Precise Orbit Determination of the GOCE re-entry phase Francesco Gini, Michiel Otten, Tim Springer, Werner Enderle, Stijn Lemmens, and Tim Flohrer

Overview The reentry phase NAPEOS POD sequence New non-gravitational force modelling: ARPA POD dynamical model Results Conclusions

Reentry phase ~ 4:00 am, thruster off 21 st October 2013

Reentry phase ~ 4:00 am, thruster off 21 st October th November 2013 ~ 17:15 pm, last useful downlink

Reentry phase ~ 4:00 am, thruster off 21 st October th November 2013 ~ 17:15 pm, last useful downlink 21 daily arcs of GPS data

Reentry phase 11 th November 2013 ~ 4:00 am, thruster off 21 st October th November 2013 ~ 17:15 pm, last useful downlink ~ 00:16 pm, h = 80 km

Reentry phase 11 th November 2013 ~ 4:00 am, thruster off ~ 00:20 pm, final re-entry Credit: Bill Chater 21 st October th November 2013 ~ 17:15 pm, last useful downlink ~ 00:16 pm, h = 80 km

POD sequence of GOCE re-entry NAPEOS NAvigation Package for Earth Orbiting Satellites (ESOC – Navigation POD software) Processing undifferenced GPS observations using the ionospheric-free linear combination, based on a fully-dynamic approach.

NAPEOS sequence A-priori orbit PSO or propagated from previous day

NAPEOS sequence Orbit fit Initialization Of Dynamical parameters A-priori orbit PSO or propagated from previous day

NAPEOS sequence Orbit fit Initialization Of Dynamical parameters Data pre-processing Data filtering & Receiver Clocks initialization A-priori orbit PSO or propagated from previous day

NAPEOS sequence Orbit fit Initialization Of Dynamical parameters Data pre-processing Data filtering & Receiver Clocks initialization “GPS Code-only” processing Orbit & Parameters Raw estimation A-priori orbit PSO or propagated from previous day

NAPEOS sequence Orbit fit Initialization Of Dynamical parameters Data pre-processing Data filtering & Receiver Clocks initialization “GPS Code-only” processing Orbit & Parameters Raw estimation Data pre-processing Data filtering based on new orbit A-priori orbit PSO or propagated from previous day

NAPEOS sequence Orbit fit Initialization Of Dynamical parameters Data pre-processing Data filtering & Receiver Clocks initialization “GPS Code-only” processing Orbit & Parameters Raw estimation Data pre-processing Data filtering based on new orbit “GPS Code+Phase” processing Orbit & Param. fine estimation A-priori orbit PSO or propagated from previous day

NAPEOS sequence Orbit fit Initialization Of Dynamical parameters Data pre-processing Data filtering & Receiver Clocks initialization “GPS Code-only” processing Orbit & Parameters Raw estimation Data pre-processing Data filtering based on new orbit “GPS Code+Phase” processing Orbit & Param. fine estimation A-priori orbit PSO or propagated from previous day Precise Orbit Determination

Software characteristics High level of accuracy through sophisticated interaction modeling Satellite specific ARPA database Off-line computation for high accuracy without overloading the POD process ARPA overview Non-gravitational forces include Aero: Aerodynamic effects SRP : Solar Radiation Pressure ERP : Earth Radiation Pressure (Alb. + IR) TRR :Thermal Re-Radiation of the spacecraft University of Padova ARPA (Aerodynamics and Radiation Pressure Analysis)

ARPA: GOCE CAD model

ARPA: SRP & ERP CAD ARPA Raytracer ARPA SRP & ERP ForcesTorques Database NAPEOS S/C properties

ARPA TRR + Aero Surface Mesh ARPA TRR & Aero ForcesTorques Database NAPEOS S/C properties

Dynamical Model ARPA model – CADNAPEOS model – Flat plate Non-gravitational force modelling (MSIS-90)

Results: post-fit RMS

16 mm 6 mm 77 mm Lower Aerodyn. Effects 16 daily arcs Higher Aerodyn. effects 5 (ARPA), 4 (NAP.) daily arcs ARPA post-fit RMS reduction ~ 2 mm (15%) Values between 0.5 – 6.9 mm ARPA extra daily arc

Results: CPR’s NAPEOS model – Along-track CPRARPA model – Along-track CPR To absorb mismodelling, especially related to the aerodynamics

Results: CPR’s NAPEOS model – Along-track CPRARPA model – Along-track CPR To absorb mismodelling, especially related to the aerodynamics ARPA CPR’s reduction Along-track ~20% Cross-track ~40% Low Aerodyn. effects High Aerodyn. effects Low Aerodyn. effects High Aerodyn. effects

Results: drag coefficients NAPEOS model – Drag coefficientARPA model – Aerodynamic Scaling factor NAPEOS model GOCE C D 1.2 – 5.0 ARPA model Aerod. scaling factor 0.92 ±0.29 Flat Plate does not model the lateral surfaces ARPA + MSIS-90 Aerod. Forces overestimation about 8% (mean value)

Aerodynamic acceleration Based on ARPA + MSIS-90 models

Results: comparison with PSO

~10 cm ~ 9 cm ~ 5 cm Attitude mismodelling with Flat Plate

Conclusions All 21 orbital daily arcs were recovered GPS carrier phase post-fit RMS is between 6 and 80 mm, increasing with higher aerodynamic forces The orbits difference with the PSO’s is between 8 and 17 cm The new non-gravitational ARPA models were tested and validated, showing: – the last daily arc was successfully computed – lower post-fit RMS (2 mm reduction) – lower CPR’s values (20% along-track, 40% cross-track)

Conclusions All 21 orbital daily arcs were recovered GPS carrier phase post-fit RMS is between 6 and 80 mm, increasing with higher aerodynamic forces The orbits difference with the PSO’s is between 8 and 17 cm The new non-gravitational ARPA models were tested and validated, showing: – the last daily arc was successfully computed – lower post-fit RMS (2 mm reduction) – lower CPR’s values (20% along-track, 40% cross-track) Thanks for your attention!

Backup slide: Attitude Attitude instability, due to aerodynamic effects (magneto-torquers saturation) Doy 294 Doy 303 Doy 294 EOL