Joshua Ashenberg

Active gravity-gradient stabilization of a satellite in elliptic orbits

Abstract A tether can be utilized as an efficient actuator for the purpose of satellite attitude control. The tether tension generates a strong passive gravity stabilization effect. The combination of tether tension with a movable attachment point mechanism results in an effective and low cost active controller. This paper reviews the concept and presents the dynamical characteristics of the configuration. It then demonstrates that a feasible three-axis control can be achieved by means of only two actuators. The primary contribution is the development of a control law that works for eccentric orbits. In this case, the dynamical system that represents the configuration becomes periodic in time, and thus impossible to control by using constant gains. The solution is a periodic control law. A combination of Floquet transformation and sampled state periodic hold feedback control is proposed as an effective pointing method for small-eccentricity orbits.

Proposed Method for Modeling the Gravitational Interaction Between Finite Bodies

A new computational approach to the problem of the mutual gravitational attraction between finite-size bodies is presented. In this case, the gravitational force acting on each body consists of contributions from the mutual interactions between all particles comprising all bodies. The current approach is mostly suitable for high-precision modeling of the gravitational perturbations acting on a satellite in the vicinity of large and irregular objects. This approach is preferable in problems such as a satellite in the vicinity of an asteroid or near a planetary ring. If the shape of the asteroid is irregular, the traditional Legendre polynomials method does not give a good approximation. The series expansion of the potential in the planetary ring problem has a convergence problem because the distance between the satellite and the ring center of mass can be small compared with the size of the ring. These difficulties are overcome by defining new integrals over the attracting body. The operations on these integrals for the purpose of methodical computation are also presented. The potential via radial basis functions is modeled, and the gradients based on these smooth functions are derived.

On the effects of time-varying aerodynamical coefficients on satellite orbits

Abstract The problem of orbital dynamics of a satellite in the atmosphere is revised for time-varying aerodynamical coefficients. A general form for aerodynamical modeling is suggested. Including the unsteady aerodynamics, results in major orbital changes, very sensitive to attitude kinematics. Representative examples for the extreme case of orbiting flat plate are demonstrated.

Gravitational torque frequency analysis for the Einstein elevator experiment

Testing the principle of equivalence with a differential acceleration detector that spins while free falling requires a reliable extraction of a very small violation signal from the noise in the output signal frequency spectrum. The experiment is designed such that the violation signal is modulated by the spin of the test bodies. The possible violation signal is mixed with the intrinsic white noise of the detector and the colored noise associated with the modulation of gravitational perturbations, through the spin, and inertial-motion-related noise. In order to avoid false alarms the frequencies of the gravitational disturbances and the violation signal must be separate. This paper presents a model for the perturbative gravitational torque that affects the measurement. The torque is expanded in an asymptotic series to the fourth order and then expressed as a frequency spectrum. A spectral analysis shows the design conditions for frequency separation between the perturbing torque and the violation signal.

Detector Configurations for Equivalence Principle Tests with Strong Separation of Signal from Noise

Testing the Equivalence Principle (EP) at a level of accuracy substantially higher than the present state of the art requires resolving a very small signal out of the instrument’s intrinsic noise and also the noise associated with the instrument’s motion and gravity gradients. In the test of the Equivalence Principle in an Einstein Elevator under development by our team, the acceleration detector spins about a horizontal axis while free falling for about 25 s inside a co‐moving capsule released from a stratospheric balloon. The characteristics of the instrument package and the configuration of the detector play a key role in the ability to extract an EP violation signal at the desired threshold level out of dynamics‐related noise. Numerical simulations of the detector’s dynamics in the presence of relevant perturbations, having assumed realistic errors and construction imperfections, show the merits of the detector configuration selected. The results illustrate that the effects of dynamics and gravity gra...

Analytical formulation of a complex mutual gravitational field

The mutual gravitational potential for proximate bodies with an arbitrary mass topology is investigated. The current research is motivated by an experiment for the verification of the equivalence principle in gravitation. The gravitation model for the experiment is complex and requires high precision. The proposed methodology is to formulate the potential in terms of inertial integrals and the so-called outer integrals. The method is general and can represent any gravitational configuration. Approximating the outer integrals by radial basis functions reduces the complexity for a real-time dynamical simulation.

The Weak Equivalence Principle (WEP) and the General Relativity Accuracy Test (GReAT) with an Einstein Elevator

The experiment GReAT (General Relativity Accuracy Test) aims at testing the Weak Equivalence Principle with a precision of several parts in 1015. The test will be performed by using a cryogenic differential accelerometer consisting of two test masses of different materials, released from a stratospheric altitude to free fall inside an evacuated capsule. The detector is spun about its horizontal axis to modulate the possible violation signal. As a result, the signal will appear at the spin frequency while the effects due to the diagonal components of the gravity gradient tensor in case of imperfect coincidence of the two proof masses centers of mass will appear at twice the rotation frequency.