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--- train:lectures:positionalastro [2024/03/18 12:14] – Roy Prouty
+++ train:lectures:positionalastro [2024/03/18 16:10] (current) – Roy Prouty
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-Since the fundamental plane is the plane of the Earth's Equator (called the Celestial Equator when projected onto the Celestial Sphere), we can re-use the familiar latitude lines to develop a new set of angular coordinates that are more objective than the Altitude and Azimuth we used before. We call these projected latitude lines lines of constant Declination. Declination is measured from the Celestial Equator, positive north, negative south.
+===Declination===
+Since the fundamental plane is the plane of the Earth's Equator (called the Celestial Equator when projected onto the Celestial Sphere), we can re-use the familiar latitude lines to develop a new set of angular coordinates that are more objective than the Altitude and Azimuth we used before. We call these projected latitude lines lines of constant Declination or DEC. Declination is measured from the Celestial Equator, positive north, negative south.
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-On Earth, we use the Prime Meridian to denote the zero-point for lines of longitude. On the Celestial Sphere under the Equatorial Coordinate System, we choose the one of the two intersections of the Celestial Equator with another plane -- the Ecliptic Plane. The Ecliptic Plane is the plane of the Solar System. It's roughly perpendicular to the rotation axis of the Sun and it's therefore the plane along which the large masses in our Solar System orbit the Sun (this is due to the formation of the Solar System and fairly complex interactions between Angular Momentum and frequent collisions 4-5 Billion Years ago!). ANYWAY. The Ecliptic is the apparent path of the Sun, Moon, and the rest of the planets in our sky (our Celestial Sphere). It's a plane, so it intersects the hollow Celestial Sphere and traces a {{https://en.wikipedia.org/wiki/Great_circle|Great Circle}} (since the Earth is also on that plane) around the Celestial Sphere. The Plane of the Celestial Equator (also containing the Earth) constitutes another Great Circle
+===Right Ascension and Equinoxes===
+On Earth, we use the Prime Meridian to denote the zero-point for lines of longitude. On the Celestial Sphere under the Equatorial Coordinate System, we choose the one of the two intersections of the Celestial Equator with another plane -- the Ecliptic Plane. The Ecliptic Plane is the plane of the Solar System. It's roughly perpendicular to the rotation axis of the Sun and it's therefore the plane along which the large masses in our Solar System orbit the Sun (this is due to the formation of the Solar System and fairly complex interactions between Angular Momentum and frequent collisions 4-5 Billion Years ago!). ANYWAY. The Ecliptic is the apparent path of the Sun, Moon, and the rest of the planets in our sky (our Celestial Sphere). It's a plane, so it intersects the hollow Celestial Sphere and traces a {{https://en.wikipedia.org/wiki/Great_circle|Great Circle}} (since the Earth is also on that plane) around the Celestial Sphere. The Plane of the Celestial Equator (also containing the Earth) constitutes another {{https://en.wikipedia.org/wiki/Great_circle|Great Circle}}. These two planes intersect and form a line that contains the Earth and intersects the Celestial Sphere at two points.
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-{{:train:lectures:celestialsphere-ecliptic.png?400|}}
+When the Earth-Sun line falls along these points, the rotation axis of the Earth is perpendicular to the Earth-Sun line. This is exactly the geometry of an Equinox. Said differently, these points on the Celestial Sphere are the points where the Ecliptic and Celestial Equator Great Circles intersect. The Sun crosses the Celestial Equator on the Equinox. When the Sun crosses S-->N, it's the March Equinox. When the Sun crosses N-->S, it's the September Equinox. **Draw this out, think about it, ponder the orbs, make this geometry make sense to you! Let's talk about it!**
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+\\
+[{{:train:lectures:celestialsphere-ecliptic.png?400|Rough geometry of the two planes, the Ecliptic and Celestial Equator. These intersect and give us the Equinoxes of date. The two planes are inclined to one another by the tilt of the Earth's rotation axis $~24^\circ$ .}}]
+\\
+\\
+The March Equinox is chosen to be the zero-point for the Equatorial Coordinate analogous to latitude -- the Right Ascension or RA. RA($\alpha$) is measured eastward along the Celestial Equator starting at the March Equinox.
