zotero/storage/NNCU6235/.zotero-ft-cache

ITINERARY 120 ISH SLIDES (FAST)

MAP PROJECTION LIVE DEMO (10 MINS)

DATABASE SUPPLAMENT

PROJECTED COORDINATE SYSTEMS AND TYPES OF PROJECTIONS

TYPES AND EXAMPLES.

SPECIAL INTEREST ON AE

CELESTIAL COORDINATES AND BASED ON ANGLES TO STARS

CELESTIAL CURVATUE

GEOGRAPHIC TO CELESTIAL 1 TO 1

ASTROGEODEDICS

SPHERE TO HEMISPHERE, AND CIRCUMFERENCESS

COSMOGRAPHY

SHOOTING FOR 90 MINUTES

MAPS HAVE BEEN LYING TO YOU ALL YOUR LIFE

DO ALL MAPS PRJECT THE GLOBE?

WHAT DO MAP PROJECTIONS ACTUALLY ‘PROJECT’
ALL MAPS PROJECT COORDINATE SYSTEMS.
MOST COMMON IS THE GEOGRAPHIC COORDINATE SYSTEM AKA (LATITUDE AND LONGITUDE)
IN ADDITION OTHER COORDINATE SYSTEMS ARE:
UTM (UNIVERSAL TRANSVERSE MERCATOR) STATE PLANE COORDINATE SYSTEM (SPCS) CARTESIAN COORDINATE SYSTEM MILITARY GRID REFERENCE SYSTEM (MGRS) LOCAL COORDINATE SYSTEMS EARTH-CENTERED, EARTH-FIXED (ECEF) COORDINATE SYSTEM GEOCENTRIC COORDINATE SYSTEM

A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others.
Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.

CELESTIAL SPHERE

1. AREA-PRESERVING PROJECTION – ALSO CALLED EQUAL AREA OR
EQUIVALENT PROJECTION, THESE PROJECTIONS MAINTAIN THE
RELATIVE SIZE OF DIFFERENT REGIONS ON THE MAP.
2. SHAPE-PRESERVING PROJECTION – OFTEN REFERRED TO AS CONFORMAL
OR ORTHOMORPHIC, THESE PROJECTIONS MAINTAIN ACCURATE
SHAPES OF REGIONS AND LOCAL ANGLES.
3. DIRECTION-PRESERVING PROJECTION – THIS CATEGORY
INCLUDES CONFORMAL, ORTHOMORPHIC, AND AZIMUTHAL PROJECTIONS, WHICH PRESERVE DIRECTIONS, BUT ONLY FROM THE CENTRAL POINT FOR AZIMUTHAL
PROJECTIONS. 4. DISTANCE-PRESERVING PROJECTION
– KNOWN AS EQUIDISTANT PROJECTIONS, THEY DISPLAY THE TRUE DISTANCE BETWEEN ONE OR TWO POINTS AND ALL OTHER POINTS
ON THE MAP.

