pireaux

Relativity and Space Geodesy S. Pireaux UMR 6162 ARTEMIS, Obs. de la Côte d’Azur, Av. de Copernic, 06130 Grasse, Francesophie.pireaux@obs-azur.fr: 

Relativity and Space Geodesy S. Pireaux UMR 6162 ARTEMIS, Obs. de la Côte d’Azur, Av. de Copernic, 06130 Grasse, France sophie.pireaux@obs-azur.fr IAU Commission 31: TIME AND ASTRONOMY, IAU General Assembly, Prague, 21st August 2006

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Outline of the speach I. Native relativistic approach wrt spacecraft trajectory : orbitography a. Needed in: precise planetary gravitational field modeling, orbitography b. Illustration: classical vs RMI prototype –Relativistic Motion Integrator- method

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I. Native relativistic approach wrt spacecraft trajectory : orbitography Ia. Needed in: - precise planetary gravitational field modeling - orbitography A good planetary gravitational field model? CHAMP GRACE STELLA or LAGEOS GOCE

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Ib. Illustration:

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IIa. Need for relativistic laser links: II. Native relativistic approach wrt photon trajectory: laser-links

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LISA = space GW detector complementary to ground detectors LISA (Laser Interferometer Space Antenna)

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3 (drag-free) stations 3 test masses of stations ? Coordinates Interdistance (L ) ij relativistic modeling of orbitography/laser links required:

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Laser link: IIb. General method for relativistic laser-links

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Motion in background metric gab = hab + hab in presence of gravitational sources (sce) : … with IAU2000 conventions

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Energy measured from spacecraft = = spacecraft 4-velocity = photon 4-wave vector where

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Contributions from gravitational sources (sce) to hab :

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Orders of magnitude : IIc. Illustration: LISA, rotation around the Sun

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LISA Flight time solution:

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Numerical estimates of geometric time delays in s over a year tAB order 0 : amplitude ~ 48 000 km/c « flexing » of triangle

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Naive estimate: LISA Frequency shift solution:

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Order 1:

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LISACODE collaboration of ARTEMIS (Côte d’Azur) – APC (Paris), in LISA FRANCE aims at includes without planets relativistic laser links (time transfer + freq. shift) classical orbito. coordinate time only mission simulations Tests of TDI data pre-processing, TDI-ranging sensitivity curves relevant order of magnitude estimates … Time scales: careful with archives and coherence Ephemeris of stations : presence of planets necessary, to provide initial conditions for photon flight times Laser link : Sun alone sufficient, but relativistic description of its field necessary

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III. Caution with relativistic time-scales IIIa. Time scales

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Numerical estimates over a one year mission… IIIb. Illustration: LISA

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Outline of the speach I. Native relativistic approach wrt spacecraft trajectory : orbitography a. Needed in: precise planetary gravitational field modeling, orbitography b. Illustration: classical vs RMI prototype –Relativistic Motion Integrator- method

Other transparencies: 

Other transparencies

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Geodesy: precise geophysics implies precise geodesy

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Laser GEOdymics Satellite 1 Aims: - calculate station positions (1-3cm) - monitor tectonic-plate motion - measure Earth gravitational field - measure Earth rotation Design: - spherical with laser reflectors - no onboard sensors/electronic - no attitude control Orbit: 5858x5958km, i = 52.6°, around Earth Mission: 1976, ~50 years (USA) CHAllenging Minisatellite Payload Aims: - precise gravity and magnetic field, their space and time variations Design: - laser reflector, GPS receiver - drift meter - magnetometer, star sensor, accelerometers Orbit: 454 km initial, near polar, around Earth Mission: ~5 years (Germany) Geodesy examples: a high-, or respectively low-altitude satellite…

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Geodesy: orders of magnitude [m/s²]

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a) Gravitational potential model for the Earth

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with and b) Newtonian contributions from the Moon, Sun and Planets LAGEOS 1

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c) Relativistic corrections LAGEOS 1

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, LAGEOS 1

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, LAGEOS 1

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Advantages: - To easily take into account all relativistic effects with “metric” adapted to the precision of measurements and adopted conventions. - Same geodesic equation for photons (light signals) massive particles (satellites without non-grav forces) - Relativistically consistent approach Advantages: - Well-proven method. - Might be sufficient for current applications. Classical approach: “Newton” + relativistic corrections for precise satellite dynamics and time measurements. Alternative and pioneering effort: develop a satellite motion integrator in a pure relativistic framework. Drawbacks: - To be adapted to the adopted space-time transformations and to the level of precision of data Geodesy: a modern view…

