Astronomy Principles and Practice Fourth Edition.pdf

66 The celestial sphere: coordinate systems
Figure 8.6. Examples 8.1 and 8.2—zenith distances at upper and lower culmination.
Hence,
DZ = 42 ◦ − 30 ◦ = 12 ◦ .
The zenith distance at upper culmination is, therefore, 12 ◦ and is north of the zenith.
ZC = ZP+ PC = 90 − φ + 90 − δ
= 180 − 48 − 60
= 72 ◦ .
The zenith distance at lower culmination is, therefore, 72 ◦ .
Example 8.2. The zenith distances of a star at upper culmination (south of the zenith) and lower
culmination are 24 ◦ and 74 ◦ respectively. Calculate the latitude of the observer and the declination
of the star.
Let the latitude and declination be φ and δ degrees respectively. Then
PF = PZ + ZF
that is
90 − δ = 90 − φ + ZF
or
φ − δ = 24 ◦ . (8.4)
Also,
PG = ZG − PZ
giving
90 − δ = ZG − 90 + φ
or
φ + δ = 180 − 74 ◦ = 106 ◦ . (8.5)
Adding equations (8.4) and (8.5) we obtain
2φ = 130 ◦ or φ = 65 ◦ N.
Substituting 65 ◦ for φ in equation (8.4) gives δ = 41 ◦ N.