Relativity in the Global Positioning System

Terms: Relativity in the Global Positioning System (289),

Terms: general relativistic corrections (227),

Boolean: relativistic AND gps (46,100), relativistic AND "global positioning system" (4,930),

Relativity in the Global Positioning System

Terms: proper time increment (55), local inertial frame (814), ECI coordinate system (110), isotropic coordinates (594), coordinate time (30,000), gps coordinate time (140), rotating geoid (121), relativity correction (143),

′( Φ0-) dτ = ds ∕c = dt 1 + c2 . (19 )

( ) ( ) 2 2(V-−-Φ0-) 2 2V- 2 2 2 2 2 2 − ds = − 1 + c2 (cdt) + 1 − c2 (dr + r dθ + r sin θdφ ). (24 )

[ ( ) 2 2 2 2 2 2] 2 2(V--−-Φ0-) 2V- dr--+-r-dθ--+-r-sin-θd-φ- 2 − ds = − 1 + c2 − 1 − c2 (cdt)2 (cdt) . (25 )

2 2 2 2 2 2 v2 = dr--+-r-dθ-+--r-sin-θdφ--. (26 ) dt2

[ (V − Φ ) v2 ] d τ = ds∕c = 1 + -----2-0- − --2 dt. (27 ) c 2c

∫ ∫ [ (V − Φ0) v2 ] dt = d τ 1 − -----2--- + --2 . (28 ) path path c 2c

1v2 − GME---= − GME--. (33 ) 2 r 2a

∫ [ 3GME Φ0 2GME ( 1 1 )] Δt = dτ 1 + ----2--+ -2-− ----2-- --− -- . (34 ) path 2ac c c a r

Living Reviews in Relativity

Terms: relativistic effects on satellite clocks (76), satellite clocks (8,030), gps clocks (28,700), cesium clocks (4,020),

Terms: coordinate clock network (2), world geodetic system (33,400), allen deviation (56), allan deviation (2,820), allan variance (12,400), short term frequency stability (542),

Cosmic UCAR Related Papers

Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC)

Terms: chip scale atomic clocks (468), chip scale atomic clock (1,300), gps timekeeping (80),

CU MEMS MEMS and Package for Chip-Scale Integration for Atomic Clocks