Improvements To Solar Radiation Pressure Modeling For Jason-2

Nikita P. Zelensky 2,1, Frank G. Lemoine 1, Stavros Melachroinos 2,1, Despina Pavlis 2,1, Douglas S. Chinn 2,1, Oleg Bordyugov 2,1

(1) Planetary Geodynamics Laboratory, Code 698, NASA Goddard Space Flight Center; Greenbelt, MD, USA

(2) SGT Inc.,Greenbelt, MD ABSTRACT

Jason-2 (OSTM, Ocean Surface Topography Mission) is the follow-on to the Jason-1 and TOPEX/Poseidon radar altimetry missions observing the sea surface. The computed orbit is used to reference the altimeter measurement to the center of the Earth, and thus the accuracy and stability of the orbit are critical to the sea surface observation accuracy. A 1-cm Jason-2 radial orbit accuracy goal is required for meeting the 2.5 cm altimeter measurement goal. Also mean sea level change estimated from altimetry requires orbit stability to well below 1 mm/yr. Although 1-cm orbits have been achieved, unresolved large draconitic period error signatures remain and are believed to be due to mis-modeling of the solar radiation pressure (SRP) forces acting on the satellite. Such error may easily affect the altimeter data, and can alias into any number of estimated geodetic quantities. Precision orbit determination (POD) at GSFC and other analysis centers employs an 8-panel “macromodel” representation of the satellite geometry and optical properties to model SRP. Telemetered attitude and modeled solar array pitch angles (SAPA) are used to orient the macromodel. Several possible improvements to SRP modeling are evaluated and include: 1) using telemetered SAPA values, 2) using the SRP model developed at UCL for the very similar Jason-1, 3) re-tuning the macromodel, 4) modifying POD strategy to estimate a coefficient of reflectivity (CR) for every arc, or else using the reduced-dynamic approach. Improvements to POD modeling are evaluated through analysis of tracking data residuals, estimated empirical accelerations, and orbit differences.

AGU Fall 2011 Meeting

San Francisco

Satellite Orbits and Attitude: Attacking the Error Budgets (G41B-0739)

Contacts:

Nikita Zelensky nzelensky@sgt-inc.com

Frank Lemoine Frank.G.Lemoine@nasa.gov

Radiation pressure acting on Jason-2

Forces due to radiation pressure include direct solar radiation, Earth Albedo and infra-red re-radiation (IR), and the effects of thermal radiation imbalance. Thermal radiation represents effects of heating/cooling of the satellite while in sunlight/shadow, and internal heat dissipation. Table 1 shows the relative magnitude of the effect from such forces on Jason-2.

The difficulty in modeling such forces is due to the complex satellite geometry and incomplete knowledge of the reflective and thermal properties of the satellite surfaces.

Various portions of the satellite are illuminated by the sun depending on the attitude regime (Table 2) and B’ angle (angle between orbit plane and sun vector – see below). The B’ or draconic period is 118 days for Jason-2. The models considered for this study are listed in Table 4.

How is the current modeling deficient? SLR residuals from the least accurate modeling, g916 (Table 5 above), do not show any obvious patterns in the B’ x orbit angle plot below. However the SLR points when so displayed show some deficiency in coverage in very high/low B’ regions. Compared to the most accurate jpl11a orbits, the crossover residuals suggest the macromodel is most deficient in the high/low B’ regions. CR estimates suggest the model is under-reflecting light in these regions. Macromodel parameters selected for tuning should be most effective in these regions.

Conclusions

1) Jason-2 Radiation force modeling has shown improvement using a tuned macromodel which includes an SA thermal component (t2_g_th), and by simply re-tuning the CR to 0.945.

2) Although the Jason-2 orbits meet or are close to the radial 1-cm goal set by altimeter analysis requirements, significant error remains at the 118-day draconic period.

3) The inability of the best models to further reduce the substantial orbit error suggests a deficiency in the macromodel sophistication, and not inadequate observability over certain regions, as PCE orbit data were included in the tuning.

4) Analysis will continue to improve Jason-2 radiation pressure modeling. Outstanding issues include:

1) use of telemetered solar array pointing angles (in progress)

2) self – shadowing

3) Jason-2 thermal emission

Table 2. Jason-2 attitude regime

Yaw mode B’ region description

sinusoidal B’ > |15 ° | Yaw = cos (orbit angle) scaled by B’

fixed low B’ < |15 ° | Yaw =0° +B’Yaw =180° -B’

fixed high B’ > |80 ° | Yaw =+90° +B’Yaw =-90° -B’

ramp up B’ => |15 ° | increase

Yaw fixed to sinusoidal transition (90 seconds)

ramp down B’ =< |15 ° | decrease

Yaw sinusoidal to fixed transition (90 seconds)

flip B’ crosses 0° Yaw =0° +B’ (10 minutes)Yaw =180° -B’ (10 minutes)

Table 1. radiation forces acting on Jason-2

acting force over cycle 1, in sinusoidal yaw, B’ : -35° to -45°

total RMS acceleration (10-9 m/s2)

macromodel pretuned

(g_th)

macromodel tuned (t2_g_th)