ALL MAPS ARE THE PROJECTING THE GRATICULE

ALL MAPS ARE THE PROJECTING THE GRATICULE

A GREAT CIRCLE IS ANY CIRCLE THAT DIVIDES A SPHERE INTO TWO EQUAL HEMISPHERES AND IS THE LARGEST POSSIBLE CIRCLE THAT CAN BE DRAWN ON A SPHERICAL SURFACE.
EVERY GREAT CIRCLE IS THE INTERSECTION OF THE SPHERE WITH A PLANE THAT PASSES THROUGH THE CENTER OF THE SPHERE. EXAMPLES ON EARTH:
THE EQUATOR IS A NATURAL EXAMPLE OF A GREAT CIRCLE BECAUSE IT DIVIDES THE EARTH INTO THE NORTHERN AND SOUTHERN HEMISPHERES.
MERIDIANS OF LONGITUDE ARE ALSO EXAMPLES OF GREAT CIRCLES AS EACH PASSES THROUGH THE NORTH AND SOUTH POLES, SPLITTING THE EARTH INTO EASTERN AND WESTERN HEMISPHERES. EACH MERIDIAN AND ITS ANTIMERIDIAN (THE LINE OF LONGITUDE 180 DEGREES ON
THE OPPOSITE SIDE OF THE GLOBE) TOGETHER FORM A GREAT CIRCLE. MERIDIANS DEFINITION:
A MERIDIAN IS A LINE OF LONGITUDE, RUNNING FROM THE NORTH POLE TO THE SOUTH POLE. BY DEFINITION, IT CONNECTS ALL POINTS WITH THE SAME LONGITUDE.
UNLIKE PARALLELS OF LATITUDE (EXCEPT FOR THE EQUATOR), ALL MERIDIANS ARE HALVES OF GREAT CIRCLES. SIGNIFICANCE OF GREAT CIRCLES IN NAVIGATION SHORTEST ROUTE:
TRAVEL ALONG A GREAT CIRCLE IS THE SHORTEST DISTANCE BETWEEN TWO POINTS ON A SPHERE. THIS PRINCIPLE IS CRITICALLY IMPORTANT IN AIR AND SEA NAVIGATION, WHERE FOLLOWING A GREAT CIRCLE ROUTE MINIMIZES TRAVEL TIME AND FUEL CONSUMPTION.
NAVIGATION AND GPS:
MODERN NAVIGATION SYSTEMS, INCLUDING GPS, UTILIZE THE CONCEPT OF GREAT CIRCLES TO CALCULATE THE MOST EFFICIENT ROUTES ACROSS THE EARTH’S CURVED SURFACE.
VISUALIZING GREAT MERIDIANS AND GREAT CIRCLES

1. CYLINDRICAL PROJECTIONS: THESE PROJECTIONS INVOLVE WRAPPING A CYLINDER AROUND THE EARTH AND PROJECTING ITS FEATURES ONTO THE CYLINDRICAL SURFACE. EXAMPLES ARE
THE MERCATOR, TRANSVERSE MERCATOR, AND MILLER CYLINDRICAL
PROJECTIONS.
CONIC PROJECTIONS: FOR THESE PROJECTIONS, A CONE IS PLACED OVER
THE EARTH, AND ITS FEATURES ARE PROJECTED ONTO THE CONICAL
SURFACE. COMMON EXAMPLES ARE THE LAMBERT CONFORMAL CONIC AND ALBERS EQUAL-AREA CONIC PROJECTIONS.
AZIMUTHAL PROJECTIONS: ALSO REFERRED TO AS PLANAR OR ZENITHAL PROJECTIONS, THESE USE A FLAT PLANE THAT TOUCHES THE EARTH AT A SINGLE
POINT, PROJECTING THE EARTH’S FEATURES ONTO THE PLANE. AZIMUTHAL
EQUIDISTANT, STEREOGRAPHIC, AND ORTHOGRAPHIC PROJECTIONS ARE EXAMPLES.
PSEUDOCYLINDRICAL PROJECTIONS: THESE PROJECTIONS RESEMBLE CYLINDRICAL PROJECTIONS
BUT EMPLOY CURVED LINES INSTEAD OF STRAIGHT LINES FOR MERIDIANS AND PARALLELS. THE
SINUSOIDAL, MOLLWEIDE, AND GOODE HOMOLOSINE PROJECTIONS ARE POPULAR EXAMPLES.

