Jozef C. van der Ha

Probability of Collisions in the Geostationary Ring

Geostationary satellites not removed from the geosynchronous altitude at the end of their useful life will expose future spacecraft orbiting in this unique region to a continual collision hazard. The probability of a collision occurring before the end of this century is less than 2 x 10 ~ , unless large space structures such as solarpower satellites become operational, in which case collisions would likely occur every few years. Fundamental data on the collision probabilities are derived from deterministic orbit propagation for a representative sample of uncontrolled objects using an intersection process in which the active satellites are described by a probability distribution within the geostationary ring. The study clearly points out that all geostationary satellites should be removed from the ring at the end of their operational lifetime in order that the collisional risk remains within acceptable bounds in the future. The cost of this remedy amounts to no more than that of one month of active station-keeping for present-day satellites.

Jet-Damping and Misalignment Effects During Solid-Rocket- Motor Burn

The present study provides an assessment of the dynamical processes that take place during the solid-rocketmotor (SRM) burn of a spin-stabilized spacecraft. We discuss the equations of motion for a system consisting of a rigid-body spacecraft and the gases in the SRM combustion chamber without specifying a model for the gas flow. In particular, we exploit the conservation of angular momentum flux from the solid propellant to the combustion gases leaving the system. We obtain a rotational equation that contains the jet-damping and misalignment effects in terms of the mass flow center and the mean exhaust velocity that summarize the action of the gases on the system for any flowfield. Compact analytical models are established that incorporate these effects. Piecewise linear approximations are adopted for the evolution of the system mass properties with respect to time during the SRM burn .W ef ound that this technique is flexible and well suited for realistic time-varying system parameters. We illustrate the application of the model using the actual conditions of the CONTOUR spacecraft during its SRM burn on 15 August 2002. I. Introduction T HE principal effects that influence the pointing stability of a spin-stabilized spacecraft during the burn of a solid rocket motor (SRM) are induced by misalignment and jet-damping torques. The former category is caused by errors in the SRM thrust vector direction and/or center-of-mass (c.m.) offsets induced by spacecraft balancing and alignment errors. The jet-damping torque originates from the resistance of the outflowing gases against a transverse rotation.

Trajectory Estimation of the Hayabusa Spacecraft During Atmospheric Disintegration

The Hayabusa spacecraft was intentionally destroyed in the atmosphere at superorbital velocity at the conclusion of its asteroid sample return mission in June 2010. This study uses single-station ground-based video observations of the reentry to analyze the breakup of the spacecraft and estimate the trajectory of 80 individual spacecraft fragments. An extended Kalman filter with batch initialization is used to estimate the position, velocity, and aerodynamic ballistic coefficients of the fragments. The breakup is characterized and compared with preflight predictions. A high area-to-mass object is seen early during the reentry, which matches closely with the predicted solar panel separation. Nearly all fragments have decreasing freestream dynamic pressure during their observed trajectories. Fragments with high drag ballistic coefficients are more likely to be observed early in the reentry. Assuming simple aluminum spheres, the estimated ballistic coefficients show that the fragments would have radius and m...

Spin Axis Attitude Determination Accuracy Model in Presence of Biases

A practical model is presented for the effects of biases on the spin axis attitude pointing orientation of a spin-stabilized spacecraft. Biases are induced by spacecraft design limitations, for example, dynamic imbalance and sensor mounting alignment errors, and by environmental effects such as the variations in the infrared Earth radius seen by the Earth sensor. The measurement equations for the sun and Earth sensors are formulated in the presence of the relevant biases. The effects of the biases on the angular measurements are established by means of a small-angle perturbation technique. The propagation of the biases into the resulting attitude solution is derived by means of a realistic single-frame attitude-determination method. The statistical properties of the expected attitude error can then be expressed in terms of the specified input biases. Furthermore, practical approaches for the reconstruction of the biases from the observed measurement residuals are provided. The models are demonstrated using actual sensor data of the Comet Nucleus Tour (CONTOUR) spacecraft collected during its phasing orbits in August 2002. The sensitivities of the sun and Earth sensor measurements and the attitude vector to the relevant biases are analyzed in detail, and the reconstruction of the biases in the infrared Earth radii is illustrated for CONTOURs final sensor coverage interval.

