MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS

ESPACEPorto, June 2009

MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS

Carlos Javier Rodriguez Solano

Technische Universität München [email protected]

3a Conferencia Alβan – Porto 2009


ESPACE

International Master‘s Program

ESPACE – Earth Oriented Space Science and Technology

www.espace-tum.de


ESPACE combines elements of engineering and science in one single interdisciplinary program

Remote Sensing

Satellite Technology

Navigation

Earth System

ESPACE

www.espace-tum.de


“The NAVSTAR GPS ( NAVigation System with Time And Ranging Global Positioning System) is a satellite-based radio navigation system providing precise three dimensional position, navigation and time information to suitably equipped users.”

Seeber (2003)

Introduction

Positions of at least 4 satellites

+

Travelled distance of the signal from the satellite’s antenna to the receiver

=Position on Earth and synchronization

of the receiver


The better the positions of the satellites are known

the higher precision that can be achieved on Earth for positioning

The International GNSS Service provides: Final Orbits with accuracy of 5 cm

Final Orbits are computed using:

1) Direct observations from the satellites to reference stations on Earth

2) Force models that include the principal perturbations to the orbit:

- Low terms of Geopotential

- Attraction of Sun and Moon

- Solar Radiation Pressure

- Solid Earth and Ocean Tides

- General Relativity

Introduction


An independent way to test the accuracy of Final Orbits is using:

Satellite Laser Ranging (SLR)

Accuracy of SLR measurements is 5 – 6 mm

NERC

This bias could come from the Earth radiation that arrives to the satellites

Not included in the modelling of Final Orbits

But there is a consistent bias of 4 – 5 cm

The GPS – SLR Orbit Anomaly.

Ziebart et al. (2007)

Introduction


Compute irradiance at satellite altitude due to emitted and reflected radiation, using:

- Albedo of the Earth (α ≈ 0.3)

- Satellite altitude (h ≈ 20000 km)

- Angle ψ, formed by satellite, Earth and Sun

Earth radiation model


After integration of and over the part of the sphere visible to the satellite,we get the total Earth´s irradiance model, which is plotted as function of ψ

emitId

reflId

Earth radiation model


GPS satellite model

The radiation coming from the Earth that impacts a satellite accelerates it due to the momentum transfer between the photons and the surface of the satellite.

GPS satellite model spherical bus + solar panel pointing to the Sun

100 times smaller as acceleration due to direct solar radiation


Numerical orbit integration

Numerical integration over one year of:

Unperturbed keplerian orbit + perturbing acceleration

Initial conditions for PRN06, one of the GPS satellites with laser retroreflectors

Semimajor axis [km] Eccentricity Inclination [deg] RAAN [deg] Argument of Perigee [deg]

26560.699 0.0062068 53.5060 155.9994 282.1291

Position in the RTN frame, perturbed – unperturbed (reference) orbit

RTN frame


Numerical orbit integration

Keplerian elements, perturbed – unperturbed (reference) orbit

Important drift in: Argument of Perigee + True Anomaly = T-component of position


Results and Discusion

Definition of different reference orbit:

- Mean keplerian elements over one revolution

- Same true anomaly as perturbed orbit

- Star of it at ∆u = 0

Possible to compare just in radial direction!

Position in the RTN frame, perturbed – reference orbit

Shift of 2 – 4 cm in radial direction, comparable with GPS – SLR Orbit Anomaly


Results and Discusion

Also very interesting, plot of radial residuals as a function of:

Sun elevation angle β0 and angle ∆u

Strong dependency with position of Sun

Twice per revolution and twice per year perturbation


Conclusions

- A not negligible effect of the Earth radiation on satellite orbits has been found

- Key factors for final results are

1) Earth radiation model with dependency on the relative position of satellite, Earth and Sun

2) Satellite model: bus, solar panel and orientation to the Sun

3) Reference orbit, suitable for the comparison in radial direction

Next steps of the Master Thesis:

- Include models in the computation of GPS orbits

- Use of real GPS and SLR data in the Bernese GPS Software

Better understanding of the GPS – SLR Orbit Anomaly,

a current limit of GPS orbits


THANK YOU!

ANY QUESTIONS?

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MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS