## E

directly on southern latitude zones. With spherical trigonometry, it can be demonstrated that the maximum and minimum declinations along the ecliptic are +e and -e, respectively. In the IAU 1976 System of Astronomical Constants, the value of the obliquity of the equinox was e = 23° 26' 21.448" = 23°439291 for the epoch 2000 a.d., but it varies with time [cf. §4.4, (4.22) for the rate of variation of e].

Figure 2.13 shows both equatorial and ecliptic systems together and the spherical triangle used to transform the coordinates of one system into the other.

The transformation equations may be obtained from applications of the sine and cosine laws of spherical astronomy to yield sin b = cos e • sin 8 + sin e • cos 8 • sin a, (2.10)

sin 8 = cos e • sin b + sin e • cos b • sin l, (2.12)

where a is the right ascension (here, expressed in angular measure: 15° = 1h), 8 is the declination, b is the celestial latitude, l is the celestial longitude, and e is the obliquity of the ecliptic (see §2.4.5 for variations in this quantity over time).

The caution regarding quadrant determination that we urged earlier (§2.2.4) is appropriate here too. Table 2.2 should resolve any ambiguities.

As an example, suppose we wish to find the ecliptic coordinates of an object at a = 18h00m00s or 270°00000 and 8 = +28°00'00" or 28°00000. At the current epoch, assuming a value e = 23°441047, from (2.6), sin b = 0.917470 • 0.469472 - 0.397805 • 0.882948 • (-1.000000)

= 0.430726 + 0.351241 = 0.781967, so that b = arcsin(0.781967) = 51 ? 44103 or 180 0 -51 ? 44103 = 128 0 55897, from the rules described in §2.2.4. It is obvious that the first value is correct because B < 90° by definition. From (2.7),

0 0