. EQUAL-AREA (EQUIVALENT) PROJECTIONS: THESE PROJECTIONS PRESERVE THE CORRECT PROPORTIONS OF AREAS, SUCH AS IN THE ALBERS EQUAL-AREA CONIC AND MOLLWEIDE PROJECTIONS.
2. CONFORMAL (ORTHOMORPHIC) PROJECTIONS: THESE PROJECTIONS MAINTAIN LOCAL ANGLES AND SHAPES, AS SEEN IN THE MERCATOR AND LAMBERT CONFORMAL CONIC PROJECTIONS.
3. EQUIDISTANT PROJECTIONS: THESE PROJECTIONS RETAIN TRUE DISTANCES FROM ONE OR TWO POINTS TO ALL OTHER POINTS, AS IN THE AZIMUTHAL EQUIDISTANT PROJECTION.
4. AZIMUTHAL PROJECTIONS: THESE PROJECTIONS PRESERVE DIRECTIONS FROM A CENTRAL POINT, INCLUDING SOME CONFORMAL, ORTHOMORPHIC, AND AZIMUTHAL PROJECTIONS.
5. COMPROMISE PROJECTIONS: THESE PROJECTIONS ATTEMPT TO BALANCE VARIOUS DISTORTIONS INHERENT IN MAP PROJECTIONS, SUCH AS THE ROBINSON AND WINKEL TRIPEL PROJECTIONS.

ALL MAPS ARE THE PROJECTING THE GRATICULE

LATITUDE AND LONGITUDE ARE INDEED BASED ON OBSERVATIONS OF THE SKY (CELESTIAL NAVIGATION) AND ARE FUNDAMENTALLY TIED TO A SPHERICAL MODEL OF THE EARTH.
THE ENTIRE SYSTEM OF LATITUDE AND LONGITUDE IS BASED ON THE PREMISE THAT THE EARTH IS SPHERICAL. THIS IS EVIDENT IN SEVERAL WAYS:
GREAT CIRCLES: BOTH LATITUDE AND LONGITUDE LINES ARE BASED ON THE CONCEPT OF GREAT CIRCLES THAT DIVIDE THE GLOBE INTO EQUAL HALVES. THE EQUATOR AND ALL MERIDIANS ARE GREAT CIRCLES.
SPHERICAL TRIGONOMETRY: [ASTRONOMICAL TRIANGLE ]THE CALCULATIONS FOR DISTANCES AND ANGLES BETWEEN DIFFERENT POINTS ON THE EARTH’S SURFACE USE SPHERICAL TRIGONOMETRY, ASSUMING THE EARTH IS A SPHERE.
NAVIGATION AND MAPPING: ALL NAVIGATIONAL AND MAPPING SYSTEMS THAT USE LATITUDE AND LONGITUDE TAKE INTO ACCOUNT THE EARTH’S INFLICTED CURVATUREFROM THE GEOGRAPHIC COORDINATE SYSTEM IT IS PROJECTIONG
GREAT CIRCLES VS. CIRCLES: A GREAT CIRCLE IS THE LARGEST CIRCLE THAT CAN BE DRAWN ON A SPHERE'S SURFACE, DIVIDING IT INTO TWO EQUAL HALVES. ON A SPHERE LIKE THE EARTH, THE SHORTEST DISTANCE BETWEEN TWO POINTS LIES ALONG THE ARC OF A GREAT CIRCLE. IN NAVIGATION, USING THE CONCEPT OF GREAT CIRCLES ACCOUNTS FOR THE
EARTH'S CURVATURE, PROVIDING THE MOST EFFICIENT AND SHORTEST PATH BETWEEN TWO POINTS.

Does the Azimuthal Equidistant polar projection display the same distances as all the other projections of the geographic coordinate system?
YES
The Azimuthal Equidistant projection preserves true distances from the central point to any other point on the map, and the great-circle distance formulas using latitude and longitude apply universally across all map projections, including the Azimuthal
Equidistant projection. Therefore, it displays the same accurate distances as other projections of the
geographic coordinate system.
The Haversine formula and the spherical law of cosines are standard methods used to calculate great-circle distances between two points on the Earth's surface using their
latitude and longitude. These formulas provide accurate distance calculations.

