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Jul 22, 2018 - collision avoidance of artificial satellites orbiting the Earth at altitudes below 1000 km. ⇨ Thermospheric density is usually given by empirical ...

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) Technische Universität München

Thermospheric density estimation using Satellite Laser Ranging observations of low Earth orbiting satellites Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, and Ganesh Lalgudi Gopalakrishnan

Deutsches Geodätisches Forschungsinstitut, Technische Universität München (DGFI-TUM), Munich, Germany

42nd COSPAR Scientific Assembly, Pasadena, CA, Unites States of America, 14 – 22 July 2018

Introduction  Knowledge on the density of the Earth’s thermosphere and exosphere is a prerequisite for  planning of satellite missions,  precise orbit determination (POD),

 orbit and re-entry prediction,  collision avoidance of artificial satellites orbiting the Earth at altitudes below 1000 km.

 Thermospheric density is usually given by empirical and physical models

 Empirical models have been derived since 1961 from following observations:  mass spectrometer,

 incoherent scatter radar,  orbital (satellite acceleration from POD) data,  accelerometer data (CHAMP, GRACE, GOCE, etc.).

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Outline  The purpose of this presentation: to show the possibility of using Satellite Laser Ranging (SLR) observations to spherical low Earth orbiting (LEO) satellites to scale (validate) thermospheric density provided by empirical thermospheric density models  Satellites used: ANDE-Castor, ANDE-Pollux and SpinSat (satellite altitude: 248 – 425 km)  Models tested: CIRA86, NRLMSISE00, JB2008, and DTM2013  Periods of low (August 2009 to March 2010) and high (January – March 2015) solar activity

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Orbit analysis approach  Atmospheric drag 𝒂𝐷 is the major non-gravitational perturbation acting on LEO satellites and depends on the thermospheric neutral density 𝜌:

1 𝐴ref 2 𝒂𝐷 = − ∙ 𝑓𝑠 ∙ 𝐶𝐷 𝜌 𝑣rel 𝒖𝐷 2 𝑚

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where 𝐴ref is the effective cross-sectional area of the satellite (known), − 𝑚 is the satellite mass (known), − 𝐶𝐷 is the dimensionless drag coefficient (is analytically computed using a Gas-Surface Interaction model, physical assumptions and key parameters),

− 𝜌 is the thermospheric neutral density (computed using a model), − 𝑣rel - relative velocity of the satellite with respect to atmosphere (computed from POD using Horizontal Wind Model 2014 (HWM14)), − 𝒖𝐷 is the drag unit vector (computed from POD).  The scale factor 𝑓𝑠 in Eq. (1) scales the thermospheric density values computed from different empirical models (is estimated from the analysis of SLR observations of spherical LEO satellites and provides scaled thermospheric density). Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Key assumptions for the analytical computation of the physical drag coefficient  The condition of “free molecular flow”: at altitudes above approximately 140 km, the mean free path of the molecules is much larger than the characteristic satellite dimension.  Sentman (1961) model is adopted as an GSI model.  The assumption of thermal flow: the incident flow at every point at the satellite’s surface is a superposition of the Maxwell-Boltzmann molecular velocity distribution and the incident velocity vector of the atmosphere relative to the spacecraft.  The gas molecules experience a fully diffuse reflection with complete accommodation.  The re-emitted particles have a Maxwell-Boltzmann velocity distribution.  We assume an average value of satellite’s surface temperature Tw = 300 K, since the sensitivity of the drag coefficient to this parameter is quite small for various satellite geometries.

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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POD and the estimated parameters  Software used: DGFI Orbit and Geodetic parameter estimation Software (DOGS)  For satellite POD, we use up-to-date models based mainly on the IERS Conventions (2010)  Arc length: 3.5 – 7 days

 Parameters estimated at each orbital arc:

Parameters

Estimated

Six Keplerian elements

once per arc

One solar radiation pressure coefficient

once per arc

Earth albedo and infrared radiation pressure coefficient

once per arc

Empirical accelerations: transversal and normal onceper-revolution cosine and sine terms

once per arc

Scale factors of the thermospheric neutral density 𝒇𝒔

6-12 h step

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Spherical geodetic satellites Mission lifetime of different spherical SLR satellites. The grey box highlights the missions with altitudes up to 1500 km for which thermospheric drag has to be considered in the POD.

We use in this study SLR observations of ANDE-Pollux, ANDECastor and SpinSat.