+==Milankovitch Cycles==
+The specific location of the CNP/CSP/CEq do change over time in cycles known as {{https://en.wikipedia.org/wiki/Milankovitch_cycles|Milankovitch Cycles}}. These cycles are symptomatic of the Precession/Nutation of the Earth's rotation axes, Orbital Eccentricity, and Orbital Obliquity. They're due to the gravitational effects of the masses in our Solar System being more in-line with the Ecliptic than our Celestial Equator! How fun!?
+\\
+\\
+=== Note on Units ===
+Degrees, Minutes, Seconds -- of arc!
+As we're all aware, the circle is split into 360 friendly units called degrees. By the time more precise units were called for (~13th Century CE), mathematicians hadn't yet introduced the radian (1720s CE). So the units of increased precision were introduced as the minute pieces of the degree (minutes of arc) and the second-most minute pieces of the degree (secundus minutae, seconds of arc). The degree is the same one you're familiar with, denoted by the raised circle ($^\circ$). The minutes and seconds of arc (also called arcminutes and arcseconds) are denoted by one or two 'ticks', respectively. In this way, $1^\circ = 60'$ and $1' = 60''$ AND $1^\circ = 3600''$.
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+\\
+{{:train:lectures:blog014-image001-degree-arcmin-arcsec.png?400|}}
+{{:train:lectures:screen_shot_2024-03-18_at_12.23.42_pm.png?400|}}
+\\
+This history of the degree and it's close relationship to the distance the Sun appears to travel through the sky in a day-night cycle is fascinating from an anthropological lens. {{https://en.wikipedia.org/wiki/Sexagesimal|Enjoy}}!
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+Declination is measured in degrees, minutes of arc and seconds of arc with $360^\circ$ if traversing any Great Circle containing the CNP and CSP. Right Ascension is measured in hours, minutes, and seconds with $24^h$ if traversing the full Celestial Equator. As we shall see, changes in $\alpha$ correspond to different angular rotations of the Earth -- or different times of day! These units can be confusing. Minutes of arc (or arcminutes) are NOT the same as minutes of RA. Furthermore, the notation of $\alpha$ & $\delta$ (RA & DEC) can be confusing. They can be given in their fully qualified notation $(D_1^\circ~D_2'~D_3'', R_1^h, R_2^m, R_3^s)$, as degree-decimals, or some fun mixture of the two! When looking at a very small Field of View, angular measures in $\alpha$ will frequently just be in terms of arcminutes or arcseconds. Pay careful attention to these notations and values. Be sure you understand the differences between them!
+\\
+\\
+==== Reconciling LCHS and Eq Systems ====
+With this Equatorial Coordinate System, an observer
+[{{:train:lectures:screen_shot_2024-03-18_at_12.35.44_pm.png?400|The LHCS projected onto the Celestial Sphere centered on the fundamental plane of the  Equatorial Coordinate System.}}]
+\\
+\\
+For an observer at a positive latitude, $\lambda$, r ($\lambda=~39^\circ$ for MD):
+  - the CNP will be located at $(ALT=\lambda^\circ, AZ=0^\circ)$
+  - the CSP will never be above the local horizon (Why?)
+  - the CEq will intersect the local meridian at $(ALT=90^\circ - \lambda, AZ=180^\circ)$
+  - Zenith will see changing RA, depending on the local time, but the $\delta$ will always be $\lambda^\circ$
+=====Stellarium Exercises=====
+Using Stellarium, let’s all do the following together …
+  - Set location to Baltimore. Note the (lat, lon)
+      - Identify the Ecliptic
+      - Set the date to your birthday and tell me your “Sun sign” – ugh
+      - Explore Local Horizon Grid
+          - Find the Pole Star and find its (alt, az) – what should it be?
+          - Enable the Local Meridian
+          - Play time forward and watch star paths
+      - Explore Equatorial Grid
+          - Enable CEq
+          - Play time forward and watch star paths
+          - Set location to North Pole, South Pole, Equator, etc
+      - Determine (alt, az) of a star in Orion, determine (RA, DEC)
+      - Determine exact time (ET) of March Equinox
+      - Back in Baltimore, identify the set of stars that never set
+          - These stars comprise the Circumpolar Region of our Local Horizon
+          - How does this region change with latitude?
+      - With Local Meridian on over Equatorial Grid: Define Transits & Sidereal Time
+          - Look up current Sidereal Time: https://www.localsiderealtime.com/
+----
+Written by Roy Prouty 20240318\\
+Reviewed by