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Equatorial, Ecliptic, and Galactic Coordinates

0:20 Diagram of the Ecliptic from Pearson's "Astronomy, A Beginner's Guide" 1:10 Meaning to find the location of the Summer Solstice, I accidentally look up 23.5 degrees above the Vernal Equinox (in Pegasus) 1:40 Correction to find (6h, 23.5°) Alt-248 2:25 Locating Taurus and the Summer Solstice between Gemini and Taurus above Orion's hand. 4:29 Errata. I say summer solstice point is (6h, 90°) but it should be (6h, 23.5°) 5:30 Identifying th (6h, 0°) point, and the equatorial plane 6:20 Equator and ecliptic appear parallel near orion, taurus, gemini, but intersect at Vernal Equinox just south of pisces 7:50 Errata: Drawing the lines toward the wrong Pisces 8:30 Alignment of stars in Cetus with Vernal Equinox. 9:10 Curvature of the ecliptic and equator on a spherical star-map. 11:10 Virgo (12h, 0°) Autumn Equinox 11:30 Sagittarius Winter Solstice 11:45 Galactic Center lies near "Teapot," Sagittarius, Winter solstice 13:10 Feature comparison of Teapot and Sagittarius 14:20 Location of M8, "The Lagoon Nebula" is almost exactly the same as the Winter Solstice (18h, -23.5°) 15:15 (18h, 0°) point on Equatorial plane, in Ophiuchus. 16:00 Global Star Map is drawn curiously inside out and backwards so that constellations look right from the outside instead of looking right from the inside. 19:30 Orthogonal vs Unit Spherical Coordinate System 20:20 Identifying directions toward Vernal Equinox, Summer Solstice, Autumn Equinox, Winter Soltice, Ecliptic North Pole in Equatorial Spherical Coordinates. 21:35 Converting Unit Spherical coordinates to Unit Orthogonal coordinates 22:45 Right-handed vs Left-Handed system. 24:20 Unit Spherical Equatorial Coordinates of Ecliptic North Pole 25:40 Calculating the orthogonal coordinates given the angles. 27:00 Equatorial Coordinates: (100-Pisces, 010-Orion, 001-Polaris) 27:30 Spherical to Orthogonal 28:40 Orthogonal to Spherical Transformation, ArcTangent 30:00 Converting Ecliptic to Equatorial Coordinates: Coordinates of Vernal Equinox, Summer Solstice, and Ecliptic North 33:30 Creating the EclipticToEquatorial Transformation Matrix 33:45 EquatorialToEcliptic (Inverse Transformation) 35:10 Convertin Galactic to Equatorial Coordinates; Galactic North Pole, Galactic Center 36:20 Finding the (010) 'galactic east' vector; Right-handed Coordinates; Cross-Product 37:45 GalacticToEquatorial and EquatorialToGalactic Transformation Matrix. 38:20 Verifying our Matrix using (3h, 30°) 38:50 The matrices are actually correct, however, when I plugged it into Mathematica I named them incorrectly. 39:20 Plugging Wikipedia data into the online tool to verify galactic center and galactic north pole. 41:40 I discovered my mistake here, and confirmed that my test should have worked if I had named them correctly.