Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.

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Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first Earth explorer core mission of the European Space Agency It was launched on March 17, 2009 into a Sun-synchronous dusk-dawn orbit and re-entered into the Earth’s atmosphere on November 11, 2013 The satellite altitude was between 255 and 225 km for the measurement phases The European GOCE Gravity consortium is responsible for the Level 1b to Level 2 data processing in the frame of the GOCE High-level processing facility (HPF) The Precise Science Orbit (PSO) is one Level 2 product, which was produced under the responsibility of the Astronomical Institute of the University of Bern within the HPF This PSO product has been continuously delivered during the entire mission Regular checks guaranteed a high consistency and quality of the orbits A correlation between solar activity, GPS data availability and quality of the orbits was found The accuracy of the kinematic orbit primarily suffers from this Improvements in modeling the range corrections at the retro-reflector array for the SLR measurements were made and implemented in the independent SLR validation for the GOCE PSO products The satellite laser ranging (SLR) validation finally states an orbit accuracy of 242 cm for the kinematic and 184 cm for the reduced-dynamic orbits over the entire mission The common-mode accelerations from the GOCE gradiometer were not used for the official PSO product, but in addition to the operational HPF work a study was performed to investigate to which extent common-mode accelerations improve the reduced-dynamic orbit determination results The accelerometer data may be used to derive realistic constraints for the empirical accelerations estimated for the reduced-dynamic orbit determination, which already improves the orbit quality On top of that the accelerometer data may further improve the orbit quality if realistic constraints and state-of-the-art background models such as gravity field and ocean tide models are used for the reduced-dynamic orbit determination

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GOCE: precise orbit determination for the entire mission

Drag coefficient is a major source of uncertainty in calculating the aerodynamic forces on satellites in low Earth orbit. Closed-form solutions are available for simple geometries under the assumption of free molecular flow; however,mostsatelliteshavecomplexgeometries,andamoresophisticatedmethodofcalculatingthedragcoefficient is needed. This work builds toward modeling physical drag coefficients using the direct simulation Monte Carlo method capable of accurately modeling flow shadowing and concave geometries. The direct simulation threedimensional visual program and the direct simulation Monte Carlo analysis code are used to compare the effects of two separate gas–surface interaction models: diffuse reflection with incomplete accommodation and quasi-specular Cercignani–Lampis–Lordmodels.Resultsshowthatthetwogas–surfaceinteractionmodelscomparewellataltitudes below ∼500 km during solar maximum conditions and below ∼400 km during solar minimum conditions. The differenceindragcoefficientofasphereat ∼800 kmcalculated usingthetwogas–surfaceinteractionmodels is ∼6% during solar maximum and increases to ∼10% during solar minimum. The difference in drag coefficient of the GRACE satellite computed using the two gas–surface interaction models at ∼500 km differs by ∼15% during solar minimum conditions and by ∼2–3% during solar maximum conditions.

Comparing Physical Drag Coefficients Computed Using Different Gas–Surface Interaction Models

Spacecraft drag modelling

Very low Earth orbits (VLEO), typically classified as orbits below approximately 450 km in altitude, have the potential to provide significant benefits to spacecraft over those that operate in higher altitude orbits. This paper provides a comprehensive review and analysis of these benefits to spacecraft operations in VLEO, with parametric investigation of those which apply specifically to Earth observation missions. The most significant benefit for optical imaging systems is that a reduction in orbital altitude improves spatial resolution for a similar payload specification. Alternatively mass and volume savings can be made whilst maintaining a given performance. Similarly, for radar and lidar systems, the signal-to-noise ratio can be improved. Additional benefits include improved geospatial position accuracy, improvements in communications link-budgets, and greater launch vehicle insertion capability. The collision risk with orbital debris and radiation environment can be shown to be improved in lower altitude orbits, whilst compliance with IADC guidelines for spacecraft post-mission lifetime and deorbit is also assisted. Finally, VLEO offers opportunities to exploit novel atmosphere-breathing electric propulsion systems and aerodynamic attitude and orbit control methods. 
However, key challenges associated with our understanding of the lower thermosphere, aerodynamic drag, the requirement to provide a meaningful orbital lifetime whilst minimising spacecraft mass and complexity, and atomic oxygen erosion still require further research. Given the scope for significant commercial, societal, and environmental impact which can be realised with higher performing Earth observation platforms, renewed research efforts to address the challenges associated with VLEO operations are required.

The Benefits of Very Low Earth Orbit for Earth Observation Missions

A critical assessment of satellite drag and atmospheric density modeling

This paper examines atmospheric drag models and data usage involved with propagating near-Earth satellites. Many studies, and even some International standards try to promote one model over another, rather than identifying the behavior of the numerous parameters necessary to select the best model for a particular mission and application. We briefly summarize existing information, and quantify sources of uncertainty in satellite propagation resulting from several atmospheric models, or from the treatment of input data indices. The goal is for researchers to understand the relative impact of using different models and data indices so they can properly assess which model and data input to use.

David A. Vallado

Papers

A critical assessment of satellite drag and atmospheric density modeling

A Critical Assessment of Satellite Drag and Atmospheric Density Modeling

Lunar shadow eclipse prediction models for the Earth orbiting spacecraft: Comparison and application to LEO and GEO spacecrafts