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Space

Explore the Newtonian viewpoint in astrometry and learn about spatial coordinate systems, reference frames, and coordinate transformations. Gain insights into inertial reference frames, parallel shifts of origin, and rotations. Discover the various spherical coordinates and their applications in astrometry.

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Space

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  1. Space • Newtonian Viewpoint • Spatial Coord. System = Reference Frame • Inertial Reference Frame • Spatial Coord. Transformation • Parallel Shift of Origin • Rotation Lecture Notes on Astrometry

  2. Inertial Reference Frame (IRF) • RF where Law of Inertia is valid • Law of Inertia: No Force = Linear Motion • Galilei’s Principle of Relativity Physics are the same in any IRF • Parallel Shift of Linearly Moving Origin: IRF to IRF Lecture Notes on Astrometry

  3. Spatial Coordinates • Rectangular Coord. • Spherical Coord. • Spheroidal Coord. Lecture Notes on Astrometry

  4. Rectangular to Spherical Lecture Notes on Astrometry

  5. Spherical to Rectangular Lecture Notes on Astrometry

  6. Various Spherical Coordinates • Horizontal • Ecliptic • Equatorial • Galactic Lecture Notes on Astrometry

  7. Horizontal Coordinates • Distance: r • Zenith Distance: z • Altitude=Elevation: a = Alt = El = 90°–z • Azimuth(al angle): A = Az Lecture Notes on Astrometry

  8. Units of Angle • radian = rad • degree = deg = ° • minute = min = arc minute = ' • second = arc second = " = arcsec = as Lecture Notes on Astrometry

  9. Units of Angle (contd.) • 1° = 60 ' = 3600 " • 180° = p radian • 1" ~ 4.848 mrad • 20" ~ 0.1 mrad = magnitude of aberration • 0.001" = mas, 0.000001" =mas, … Lecture Notes on Astrometry

  10. Ecliptic Coordinates • Ecliptic = Mean Orbital Plane of Earth • Obliquity of Ecliptic: e • Solar System Bodies • Radius (Vector): r • (Ecliptic) Longitude: l • (Ecliptic) Latitude: b Ecliptic e Equator Equinox Lecture Notes on Astrometry

  11. Equatorial Coordinates P • Basic Expression • Right Ascension: R.A. = a • Declination: Decl. = d • Parallax: p p r S AU E Lecture Notes on Astrometry

  12. Units of Length • SI meter Speed of Light: c = 299792458 m/s • Astronomical Unit of length (AU) Rough: Mean radius of Earth’s orbit Precise: AU = c t, t = 499.00478353… s • Parsec (pc), Light Year (ly) 1 pc = AU/sin 1” ~ 30.9 Pm ~ 3.26 ly 1 ly = c x 1 jy ~ 9.5 Pm Lecture Notes on Astrometry

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