Solar radiation pressure 121.2 113.4

Albedo + IR 15.0 15.9

Thermal imbalance SA+ 1.4 6.5

Table 4. Jason2 satellite radiation pressure models considered

macromodel: Jason1 8 plates oriented to approximate the geometry and the optical reflective properties (CNES 2008). Two representations are considered, one using the geometric surface area and a-priori values, and the other using the optical area (geometric area scaled by the sum of the specular+diffuse+absorbed reflectivity coefficients) and values tuned by CNES (CNES 2008).

ucl : developed for Jason1 using a finite element approach and includes the effects of self-shadowing and solar array (SA) thermal imbalance (Ziebart 2004)

thermal SA+ : solar array panel facing sun thermal imbalance developed for TOPEX/Poseidon (Marshall et al., 1992, Luthcke et al., 1992)

CR : coefficient of reflectivity scale for total effect of radiation pressure model.

Jason-2 radiation pressure orbit error

Spectral analysis of radial differences between the jpl11a and g916 orbits sampled at fixed geographic locations show the most power at the draconic 118-day period, and indicate error due to radiation pressure. This error is thought to largely reside in the g916 orbits, as the jpl11a orbits are considered to be the most accurate. The 118-day amplitude projected geographically shows 9-12 mm signals in the North Atlantic and Pacific waters near Australia.

Table 5. Orbit description and tests

orbit description CR RMS residuals cycles 1-105

DORIS (mm/s)

SLR (cm)

Xover (cm)

g916 std1007 standards (geometric area pre-tuned macromodel, SLR + DORIS dynamic, CR = 0.916) 0.916 0.3717 1.178 5.461

g945 std1007, CR = 0.945 0.945 0.3717 1.187 5.450

g945_rd std1007, CR = 0.945, reduced-dynamic 0.945 0.3708 1.099 5.396

g_crarc std1007, estimate CR in orbit solution / arc est. 0.3716 1.511 5.451

ucl std1007, Jason-1 UCL model 1.000 0.3717 1.186 5.457

g_th std1007, TOPEX Solar Array +face thermal model 0.954 0.3717 1.187 5.451

o std1007, optical area pre-tuned macromodel 0.988 0.3717 1.199 5.454

o_th as o, TOPEX Solar Array +face thermal model 1.000 0.3717 1.199 5.455

jpl11a JPL GPS RLSE11a orbit, considered the most accurate

---- 0.3712 1.197 5.326

t1_g as g945, macromodel tuned using SLR+DORIS 1.136 0.3719 1.261 5.520

t1_g_th as g_th, macromodel tuned using SLR+DORIS 0.945 0.3717 1.190 5.451

t2_g_th as g_th, , macromodel tuned using SLR+DORIS, plus jpl11a orbit positions every minute (pce data) 0.945 0.3716 1.191 5.449

A series of 11 SLR/DORIS POD tests were performed and are compared to the jpl11a (Table 5). For these tests the macromodel was tuned with and without the SA+ thermal component (Table 6). This model was tuned including jpl11a PCE data (t2_g_th) which are highly precise orbit positions. In a separate POD test over 112 cycles the use of such data improves the crossover residuals from 5.479 cm (SLR/DORIS) to 5.425 cm (PCE). The tests show that compared to g916 (GSFC std1007) the t2_g_th macromodel performs best and just tuning the CR to 0.945 is almost as good. The best POD improvement is for the reduced-dynamic (g945_rd). In addition to residual fits, the improvements are seen by a reduction in the estimated empirical acceleration amplitudes and better agreement with the jpl11a orbits. The remaining excursions in the empirical accelerations occur at ramp times, and are likely due to the inability of the external attitude, sampled at about 30 seconds, to account for the rapid 90-second transition. No improvement is seen for g_crarc as the SLR/DORIS CR estimate is highly correlated with the empirical parameters.

Radiation pressure model test Results

References

CNES, website page 2008, http://www.aviso.oceanobs.com/en/calval/orbit/precise-orbit-determination-verification/index.html#c6061

Luthcke SB, and Marshall JA, Nonconservative force model parameter estimation strategy for TOPEX/Poseidon precision orbit determination, NASA Technical Memorandum 104575, November 1992.

Marshall JA, Luthcke SB, Antreasian PG, Rosborough GW, Modeling radiation forces acting on TOPEX/Poseidon for precision orbit determination, NASA Technical Memorandum 104564, June 1992.

Ziebart M, Generalized analytical solar radiation pressure modeling algorithm for spacecraft of complex shape, J. Spacecraft Rockets 41 (5), 840-848, 2004.

Zelensky NP, Lemoine FG, Ziebart M, et al., DORIS/SLR POD modeling improvements for Jason-1 and Jason-2, Advances in Space Research 46 (2010) 1541-1558.

Radiation pressure model tuning considerations

absolute value SLR residuals (mm) number SLR points

B’ by orbit angle 5°x5° gridded values cycles 1-84

Table 6.

Acknowledgements: We acknowledge the NASA Physical Oceanography program and the MEaSURE's project for their support, as well as the International Laser Ranging Service (ILRS), the International DORIS Service (IDS), and the International GNSS Service for their continued support.