Horizontal Coordinate System (Altitude-Azimuth): - Coordinates: Altitude, Azimuth
Equatorial Coordinate System (Right Ascension - Declination): - Coordinates: Right Ascension, Declination
Geographic Coordinate System longitude/latitude
Geocentric Coordinate Systems Cartesian coordinates (X, Y, Z) or spherical coordinates (radius, latitude, longitude).
X: Distance from the center of the Earth to the point in the plane of the equator, along the prime meridian. Y: Distance from the center of the Earth to the point in the plane of the equator, 90 degrees east of the prime meridian. Z: Distance from the center of the Earth to the point along the axis of rotation (positive towards the North Pole).
Ecliptic Coordinate System: - Coordinates: Ecliptic Longitude, Ecliptic Latitude
Galactic Coordinate System: - Coordinates: Galactic Longitude, Galactic Latitude
Supergalactic Coordinate System: - Coordinates: Supergalactic Longitude, Supergalactic Latitude

Cartesian coordinates (X, Y, Z) or spherical coordinates (radius, latitude, longitude).
X: Distance from the center of the Earth to the point in the plane of the equator, along the prime meridian. Y: Distance from the center of the Earth to the point in the plane of the equator, 90 degrees east of the prime meridian. Z: Distance from the center of the Earth to the point along the axis of rotation (positive towards the North Pole).
Spherical Coordinates
Radius (r): Distance from the Earth's center to the point. Latitude (φ): Angle between the point and the equatorial plane. Longitude (λ): Angle from the prime meridian to the point's projection onto the equatorial plane.

The concepts of longitude and latitude are fundamentally based on measurements derived from observing celestial bodies and are designed for a spherical model of the Earth. These geographic coordinates form a grid system used to pinpoint locations on the globe (GRATICULE)

The entire system of latitude and longitude is based on sphericity.
- Great Circles: Both latitude and longitude lines are based on the concept of great circles that divide the globe into equal halves. The equator and all meridians are great circles.
- Spherical Trigonometry: The calculations for distances and angles between different points on the Earth’s surface use spherical trigonometry, assuming the Earth is a sphere.
- Navigation and Mapping: All navigational and mapping systems that use latitude and longitude take into account the Earth’s curvature. For example, flight routes and maritime courses plotted using these coordinates reflect adjustments for the globe’s shape.
- Great Circles vs. Circles: A great circle is the largest circle that can be drawn on a sphere's surface, dividing it into two equal halves. On a sphere like the Earth, the shortest distance between two points lies along the arc of a great circle. In navigation, using the concept of great circles accounts for the Earth's curvature, providing the most efficient and shortest path between two points. In contrast, a circle (in the context of a two-dimensional plane) does not account for the varying distances and directions encountered on a three-dimensional spherical surface due to curvature -

Any rotating sphere has two poles at each end of the axis of rotation, and an equator which bisects the sphere in a plane that is perpendicular to the axis of rotation. However, In reality,
In reality, we are only seeing a half sphere, or a hemisphere of stars at any one time. The tricky part is that they, and everyone else, assume that when the celestial objects are out of sight, they are actually beneath
our feet, executing a perfect circle before returning the following day.
Never the less, they have denoted both celestial poles and the celestial equator, imagining this sphere to continue beneath your feat. The great part is that although the objects are actually across the earth, the
math for a sphere depeneding on angles taken from the bottom hemisphere actually work perfectly.
That is to say, if you use math to predict when you will see objects return, they could be represented equally well in either coordinate system.
***The celestial sphere conceptualizes imaginary lines inscribed on the celestial sphere through the use of coordinate systems. These lines rotate with the celestial sphere, and therefore do not depend on the observer's location, time of observation, or horizon, but
are linked to the axis rotation of the sky.

THE NIGHT SKY LOOKS LIKE AN UPSIDE DOWN BUT BOWL, AS IT TURNS AROUND DURING THE NIGHT .... AND THIS MAKES IT IS EASY TO THINK OF IT AS A GIANT SPHERE.

