Astronomy Principles and Practice Fourth Edition.pdf

so that we have
But
Hence,
Similarly,
ZC = ζ A + k tan ζ A ZD = ζ B + k tan ζ B .
ZC = PC − PZ = 90 − δ − (90 − φ) = φ − δ.
Atmospheric refraction 117
φ − δ = ζ A + k tan ζ A . (10.9)
ZD = ZP+ PD = 90 − φ + 90 − δ = 180 − φ − δ
so that
180 − φ − δ = ζ B + k tan ζ B . (10.10)
If the observer’s latitude were accurately known, the two equations (10.9) and (10.10) in the two
unknowns δ and k could be solved to yield values of δ and k. But because of small changes in the
Earth’s crust, small variations take place in the latitude of the telescope used. In practice, therefore, at
least two circumpolar stars are observed, within a short period of time, so that two more equations are
obtained, namely
φ − δ ′ = ζ A ′ + k tan ζ A ′ . (10.11)
180 − φ − δ ′ = ζ B ′ + k tan ζ B ′ . (10.12)
The four equations (10.9)–(10.12) are now solved to give values of δ, δ ′ , φ and k.
10.2.4 Horizontal refraction
When the Sun or Moon is observed rising or setting, the observed zenith distance of its centre is 90 ◦ .
For such a zenith distance, the refraction amounts to 35 ′ and is called the horizontal refraction. Since
the angular diameter of these bodies is about 30 ′ , they are, in fact, below the horizon when their centres
are seen to be on the horizon. In the case of the Sun, therefore, horizontal refraction lengthens the time
interval during which it is daylight, sunrise and sunset taking place earlier and later respectively than
they would occur if refraction were absent. Tables which provide accurate sunrise and sunset times for
any location take account of horizontal refraction—a point not mentioned in section 8.11.
Table 10.1 shows how quickly refraction diminishes with altitude. Because of this, an extended
body like the Sun is decidedly oval in shape near rising and setting, the refraction of the upper and
lower limbs being different.
Table 10.1. Variation of apparent altitude with angle of refraction.
Apparent altitude
Angle of refraction
0 ◦ 35 ′ 21 ′′
1 ◦ 24 ′ 45 ′′
2 ◦ 18 ′ 24 ′′
3 ◦ 14 ′ 24 ′′
4 ◦ 11 ′ 43 ′′
10 ◦ 5 ′ 18 ′′
30 ◦ 1 ′ 41 ′′
60 ◦ 0 ′ 34 ′′
90 ◦ 0 ′ 0 ′′