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a) Method: GINS provides template orbits to validate the RMI orbits - simulations with 1) Schwarzschild metric => validate Schwarzschild correction 2) (Schwarzschild + GRIM4-S4) metric => validate harmonic contributions 3) Kerr metric => validate Lens-Thirring correction 4) GCRS metric with(out) Sun, Moon, Planets => validate geodetic precession (other bodies contributions) (…)

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Earth rotation model c) diagram: GINS with i=1,2,3 spatial indices

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Earth rotation model d) diagram: RMI with a=0,1,2,3 space-time indices

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Geodesy: principle of accelerometers…

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[Bize et al 1999] Europhysics Letters C, 45, 558 [Chovitz 1988] Bulletin Géodésique, 62,359 [Fairhaid_Bretagnon 1990] Astronomy and Astrophysics, 229, 240-247 [Hirayama et al 1988] [IAU 1992] IAU 1991 resolutions. IAU Information Bulletin 67 [IAU 2001a] IAU 2000 resolutions. IAU Information Bulletin 88 [IAU 2001b] Erratum on resolution B1.3. Information Bulletin 89 [IAU 2003] IAU Division 1, ICRS Working Group Task 5: SOFA libraries. http://www.iau-sofa.rl.ac.uk/product.html [IERS 2003] IERS website. http://www.iers.org/map [Irwin-Fukushima 1999] Astronomy and Astrophysics, 348, 642-652 [Lemonde et al 2001] Ed. A.N.Luiten, Berlin (Springer) [Moyer 1981a] Celestial Mechanics, 23, 33-56 [Moyer 1981b] Celestial Mechanics, 23, 57-68 [Moyer 2000] Monograph 2: Deep Space Communication and Navigation series [Soffel et al 2003] prepared for the Astronomical Journal, asro-ph/0303376v1 [Standish 1998] Astronomy and Astrophysics, 336, 381-384 [Weyers et al 2001] Metrologia A, 38, 4, 343 Relativistic time transformations Geodesy: bibliography

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[Damour et al 1991] Physical Review D, 43, 10, 3273-3307 [Damour et al 1992] Physical Review D, 45, 4, 1017-1044 [Damour et al 1993] Physical Review D, 47, 8, 3124-3135 [Damour et al 1994] Physical Review D, 49, 2, 618-635 [IAU 1992] IAU 1991 resolutions. IAU Information Bulletin 67 [IAU 2001a] IAU 2000 resolutions. IAU Information Bulletin 88 [IAU 2001b] Erratum on resolution B1.3. Information Bulletin 89 [IAU 2003] IAU Division 1, ICRS Working Group Task 5: SOFA libraries. http://www.iau-sofa.rl.ac.uk/product.html [IERS 2003] IERS website. http://www.iers.org/map [Klioner 1996] International Astronomical Union, 172, 39K, 309-320 [Klioner et al 1993] Physical Review D, 48, 4, 1451-1461 [Klioner et al 2003] astro-ph/0303377 v1 [Soffel et al 2003] prepared for the Astronomical Journal, asro-ph/0303376v1 [GRGS 2001] Descriptif modèle de forces: logiciel GINS [Moisson 2000] (thèse). Observatoire de Paris [McCarthy Petit 2003] IERS conventions 2003 http://maia.usno.navy.mil/conv2000.html. Metric prescriptions RMI

Principle of ground-space time transfer:: 

Principle of ground-space time transfer: T2L2 (optical telemetry with 2 laser links) Follow evolution of time aboard wrt ground time: Rebuild triplets (TA, Tsat, TC) Compute ground-satellite delay: Date laser pulses: Departure from ground station: TA Arrival aboard: Tsat= TB Echo return on ground: TC Clock Retro-reflectors Detection Clock Laser telemetry station

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Common view On-board oscillator noise sx(0.1 s) Non-Common view On-board oscillator noise sx(t3) Principle of ground-ground time transfer:

Method:: 

Mesure PPN parameter g (Shapiro effect) Planet Telemetry Asteroid masses Pioneer effect … TIPO Telescope TIPO (Télémétrie Interplanétaire Optique) Scientific objectives of TIPO: Method:

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Orbital motion of sces during photon flight time:

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~ 10-15 ~ 10-12 T2L2, rotation around the Earth: ~ 10-9

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Collaborations in LISA FRANCE LISA France: - APC, Paris 7 - ARTEMIS, OCA - CNES - IAP Paris - LAPP Annecy - LUTH Observatoire de Paris-Meudon - ONERA - Service d'Astrophysique CEA