Long-Term Attitude Drift of Spinning Spacecraft Under Solar Radiation Torques

Solar radiation pressure effects have been exploited by satellites for about four decades. Concepts have been developed for using solar radiation forces and torques in practical applications, for instance, for orbit stationkeeping and attitude stabilization of geostationary communications satellites. The forces and torques induced by solar radiation pressure can substantially alter the orbital and attitude behavior of spacecraft, especially in long-duration missions. The present work analyzes the long-term effect of the solar radiation torques on the evolution of the spin-axis attitude pointing of any type of spacecraft (e.g., Earth-orbiting spacecraft, deep space probes, and solar sails). Analytic models are presented that can be applied to a spacecraft of an arbitrary geometrical shape. Compact results are established that predict the annual drift of the spacecraft spin axis under solar radiation torques. The models presented will be useful for the design of spacecraft attitude control systems as well as for space mission planning, including hibernation concepts.

Equal-Chord Attitude Determination Method for Spinning Spacecraft

The equal-chord method offers a straightforward and low-cost technique for the determination of the spin-axis attitude using sun and Earth sensor data. The Earth aspect angle follows from the time at which the chord lengths measured by the Earth sensors two pencil beams are equal. An estimation technique is not required, but linear or quadratic fitting of the sensor data should be performed to remove the random errors. The accuracy of the attitude solution obtained by the equal-chord method in the presence of the relevant biases is evaluated. The result is insensitive to uniform biases in the measured chord angles, caused for instance by errors in the Earths infrared horizon. Finally, the application of the method is demonstrated using actual flight data of the CONTOUR spacecraft.

Spin-Axis Attitude Determination Using In-Flight Data

The paper presents a practical spin-axis attitude determination approach based on the Tanygin–Shuster algorithm. The technique is illustrated by means of sensor measurement data originating from two satellites with very different orbit and attitude characteristics. The most appropriate data intervals are identified using criteria based on measurement sensitivities. A minimum-variance technique is formulated for establishing the Earth aspect angle from the measured chord angles. The chain of covariance transformations from the fundamental sensor measurement errors to the final attitude error is presented. The unit-vector normalization technique, which is an inherent part of the Tanygin–Shuster method, is found to be beneficial for the stability of the attitude determination results under unknown biases, especially in cases in which only a subset of the measurement angles are available.

Two-Sun-Cones Attitude-Determination Method

Spin stabilization offers a straightforward concept for spacecraft attitude stabilization. In the case of Earth-orbiting satellites, the determination of the spin-axis pointing direction is usually accomplished by using sun and Earth sensor measurements. For deep-space missions, however, useful Earth sensor measurements are not available. This paper presents a technique for the spin-axis attitude determination using only sun sensor data collected at two different instants of time. The spin-axis attitude corresponds to one of the intersections of the two available sun angle cones. The application of the method is validated with the help of actual in-flight sun sensor measurements from the comet nucleus tour satellite. The results indicate that the achievable attitude-determination accuracy is of the order of a degree after a number of hours. After less than two days, the error is below a tenth of a degree.

Stability of Spinning Satellite Under Axial Thrust, Internal Mass Motion, and Damping

The paper extends and clarifies the stability results for a spinning satellite under axial thrust in the presence of internal damped mass motion. It is known that prolate and oblate satellite configurations can be stabilized by damped mass motion. Here, the stability boundaries are established by exploiting the properties of the complex characteristic equation and the results are interpreted in terms of the physical system parameters. When the thrust level is the only free parameter, both prolate and oblate satellites can be stabilized provided that the thrust is within a specified range. This result is in contrast to the well-known maximum-axis rule for a free spinner where damping is always stabilizing (destabilizing) for an oblate (prolate) satellite. When adding a suitable spring-mass system, the minimum value of the spring constant that stabilizes the configuration can be established. In practice, however, the damping may well be too weak to be effective. Numerical illustrations are presented for the...

Modeling and Validation of Thermal Radiation Acceleration on Interplanetary Spacecraft

Precisemodeling of nonconservative forces is becoming increasingly important for deep-space and interplanetary missions, especially those with strict targeting requirements. Apparent errors in the solar radiation pressure model are often corrected with estimated scale factors in the orbit determination process. For example, several European Space Agency deep-space spacecraft have estimated solar radiation pressure scale factors between 1.05 and 1.15. This work shows that including separate thermal accelerationmodels can account formany of these apparent errors in the solar radiation pressure modeling. Using the Rosetta spacecraft as an example, a steady-state thermal model that is applicable to the cruise phases of interplanetary missions is described. The surface temperatures on the spacecraft body are solved in closed form,whereas those on the solar panel front and rear surfaces are solvedwith an iterative numerical procedure. The thermal model is validated by comparing the predicted thermal radiation acceleration with the remaining unmodeled acceleration extracted from the operational orbit estimates. The solar array temperatures from this model also agree with finite element method results and thermistor telemetry to within several degrees.