IN REALITY, WE ARE ONLY SEEING A HALF SPHERE, OR A HEMISPHERE OF STARS AT ANY ONE TIME. THE TRICKY PART IS THAT THEY, AND EVERYONE ELSE, ASSUME THAT WHEN THE CELESTIAL OBJECTS ARE OUT
OF SIGHT, THEY ARE ACTUALLY BENEATH OUR FEET, EXECUTING A PERFECT CIRCLE BEFORE RETURNING THE FOLLOWING DAY.
NEVER THE LESS, THEY HAVE DENOTED BOTH CELESTIAL POLES AND THE CELESTIAL EQUATOR, IMAGINING THIS SPHERE TO CONTINUE BENEATH YOUR FEAT. THE GREAT PART IS THAT ALTHOUGH THE OBJECTS ARE ACTUALLY ACROSS THE EARTH, THE MATH FOR A SPHERE DEPENEDING ON ANGLES TAKEN
FROM THE BOTTOM HEMISPHERE ACTUALLY WORK PERFECTLY.
THAT IS TO SAY, IF YOU USE MATH TO PREDICT WHEN YOU WILL SEE OBJECTS RETURN, THEY COULD BE REPRESENTED EQUALLY WELL IN EITHER COORDINATE SYSTEM.

Celestial Sphere: All of these systems conceptualize the sky as a spherical surface with the observer at its center. This spherical model is critical as it mirrors the true nature of the sky as observed from Earth, which appears dome-like due to the Earth’s curvature and the vast distances of celestial objects.
Observer-Centric Modeling: In systems like the Horizontal Coordinate System, the observer’s horizon and zenith define the fundamental plane and the highest point directly overhead, respectively. This setup naturally forms a sphere segment from the observer’s perspective, reinforcing the idea of curvature as it relates to the observer’s immediate environment.
Spherical Geometry: The use of spherical geometry in these coordinate systems is crucial for managing angular measurements and relationships between objects in the sky. Spherical trigonometry, which is employed to calculate positions and convert between coordinate systems, depends on the principles of spherical geometry—confirming that the sky’s curvature is not merely perceived but geometrically integral to the systems.
Reference Planes and Great Circles: Each coordinate system uses specific reference planes (such as the celestial equator or ecliptic plane) and measures angles along these planes. These planes, intersecting the celestial sphere, create great circles that are the shortest paths between points on the sphere, emphasizing the inherent spherical nature of the sky.
Equatorial and Ecliptic Systems: These systems further underscore curvature by aligning their primary coordinates with Earth’s rotation axis and orbit around the Sun, respectively. The Right Ascension and Declination in the Equatorial system, or Ecliptic Longitude and Latitude in the Ecliptic system, are measured in terms of angles on the celestial sphere, consistent with spherical coordinates.

Coordinate systems based on angles to the stars, such as the Horizontal, Equatorial, Ecliptic, and Galactic coordinate systems, inherently assume and account for the curvature of the celestial sphere.
This curvature is essential for accurately mapping the positions and movements of celestial objects as seen from an observer's vantage point on Earth.
This is the only thing in our world that IS CURVED! The celestial sphere (which represents all tangent points from any observer and a fundamental plane through the middle) inherently uses spherical trigonometry and a host of other factors that require us to treat it as a curved sphere

Coordinate Systems and the Celestial Sphere: Takes into account the apparent curvature of the sky as seen from the observer's vantage point.
Coordinate systems based on angles to the stars account for the curvature of the celestial sphere by treating the sky as a spherical surface surrounding the observer.
The altitude measures how high an object is in the sky, directly accounting for the observer’s horizon. - The azimuth provides the horizontal direction, with the horizon forming the fundamental plane

Each system defines a fundamental plane (horizon, celestial equator, ecliptic, or galactic plane) that helps in positioning objects on the curved celestial sphere.
Angles are measured relative to the fundamental plane and other reference points (e.g., vernal equinox for right ascension, north point for azimuth).
Calculations on the celestial sphere use spherical trigonometry to account for the curvature. This allows for accurate transformations between different coordinate systems.
Transformation Equations: Equations transform coordinates between different systems (e.g., from horizontal to equatorial coordinates).

