MODELLING OF EARTH

1
MODELLING OF EARTHS RADIATION FOR GPS SATELLITE
ORBITS
Carlos Javier Rodriguez Solano Technische
Universität München carlos.rodriguez_at_mytum.de 3a
Conferencia Alßan Porto 2009
2
ESPACE
International Masters Program
ESPACE Earth Oriented Space Science and
Technology
www.espace-tum.de
3
ESPACE
ESPACE combines elements of engineering and
science in one single interdisciplinary program
www.espace-tum.de
4
Introduction
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)
5
Introduction
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

6
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
7
Earth radiation model

• ? Compute irradiance at satellite altitude due to
  emitted and reflected radiation, using
• Albedo of the Earth (a 0.3)
• Satellite altitude (h 20000 km)
• Angle ?, formed by satellite, Earth and Sun

8
Earth radiation model
After integration of and over
the part of the sphere visible to the
satellite, we get the total Earths irradiance
model, which is plotted as function of ?
9
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
10
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
11
Numerical orbit integration
Keplerian elements, perturbed unperturbed
(reference) orbit
12
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

13
Results and Discusion
Also very interesting, plot of radial residuals
as a function of Sun elevation angle ß0 and
angle ?u
Strong dependency with position of Sun Twice per
revolution and twice per year perturbation
14
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

15
THANK YOU! ANY QUESTIONS?