Height of the pole and the sky at different latitudes
Lessons 9–10 · 2 lessons · M. Mamadazimov. Astronomy Grade 11, 1st edition. DAVR NASHRIYOTI, Tashkent, 2018
10
The daily apparent rotation of the celestial sphere at different latitudes
Textbook: pp. 16–18
GoalExplain how the daily motion looks at different latitudes and decide from declination whether a body is circumpolar or never rises.
New words
circumpolar star · qutbdosh yulduzstar that never rises · chiqmaydigan yulduzdiurnal parallel · sutkalik parallelhorizon · ufq
Explanation
Bodies move along small circles parallel to the celestial equator, called diurnal parallels. At the geographic pole (φ = 90°) all stars circle parallel to the horizon and none rises or sets. At the equator (φ = 0°) the diurnal parallels are perpendicular to the horizon; every star rises and sets and each is visible for half of the day. At middle latitudes some stars never set – in the northern hemisphere a star is circumpolar if δ ≥ 90° – φ; if δ ≤ –(90° – φ) it never rises; the rest rise and set. That is why the Southern Cross (δ ≈ –60°) cannot be seen from Tashkent, while the Big Dipper never sets there.
At Termez (φ ≈ 37°) stars with δ ≤ –(90° – 37°) = –53° never rise. Sirius (δ ≈ –17°) rises and sets every day.
Class activity
With an adult in the evening put a phone on a tripod and take a 20–30 minute long exposure towards the Pole Star: the star trails form arcs around the pole. You can also analyse a ready-made photo like this.
Practice
1
How do the stars move at the geographic pole?
Along circles parallel to the horizon; none rises or sets.
2
At latitude 45° what is the smallest declination of a circumpolar star?
45
3
Is a star with δ = –70° visible at φ = 41°?
No: –70° < –(90° – 41°) = –49°, so it never rises.
4
Why does every star rise and set at the equator?
Because the poles lie on the horizon and the diurnal parallels are perpendicular to it and cross it.