## Abstract

Introduction

This paper presents developments to a set of high fidelity spacecraft surface force models. These models address the problem of errors in orbital prediction and orbital determination due to un-modeled and under-modeled surface forces on spacecraft. These models have been validated individually but in this paper the most recently developed models are applied together to give an insight into how they effect a spacecraft in orbit. A significant reduction in error between the predicted orbit and tracking data is shown when all the models are added to the orbital propagator.

Surface Forces

Spacecraft surface forces, while orders of magnitude smaller than gravitational forces are extremely important for accurate determination and propagation of spacecraft orbits. This paper will outline an improved approach to modelling four of these surface forces and their effects.

Solar Radiation Pressure (SRP)

SRP is the force exerted on a spacecraft's surface due to collision with photons originating from the sun. It is typically modelled using a a cannonball or box and wing spacecraft model. The acceleration due to incident flux on these primitives can be computed quickly but does not take into account all of the spacecraft geometry and material properties. In our approach a ray tracing technique is used on a complete model of the spacecraft . This involves calculating how incident light intersects the spacecraft geometry and the resultant force when it does. The model also allows for secondary intersection due to reflection and fully models spacecraft self-shadowing. For this study the resolution of the model has been significantly increased with a 1mm ray grid size and the spacecraft response to 10,000 different incident flux vectors calculated.

Thermal Re-Radiation (TRR)

TRR modelling utilises the same spacecraft model and material properties and calculates the thermal response of the material and the resultant emission of thermal photons. This is then used to calculate the resultant force on the spacecraft . A novel element of the approach lies in detailed modelling of the space vehicle multi-layered insulation (MLI).

Earth Radiation Pressure (ERP)

The ERP model again uses the photon-spacecraft interaction model used by the SRP model. The difference is the that instead of a solar flux, a flux is computed that incorporates the fluxes both emitted from and reflected by the Earth. These fluxes are based on the CERES mission earth radiation fluxes.

Antenna Thrust (AT)

Antenna thrust is the recoil of the emitted photons from communications antennae and while small has a constant direction which makes its effect consistent in direction with respect to the spacecraft geometry.

Validation

As validation of these methods a 12 hour orbit of a GPS IIR satellite was propagated. A full orbit and its initial conditions were taken from the JPL precise ephemeris. An orbit is then propagated from those initial conditions and compared to the precise orbit to ascertain how the error between the orbit propagation and the true orbit changed over time.

The spacecraft dynamic model was numerically integrated using an 8th order embedded Runge-Kutta integrator with adaptive step-size control, a high order (15x15) GRACE gravity field, periodic variations to the gravity field coefficients incorporating polar motion and solid Earth tides, third body accelerations for the Sun, Venus, the Moon, Mars and Jupiter and general relativistic forces.

The results show a consistent and significant reduction in orbit error with the introduction of each surface force model. This leads to a total error after 12 hours of less then 10cm along track when all of the surface models are applied.

This paper presents developments to a set of high fidelity spacecraft surface force models. These models address the problem of errors in orbital prediction and orbital determination due to un-modeled and under-modeled surface forces on spacecraft. These models have been validated individually but in this paper the most recently developed models are applied together to give an insight into how they effect a spacecraft in orbit. A significant reduction in error between the predicted orbit and tracking data is shown when all the models are added to the orbital propagator.

Surface Forces

Spacecraft surface forces, while orders of magnitude smaller than gravitational forces are extremely important for accurate determination and propagation of spacecraft orbits. This paper will outline an improved approach to modelling four of these surface forces and their effects.

Solar Radiation Pressure (SRP)

SRP is the force exerted on a spacecraft's surface due to collision with photons originating from the sun. It is typically modelled using a a cannonball or box and wing spacecraft model. The acceleration due to incident flux on these primitives can be computed quickly but does not take into account all of the spacecraft geometry and material properties. In our approach a ray tracing technique is used on a complete model of the spacecraft . This involves calculating how incident light intersects the spacecraft geometry and the resultant force when it does. The model also allows for secondary intersection due to reflection and fully models spacecraft self-shadowing. For this study the resolution of the model has been significantly increased with a 1mm ray grid size and the spacecraft response to 10,000 different incident flux vectors calculated.

Thermal Re-Radiation (TRR)

TRR modelling utilises the same spacecraft model and material properties and calculates the thermal response of the material and the resultant emission of thermal photons. This is then used to calculate the resultant force on the spacecraft . A novel element of the approach lies in detailed modelling of the space vehicle multi-layered insulation (MLI).

Earth Radiation Pressure (ERP)

The ERP model again uses the photon-spacecraft interaction model used by the SRP model. The difference is the that instead of a solar flux, a flux is computed that incorporates the fluxes both emitted from and reflected by the Earth. These fluxes are based on the CERES mission earth radiation fluxes.

Antenna Thrust (AT)

Antenna thrust is the recoil of the emitted photons from communications antennae and while small has a constant direction which makes its effect consistent in direction with respect to the spacecraft geometry.

Validation

As validation of these methods a 12 hour orbit of a GPS IIR satellite was propagated. A full orbit and its initial conditions were taken from the JPL precise ephemeris. An orbit is then propagated from those initial conditions and compared to the precise orbit to ascertain how the error between the orbit propagation and the true orbit changed over time.

The spacecraft dynamic model was numerically integrated using an 8th order embedded Runge-Kutta integrator with adaptive step-size control, a high order (15x15) GRACE gravity field, periodic variations to the gravity field coefficients incorporating polar motion and solid Earth tides, third body accelerations for the Sun, Venus, the Moon, Mars and Jupiter and general relativistic forces.

The results show a consistent and significant reduction in orbit error with the introduction of each surface force model. This leads to a total error after 12 hours of less then 10cm along track when all of the surface models are applied.

Original language | English |
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Title of host publication | AIAA/AAS Astrodynamics Specialist Conference |

Place of Publication | Reston, VA |

Number of pages | 8 |

ISBN (Electronic) | 9781624103087 |

DOIs | |

Publication status | Published - 4 Aug 2014 |

Event | AIAA/AAS Astrodynamics Specialist Conference 2014 - California, San Diego, United States Duration: 4 Aug 2014 → 7 Aug 2014 |

### Publication series

Name | AIAA SPACE Forum |
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Publisher | AIAA |

### Conference

Conference | AIAA/AAS Astrodynamics Specialist Conference 2014 |
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Country/Territory | United States |

City | San Diego |

Period | 4/08/14 → 7/08/14 |

## Keywords

- precise orbit determination
- spacecraft
- high fidelity surface force modelling
- orbital prediction
- solar radiation pressure
- thermal re-radiation
- Earth radiation pressure
- antenna thrust