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| Overview of the Sky |
1. Since the celestial equator is the zero measure of declination, anything on the celestial equator has a declination of zero.
3. The Sun completes a 360° path around the sky in 365 days, so in one day it moves 360/365 or a little less than 1°.
5. The Sun and Moon always move eastward with respect to the background stars. The Moon actually does orbit the Earth and never reverses its direction of revolution. The Earth never reverses its direction around the Sun so the Sun's motion in our sky is always eastward.
7. Venus is directly in between the Earth and the Sun when it is new (thus in inferior conjunction). The synodic period is the time from one inferior conjunction to the next, so Venus will be at the new phase every 584 days.
9. Jupiter is at full phase at both opposition and at conjunction because the fully illuminated hemisphere faces Earth.
11. When a superior planet is at quadrature, the angle between the planet and the Sun is 90°. The Earth turns 15° in one hour and will turn 90° in six hours. When Mars is 90° east of the Sun, it will set six hours after sunset and rise six hours after the Sun rises (rises at noon, sets at midnight ). When 90° west of the Sun, Mars sets at noon and rises at midnight.
13. Maximum elongation for Venus is approximately 45°. It takes three hours for Earth to rotate through 45°, so it will rise three hours before the Sun and be to the west of the Sun in our sky. Venus is much easier to see in a dark sky, because of its larger angle with the Sun.
15. The right ascension of Procyon is 7 hr 36 min, so this is the local sidereal time when Procyon is on the celestial meridian.
17. For orbital radius R
C = circumference = 2 x pi x R = 2 x 3.14 x 384,000 km = 2,411,520 km
The period P is
Therefore, the average speed is
19. The Moon completes a 360° circuit of the sky in about 27 days. For each day it will move 360°/27 = 13.3° and in one hour it will move 0.54°.
21. Both subtend 0.5° as seen in our sky. The Moon is 400 times smaller than the Sun and the Sun is 400 times further away than the Moon.
23. There is a 5° angle between the orbit of the Moon around Earth and the ecliptic plane. Thus, usually the Moon will pass north or south of the Sun, not directly in front of it as seen from Earth.
27. 2450 km
29. Because of the synchronous orbit of the Moon, the Earth would appear to remain in the same position in the sky (it would not move across the sky as the Moon moves across ours). But the Earth would be observed to rotate on its axis as we watched.
31. Mercury is always near the Sun, so it is hard to see and study. When Mercury is on opposite sides of the Sun, it is a "morning star" or "evening star," so it took ancient astronomers some time to realize that these were the same planet. By the time of later Greek astronomy this fact was well established.
33. Since Saturn is the most distant planet visible the naked eye, its period of about thirty years was the longest planetary timescale.
35. ε-Canis Minoris and γ-Aquari.
37. If the sidereal period is much larger than for Earth we obtain P ~ PE and the synodic period approaches the sidereal period of the Earth. This has a simple physical interpretation. For the outermost planets the period is so long that essentially they can be considered to be fixed on their orbit in the time that Earth makes one revolution. If the sidereal period is much shorter than for the Earth, the synodic period approaches the sidereal period of the planet. This latter case is not very well realized in the Solar System because there are only two inferior planets and they have sidereal periods not that much shorter than for Earth.