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Satellites ANDE-Pollux, ANDE-Castor and SpinSat

ANDE-Castor (left), ANDE-Pollux (center) and SpinSat (right), image credit: NRL

Diameter (m)

Mass (kg)

𝑨𝐫𝐞𝐟 / m (𝐦𝟐 /kg)

Drag coefficient 𝐶𝐷 (-)

Initial altitude (km)

ANDE-P

0.483

27.442

0.006666

2.115±0.002

350

ANDE-C

0.483

47.450

0.003855

2.115±0.002

350

SpinSat

0.558

52.650

0.004645

2.126±0.002

425

Satellite name

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Results: scaling factors estimated from ANDE-P data - The estimated scaling factors for JB2008 model are most close to 1 among four models tested. - On the contrary, the estimated scaling factors for CIRA86 and NRLMSISE00 models mostly differ from 1. - DTM2013 provides the smallest standard deviations of the scaling factors. Satellite

Altitude (km)

Time span

Solar activity

ANDE-P

248 – 369

~1.5 months (16 August 2009 – 3 October 2009)

low

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Thermospheric densities computed using four models (period 16 August – 3 October 2009, ANDE-P orbit)

NRLMSISE00 (blue), CIRA86 (green), DTM2013 (orange) and JB2008 (magenta) Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Thermospheric densities scaled using estimated scaled factors from ANDE-P SLR observations (same period)

NRLMSISE00 (blue), CIRA86 (green), DTM2013 (orange) and JB2008 (magenta) Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Results: scaling factors estimated from ANDE-C data - The same qualitative conclusions on the mean and standards deviations of the scaling factors estimated from the ANDE-C data, as obtained from the ANDE-P data. - The numbers slightly differ, as compared to those obtained from the ANDE-P data, since the time span is 5 months longer. - A trend in thermospheric scaling factors is visible. Satellite

Altitude (km)

Time span

Solar activity

ANDE-C

297 – 350

~7 months (16 August 2009 – 26 March 2010)

low

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Results: scaling factors estimated from SpinSat data The estimated scaling factors of all three models are a bit larger than 1 meaning that the models slightly underestimated the thermospheric density in the period of high solar activity (January – March 2015). The NRLMSISE00 model provides the smallest standard deviation among the models tested. Satellite

Altitude (km)

SpinSat

393 – 425

Time span ~3 months (29 December 2014 – 29 March 2015)

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

Solar activity high 13

Summary Mean and standard deviations of the thermospheric density scaling factors of each thermospheric model (the wind model HWM14 is included) estimated using SLR measurements to each of three satellites at the given time spans Thermospheric model

ANDE-P

ANDE-C

SpinSat

16.08.2009 – 03.10.2009,

16.08.2009 – 26.03.2010,

29.12.2014 – 29.03.2015,

low solar activity

low solar activity

high solar activity

248 < h < 369 km

297 < h < 350 km

393 < h < 425 km

CIRA86

0.65 ± 0.26

0.68 ± 0.20

1.04 ± 0.25

NRLMSISE00

0.65 ± 0.25

0.68 ± 0.20

1.05 ± 0.23

JB2008

0.89 ± 0.27

0.97 ± 0.21

1.11 ± 0.23

DTM2013

0.79 ± 0.24

0.83 ± 0.16



Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Conclusions and outlook  A capability to estimate thermospheric density using Satellite Laser Ranging observations of low Earth orbiting satellites is illustrated.  Time series of scaling factors of the thermospheric density provided by 4 empirical models (CIRA86, NRLMSISE00, JB2008, DTM2013) have been derived using SLR observations of three spherical LEO satellites (ANDE-P, ANDE-C and Spinsat) at the periods of low (August 2009 to March 2010) and high (January – March 2015) solar activity.  The scaling factors of thermospheric density derived from SLR observations of satellites ANDE-P and ANDE-C agree well within the standard deviations for the overlapping period .  Scaling factors of CIRA86, NRLMSISE00, and JB2008 models change depending on the level of solar activity. These models overestimate the thermospheric density at the period of low solar activity and slightly underestimate it at the period of high solar activity.  Scaled thermospheric densities agree much better with each other than the initial thermospheric density given by the models tested in this study.  We are going to test a physical model: Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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Publications

 Panzetta F., Bloßfeld M., Erdogan E., Rudenko S., Schmidt M., Müller H.: Towards thermospheric density estimation from SLR observations of LEO satellites - A case study with ANDE-Pollux satellite. Journal of Geodesy, DOI: 10.1007/s00190-018-1165-8, 2018.  Rudenko S., Schmidt M., Bloßfeld M., Xiong C., Lülhr H.: Calibration of empirical models of thermospheric density using satellite laser ranging observations to near-Earth orbiting spherical satellites, IAG Symposia Kobe Proceedings 2017, accepted.

Acknowledgements This study was partly supported by the German Research Foundation (DFG) within the project “Interactions of low-orbiting satellites with the surrounding ionosphere and thermosphere (INSIGHT)”.

Deutsches Geodätisches Forschungsinstitut (DGFI-TUM) | Technische Universität München

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