Parallel Shift of Origin
• Galactic Center in Quasar RF
– Cosmic Expansion
• Local Standard of Rest in Galactic RF
– Local Standard of Rest (LSR) = Solar System
Barycenter (SSB)
– Local Circular Motion … Oort’s Constant
1999-2000
Lecture Notes on Astrometry
Parallel Shift of Origin (contd.)
• Geocenter in Solar System Barycentric RF
– Ephemeris
• Terrestrial RF & Geocentric RF
– Earth Rotation
• Observer in Terrestrial RF
– Rest
– Moving (airplane observatory)
1999-2000
Lecture Notes on Astrometry
Ephemeris
• Reference on Complex Motion
– Planets, Moon, natural satellites, minor planets
– Rotation of planets/satellites
• Astronomical Almanac (US+UK)
• Japanese Ephemeris (天体位置表）
• DE series (NASA/JPL), DE405/406
– State-of-the-art
– Machine callable
– ITRFnn, WGS84, GRS80, Tokyo Datum
1999-2000
Lecture Notes on Astrometry
Theory of Coordinate Transform.
• General Coordinate Transformation
xk  X j  X j xk , t 
• Taylor Expansion w.r.t. New Coordinates
3 X
j
0, t xk  
X j  X j 0, t   
k 1 xk
3
 Aj t    B jk t xk  
k 1
1999-2000
Lecture Notes on Astrometry
Linear Coordinate Transform.
• Affine Transformation
X  At   Bt x
• Static: 12-Parameters Transformation
X  A  Bx
1999-2000
Lecture Notes on Astrometry
Decomposition of B-Matrix
B  D S 
• Expansion/Contraction = Diagonal
D jk  0 if j  k
• Shear = Off-Diagonal+Symmetric
S jk  Skj S jk  0 if j  k 
• Infinitesimal Rotational Displacement =
Anti-Symmetric   
jk
1999-2000
Lecture Notes on Astrometry
kj
7-Parameter Transformation
• Static Transf. among Similar & Parallel RFs
– Origin Shift
– Scale Factor = Isotropic Expansion/Contraction
– Infinitesimal Rotational Displacement
X  X0  sI  x
• Example: Geocentric RFs
– ITRFnn, WGS84, GRS80, Tokyo Datum
1999-2000
Lecture Notes on Astrometry

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