (click here).
It is unfortunate that the obliquity of the ecliptic, used in Eqs. (3 (click here)) and (4 (click here)), and the angular distance from the sun, used in Eqs. (11 (click here)) and (12 (click here)), both are designated by the same letter . However we did not want to change the commonly used notations. In practice this dual meaning rarely should lead to confusion.
Figure 2: Relation between the coordinates used for presenting zodiacal light measurements. is counted positive towards east, i is counted positive counterclockwise from the ecliptic west of the Sun
The reader is cautioned that in some papers the differential helioecliptic
longitude may be called "elongation" or may
be designated as "", contrary
to our definition of elongation as the angular distance from
the sun to the field-of-view.
Figure 3: Relation between coordinates (lines) and (underlying dotted grid) for equinox 2000
Figure 4: Relation between coordinates (lines) and l, b (underlying dotted grid) for equinox 2000
Figure 5: Relation between coordinates l, b (lines) and (underlying dotted grid) for equinox 2000 - alternative projection
Figure 6: Relation between coordinates (lines) and l, b (underlying dotted grid) for equinox 2000
Figure 7: Relation between coordinates l, b (lines) and (underlying dotted grid) for equinox 2000 - alternative projection
|Site||IB(max)||IB(min)||IV(max)||IV(min)||Solar flux||Corresponding dates||ref.|
|(22.20)||(20.85)||168||80-12-06; 80-06-08; 88-12-05|
|(22.94)||116||78-02-08; 87-12-16; 87-12-19;|
|(22.02)||94||87-12-15; 87-12-16; 87-12-19;|
|23.05(22.98)||176||89-05-06; 90-06-26; 93-06-21|
|(21.16)||206||89-05-04; 91-06-11; 91-06-16|
|San Benito Mt.||22.37||21.32||233||80-04-11; 81-07-28; 82-06-22||3.|
|23.08||78||76-04-30; 87-04-25; 87-06-29|
|22.07||76||76-04-30; 87-04-28; 87-06-29|
|Kitt Peak||22.65||114||88-01-21; 88-03-17; 88-06-14||4.|
|22.98||75||86-12-02; 86-12-30; 87-06-22|
|21.60||114||87-11-20; 88-03-17; 88-06-14|
|22.01||75||86-12-02; 86-12-31; 87-06-22|
|Crimea||21.91||21.10||122||68-04-28; 71-04-25; 70-08-09||5.|
|23.05||22.05||136||68-03-29; 68-04-06; 68-04-28|
|Hawaii||22.27||210||88-11-13; 89-03-28; 89-09-12||6.|
|23.03||142||87-08-26; 87-11-13; 89-06-10|
|21.21||166||85-12-13; 88-11-13; 89-03-28|
|22.05||102||86-06-02; 87-08-26; 88-07-18|
|McDonald||22.54||21.54||138||60-02-04; 72-12-30; 73-01-12||7.|
|Observatory||23.01||156||60-01-27; 72-01-11; 72-01-15|
|21.92||159||60-01-27; 72-01-15; 73-01-08|
|1. Mattila et al. (1996a).|
|2. Leinert et al. (1995), Leinert et al. (1996, unpublished).|
|3. Walker (1988).|
|4. Pilachowski et al. (1989).|
|5. Lyutyi & Sharov (1982).|
|6. Krisciunas (1990).|
|7. Kalinowski et al. (1975).|