Tidal Corrections to Direction Observations

1
Tidal Corrections toDirection Observations
Catherine Le Cocq SLAC - Metrology Department -
Advanced Methods Group
2
Displacement-Strain Relation
Displacement vector u u PP x-x
Final state
Strain tensor e
Original state
3
Angular Formula
2 infinitesimal vectors q and r
transform into q and r
Final state
Introducing ??-? ? and ? the cosine directors
of q and r
Original state
4
Surface Strain
5
Mathematical Cartography
Original state sphere or ellipsoid as a model
of earth
p (?,?)
Final state plane or map
P(X,Y)
Fundamental quadratic form
Linear alteration
Angular alteration ? A-? V-?-?
6
Tidal Displacement Vector
At point P (r,?,?), the tidal displacement vector
u is given in spherical coordinates by
North-South horizontal component
East-West horizontal component
Vertical component
W is the tidal potential, g is the mean gravity
at point P h and l are the first and third Love
numbers
7
Tidal Potential
8
Tidal Strain Tensor
9
Computational Steps
Local Sideral Time s
Celestial Coordinates ?,?
Hour Angle H
Strain Tensor e
10
Azimuth Variations
? 3725 ? 1221230 h0 on 11-7-2000 at
1AM
1.08e-8 degree
4.39e-7 degree
11
Time Variations
Same location between 11-6-2000 and 11-9-2000
with ? -?/2