Force models for GPS Orbit modeling Paul Ries, Jet Propulsion Lab, California Institute of Technology Copyright 2017 California Institute of Technology. U.S. Government Sponsorship acknowledged.

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries Outline Radiation Pressure Solar radiation pressure Earth Radiation Attitude modeling Thermal forces Antenna Thrust Gravity Based on: ftp://ftp.igs.org/pub/center/analysis/ giant disclaimer about analysis centers not necessarily being up to date and being cryptic 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Solar Radiation pressure models Solar radiation pressure results from reflection of sunlight CODE/ECOMM/DYB model (Beutler et al, 1994) Estimate SRP during each analysis run with several different components (Direct, y-axis, Direct cross y-axis, once per rev) JPL Model (Bar-Sever and Kuang 2005) Empirically determined solar radiation pressure model from several years of data on each satellite, plus tightly constrained terms (solar scale, y-bias, stochastic impulses) Difference between JPL style model and DYB style model at cm level (Sibthorpe et al 2011) 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Solar radiation pressure models CODE DYB-style Model CODE, GFZ, NOAA, USNO DYB with box-wing model ESA, GRG DYB with other apriori MIT, SIO empirical GSPM model NRCAN+JPL Important to Note: still substantial variations within each category 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries Attitude models Nominal: keeps solar panels pointed towards the sun and antenna pointed towards earth Essential component of other radiative forces Eclipse modeling causes substantial differences (2-3 cm RMS) between solutions 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries Attitude models None NOAA, USNO Nominal CODE, NRCan, ESA, GFZ, MIT, SIO, WHU Nominal + eclipse solution GRG, JPL 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Earth Radiation Pressure The force of of reflected visible and emitted IR light on a GNSS satellite Model variations can introduce bias at the cm level (see e.g. Rodriguez et al 2012, Ziebart 2009) 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Earth Radiation Pressure Rodriguez-Solano et al 2012 GFZ, NOAA, CODE Knocke-Ries Model JPL, NRCan Other similar model GRG (incorporates ECMWF), ESA No model WUH, USNO, SIO, MIT 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Thermal models for the future? Direct thermal effect non-uniform temperature and/or non-spherical shape few meter level, but often absorbed by model parameters (Adhya et al 2005) Yarkovsky effect tentatively detected at 10 cm level for Galileo (Svehla et al 2016) force created by asymmetric thermal emission on rotating body 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries Antenna Thrust Thrust from transmitting navigation message typically in radial direction magnitude of 10s of cm/orbit 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries Antenna Thrust No information MIT, GRG, USNO, WHU None ESA (as of 2015… but…), SIO http://acc.igs.org/orbits/thrust-power.txt CODE, NRCan, JPL Rodriguez-Solano 2012 (constant 80W) GFZ, NOAA 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries Gravity field EGM2008, 12x12 CODE, NRCan, GFZ, JPL, NOAA EIGEN-GLO5C 12x12 ESA EIGEN_6S (TVG) GRG EGM 96 9x9 MIT, SIO JGM3 12x12 USNO EIGEN-GLO4S1 12x12 WHU Emphasize that differences for MEO's probably don't matter, but matter much more for LEOs 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Gravity – 3rd body perturbers Can analytically compute max acceleration at conjunction/opposition and integrate for one MEO orbit Effects of bodies through Saturn are significant Differences beyond Saturn make little difference Body One orbit effect Moon 3.8 km Sun 1.4 km Venus 5.7 cm Jupiter 1.1 cm Mars 7.6 mm Mercury 7.1 mm Saturn 0.6 mm Uranus 12 μm Ceres 0.1 μm Pluto 0.4 nm 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Gravity – 3rd body perturbers Sun and Moon USNO, MIT, SIO Sun, Moon, Jupiter, Venus, Mars CODE, NOAA All Planets + Sun and Moon JPL, NRCAN, GRG All Planets + Sun, Moon, and Pluto WHU, ESA, GFZ 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Can we eliminate biases? Force Model Ease of convergence Reason Solar radiation pressure Challenging SRP model directly related to estimation strategy Earth radiation pressure Earth radiation pressure directly related to estimation strategy (can be absorbed by SRP parameters) Attitude modeling Possible ACs can probably converge on most of attitude model, but more research needed into non-nominal models Antenna Thrust Viable Many ACs already using same model, easy to implement uniformly 3rd body perturbers Most ACs already have the largest, only a few ACs need to update Gravity field A few ACs need to update model, differences probably small at MEO 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

Further Consideration for LEOs: Time-varying gravity, gravity field agreement drag for future GNSS: orbit normal attitudes thermal models 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries

2017 Unified Analysis Workshop - Force models for GPS - Paul Ries References ADHYA, S., ZIEBART, M., SIBTHORPE, A., ARROWSMITH, P. and CROSS, P. (2005), Thermal Force Modeling for Precise Prediction and Determination of Spacecraft Orbits. Navigation, 52: 131–144. doi:10.1002/j.2161-4296.2005.tb01740.x Bar-Sever Y, Kuang D (2005) New empirically derived solar radi- ation pressure model for global positioning system satellites during eclipse seasons. The Interplanetary Network Progress Report 42-160. http://ipnpr.jpl.nasa.gov/progress_report/42-160/title.htm Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M (1994) Extended orbit modeling techniques at the CODE processing center of the International GPS Service for geodynamics (IGS): theory and initial results. Manuscr Geod 19: 367–386 Knocke, P. C., Ries, J. C., Tapley, B. D., American Astronautical Society., American Institute of Aeronautics and Astronautics., & AAS/AIAA Astrodynamics Conference. (1988). Earth radiation pressure effects on satellites. Washington, D.C: American Institute of Aeronautics and Astronautics. Rodriguez-Solano, C.J., Hugentobler, U., Steigenberger, P. et al. J Geod (2012) 86: 309. doi:10.1007/s00190-011-0517-4 Sibthorpe, A., Bertiger, W., Desai, S.D. et al. J Geod (2011) 85: 505. doi:10.1007/s00190-011-0450-6 Svelha, D., Rothacher, M., Cacciapouti, L. (2016), Thermal Re-Radiation Acceleration in the GNSS Orbit Modelling Based on Galileo Clock Parameters. IGS Workshop presentation. Ziebart, M. Springer, T., Flohrer, C., Sibthorpe, A., Haines, B., Bar-Sever, Y. (2009), The GPS-SLR bias: dynamics, attitude and current experiments. International Technical Laser Workshop on SLR Tracking of GNSS Constellations, Metsovo, Greece 2017-07-08 2017 Unified Analysis Workshop - Force models for GPS - Paul Ries