When you perform calculations such as distances using azimuthal transformations, whether the Earth is considered flat or spherical in model, the
distances like those measured in nautical miles remain consistent.
This is because the formulas that calculate distances based on angles to the stars (like the Haversine formula) remain valid regardless of the underlying shape assumption of the Earth.
This means that for navigation and mapping, using either a flat or spherical model does not impact the practical outcomes when using properly adjusted coordinate transformations. Measurements like nautical and statute miles retain
their values and utility PRECISELY because their definition ties back to the coordinate system (latitude and longitude), which remains invariant between
transformations.

BOTH SYSTEMS ARE BASED ON GREAT CIRCLES: LATITUDE AND DECLINATION ARE MEASURED FROM THE EQUATORIAL PLANES (EARTH’S EQUATOR AND CELESTIAL EQUATOR), WHILE LONGITUDE AND RIGHT ASCENSION ARE MEASURED FROM PRIME MERIDIANS (GREENWICH FOR EARTH AND THE VERNAL EQUINOX FOR THE SKY).
EACH USES A FNDAMENTAL CIRCLE (EQUATOR) AND A STARTING POINT FOR MEASURING EAST-WEST COORDINATES (GREENWICH MERIDIAN FOR LONGITUDE, VERNAL EQUINOX FOR RIGHT ASCENSION).
TIME IS INTRINSICALLY LINKED TO THESE COORDINATE SYSTEMS. EARTH’S ROTATION, WHICH DEFINES THE MEASUREMENT OF A DAY, AFFECTS BOTH LONGITUDE (THROUGH TIME ZONES) AND RIGHT ASCENSION (THROUGH THE SIDEREAL DAY, ABOUT FOUR MINUTES SHORTER THAN THE SOLAR DAY).
THE PRACTICE OF CELESTIAL NAVIGATION INVOLVES MEASURING THE ANGLES BETWEEN CELESTIAL BODIES AND THE HORIZON, AND COMPARING THESE OBSERVATIONS WITH TABLES BASED ON RIGHT ASCENSION AND DECLINATION. THIS DATA CAN THEN BE TRANSLATED INTO TERRESTRIAL LATITUDE AND LONGITUDE FOR NAVIGATION.
LATITUDE TO DECLINATION: THE CELESTIAL SPHERE USES DECLINATION (Δ) INSTEAD OF LATITUDE, BUT BOTH MEASURE THE ANGULAR DISTANCE NORTH OR SOUTH OF THE EQUATOR. THUS, EARTH'S LATITUDE IS DIRECTLY PROJECTED ONTO DECLINATION:𝛿=LATITUDE
LONGITUDE TO RIGHT ASCENSION: RIGHT ASCENSION (Α) IS ANALOGOUS TO LONGITUDE, ALTHOUGH IT IS MEASURED IN TIME UNITS (HOURS, MINUTES, AND SECONDS) ON THE CELESTIAL SPHERE. LONGITUDE IS CONVERTED TO RIGHT ASCENSION THROUGH A SCALING FACTOR(1 HOUR EQUALS 15 DEGREES).
THE RELATIONSHIP ALSO INVOLVES THE EARTH’S ROTATION AND THE POSITION OF THE VERNAL EQUINOX:𝛼=GST+LONGITUDE (WHERE GST IS GREENWICH SIDEREAL TIME, ADJUSTED FOR THE EARTH'S ROTATION TO ALIGN WITH THE VERNAL EQUINOX).
THE EARTH'S ROTATIONAL AXIS PROJECTS OUTWARD TO DEFINE THE NORTH AND SOUTH CELESTIAL POLES ON THE CELESTIAL SPHERE. IF YOU WERE STANDING AT THE EARTH'S NORTH POLE, FOR INSTANCE, THE CELESTIAL NORTH POLE WOULD BE DIRECTLY OVERHEAD.
THE EARTH'S EQUATOR PROJECTS DIRECTLY OUTWARDS TO FORM THE CELESTIAL EQUATOR. THIS IS THE FUNDAMENTAL PLANE OF THE CELESTIAL COORDINATE SYSTEM, ANALOGOUS TO THE EQUATOR ON EARTH.