Chapter 1. Celestial Sphere
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1. Celestial Sphere and Coordinate System
1. Celestial Sphere and Coordinate System
⑴ Celestial Sphere
① An imaginary infinite spherical sky with the observer on Earth as the center.
② Earth’s center is the center of the celestial sphere.
⑵ Positions on the Celestial Sphere
① Zenith and Nadir : The points where the observer’s vertical line intersects the celestial sphere.
○ Vertical Circles : Circles passing through the zenith and nadir.
② Horizon and Others
○ Horizon : Circle formed by extending the plane of the horizon to intersect the celestial sphere.
○ Altitude Circle : All circles parallel to the horizon.
○ Meridian : Equator of the celestial sphere, also known as vertical circle.
③ Poles
○ North Pole and South Pole of the Celestial Sphere : Points where Earth’s axis of rotation intersects the celestial sphere.
○ Equator of the Celestial Sphere : Circle formed by extending Earth’s equator to intersect the celestial sphere.
○ Hour Circles : Circles passing through the celestial sphere’s north and south poles.
④ Meridian : The unique circle passing through zenith, nadir, and celestial poles.
⑤ When considering an observer on the opposite side of the Earth’s center, simply reverse the observer’s orientation for the same celestial sphere.
○ This is useful for extending interpretations from the Northern Hemisphere to the Southern Hemisphere.
⑶ Coordinates of Celestial Objects
① Equatorial Coordinate System
○ Latitude
○ Longitude
○ Example : When it is 00:20 AM on January 26th in Location A (34.2°N, 135°E), what time is it in Location B (34.2°N, 120°W)?
② Horizontal Coordinate System : Interpreted with zenith, nadir, and the horizontal plane as the center.
○ Cardinal Points
○ North Point : Point closest to the celestial pole in the intersection of the horizon and the meridian.
○ South Point : Point closest to the southern celestial pole in the intersection of the horizon and the meridian.
○ East Point : Point 90° east from the north point along the horizon.
○ West Point : Point 90° west from the north point along the horizon.
○ Horizontal Coordinates : Coordinate system indicating celestial object’s position using azimuth and altitude relative to the horizon and the north point.
○ Azimuth (A) : Angle clockwise from the north point when projecting a star onto the horizon.
○ Altitude (h) : Angle measured vertically from the horizon to the celestial object.
○ Zenith Distance (Z) : Angle from zenith to the celestial object.
○ When observing the same star from two points with different latitudes, the time the star stays above the horizon increases with higher latitude.
○ Reason : The angle between the hour circle and the horizon decreases, resulting in longer visibility.
○ As the time the star is above the horizon increases, the difference in azimuth angle when the star rises and sets also increases.
○ (Note) Considering circumpolar stars in the Northern Hemisphere can help understand this phenomenon.
○ When observing two stars rising, the higher the star’s declination, the longer it stays above the horizon.
○ (Note) Considering circumpolar stars in the Northern Hemisphere can help understand this phenomenon.
○ The difference in azimuth angles of two stars when they rise is greater at higher latitudes.
○ Combining the above two phenomena leads to understanding.
③ Equatorial Coordinate System : Interpreted with celestial poles and equator as the center.
○ Right Ascension (α) : Angle between the vernal equinox and the hour circle of a celestial object. 0h to 24h, 1h = 15°.
○ From the vernal equinox along the celestial equator to the celestial object. West → East.
○ Right ascension of the vernal equinox is defined as 0h.
○ Declination (δ) : Altitude of a star when it is located due south. -90° ± 90° (North (+), South (-)).
○ From the celestial equator along the hour circle to the celestial object. Upward or downward.
○ Vernal Equinox, Autumnal Equinox : Declination = 0°.
○ Summer Solstice : Declination = 23.5°.
○ Winter Solstice : Declination = -23.5°.
○ Equatorial Coordinates : Coordinate system representing celestial object’s position using right ascension and declination.
○ Feature : Coordinates remain constant regardless of time and location.
④ Meridian Altitude
○ Definition : Altitude of a celestial object when it is located on the southern meridian.
○ Meridian Altitude = 90° - Latitude + Declination
○ 90° - Latitude : Altitude of the intersection between the celestial equator’s declination and the southern meridian in the horizontal coordinate system.
○ (Note) Meridian altitude should be considered with respect to the horizontal coordinate system.
⑤ Ecliptic Coordinate System
○ Ecliptic Coordinates : Coordinates representing star positions with the ecliptic plane as the reference.
○ Ecliptic Latitude, Ecliptic Longitude
○ Since the Sun orbits counterclockwise around the ecliptic, ecliptic latitude becomes zero, but ecliptic longitude increases like time.
⑷ Names of Stars
① Equatorial Stars in the Northern Hemisphere
② Equatorial Stars near the Ecliptic
③ Equatorial Stars in the Southern Hemisphere
④ 12 Zodiac Constellations : Dividing the ecliptic into 12 equal parts of 30° each, centered on the vernal equinox, and selecting stars closest to those division points, creating 12 constellations.
2. Time and Calendar
⑴ Sidereal Time and Solar Time
① Sidereal Time : Time determined by the position of stars.
② Solar Time : Time determined by the position of the Sun.
⑵ Solar Time
① Apparent Solar Time
② Mean Solar Time
③ Equation of Time = Apparent Solar Time - Mean Solar Time = Mean Sun’s Right Ascension - Apparent Sun’s Right Ascension
⑶ Standard Time and Local Time
① Local Mean Solar Time = GMT + L ／15
② 1 Solar Year = 365.2422 Mean Solar Days = 366.2422 Sidereal Days
⑷ Earth’s Revolution and Seasons
⑸ Calendar
① Lunar Calendar
② Solar Calendar
⑹ Tidal Motion
① French Republican Calendar
② World Calendar
Input : 2019.04.07 09:25