Lessons 11–12 · 2 lessons · M. Mamadazimov. Astronomy Grade 11, 1st edition. DAVR NASHRIYOTI, Tashkent, 2018
11
Culmination of celestial bodies and culmination heights
Textbook: p. 19
GoalKnow the definition of culmination and calculate a body’s culmination altitude from latitude and declination.
New words
culmination · kulminatsiyaupper culmination · yuqori kulminatsiyalower culmination · pastki kulminatsiyazenith distance · zenit masofasi
Explanation
Culmination is the moment a body crosses the celestial meridian; its altitude is then the greatest (upper culmination) or the smallest (lower culmination) of the day. In the northern hemisphere a body with δ < φ passes south of the zenith at upper culmination and its altitude is h = 90° – φ + δ (zenith distance z = φ – δ). If δ > φ the body passes north of the zenith and h = 90° + φ – δ. At the lower culmination of a circumpolar star the altitude is h = φ + δ – 90°. For the Sun δ varies through the year from –23°26′ to +23°26′, so its noon altitude changes too; at Tashkent (φ ≈ 41°) it is ≈ 72° at the summer solstice, ≈ 49° at the equinox and ≈ 26° at the winter solstice.
Worked examples
Sirius (δ ≈ –17°) at Tashkent (φ = 41°) rises at upper culmination to h = 90° – 41° – 17° = 32°.
For Vega (δ ≈ +39°) at φ = 41° we have δ < φ, so h = 90° – 41° + 39° = 88°: it passes almost through the zenith.
Class activity
In a planetarium app look up the upper-culmination altitude of three bright stars for your city and compare with the formula. Do not observe the Sun.
Practice
1
What is culmination?
The crossing of the celestial meridian by a body.
2
What is the upper-culmination altitude of a star with δ = +10° at φ = 40°?
60
3
For φ = 41° and δ = +70°, on which side of the zenith does the star culminate, and at what altitude?
North of the zenith; h = 90° + 41° – 70° = 61°.
4
Why does the Sun’s noon altitude differ between summer and winter?
Because the Sun’s declination changes during the year: large in summer, negative in winter.