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Some of the technology developed in building a drag-free satellite simulator for laboratory use is described. The design decisions made in order to achieve a 10 to the -11th power g perturbation level for the navigation satellite is discussed. The control system development that will make possible drag-free operation of spinning satellites to reduce perturbation levels by averaging is described.
The use of radio tracking of a solar probe to estimate accurately the coefficient of the second zonal harmonic of the sun's gravitational field was examined. Preliminary results indicate that the coefficient can be estimated with a standard error of 10 to the minus 8th power or less, provided that the probe is equipped with a suitable drag-free system to compensate for the effects of non-gravitational accelerations. For signal paths that pass near the sun, dual-band ranging to the probe can provide the tracking accuracy needed to insure that the standard of error is equal to or less than 10 to minus 8th power. The possibility of achieving such accuracy with a single-band radio uplink and a dual-band downlink is discussed.
The metric tensor is given for describing the dynamical effects of the sun on a solar probe and the gravitational redshift of a probe-based clock in a covariance analysis for the detectability of the solar quadrupole moment and the solar angular momentum. Unknown parameters were determined by least squares fit to the probe tracking data. A polar orbit was assumed with perihelion at 5 solar radii and with an earth-sun-probe angle of 135 deg at perihelion. Tracking was assumed to be Doppler only, with a basic uncertainity of .1 mm/sec in the radial velocity. A drag-free system which could reduce nongravitational forces below the level of 2 times 10 to the minus 12th power was found necessary to preserve this same level of accuracy. Both one way and two way Doppler were supposed in order to determine the gravitational redshift as well as the pure spacecraft dynamics.
The Triad satellite is maintained within 1 mm of its proof mass (a small metal ball) in a purely gravitational orbit, using a drag-free control system, named Discos, as the disturbance compensation system. The Discos proof mass is surrounded by an outer shell which holds fuel tanks and cold gas jets. The shell shields the proof mass from such nongravitational forces as radiation pressure, atmospheric drag, and micrometeorite impact. Whenever these forces displace the outer shell relative to the proof mass, an error signal is generated by a capacitive bridge sensor, and the satellite is propelled by gas jets to remain centered on the proof mass when the error reaches 1 mm. Local atmospheric densities near 800 km were measured, using ball position data, and the observed accelerations were corrected for the effects of solar radiation pressure. The measured densities reveal a greater dependence on latitude than that indicated by balloon satellites, and also a dependence on longitude. Only a small dependence on Kp, however, was observed in the region where the measurements were made.
At very low altitudes, the effect of atmospheric drag results in drastically reduced orbit lifetimes and considerable uncertainty in satellite motions. The concept suggested herein employs a DISturbance COmpensation System (DISCOS) on each of a pair of satellites at very low altitudes to provide refined measurements of the earth's gravitational field. The DISCOS maintains the satellites in orbit and essentially eliminates motion uncertainties due mostly to drag and to a lesser extent from solar radiation pressure. By a closed-loop measurement of the relative rangerate between the two low satellites, one can determine the earth's gravitational field with a considerably greater accuracy than could be obtained by tracking a single satellite.
A disturbance compensation system for satellites based on the drag-free concept was mechanized and flown, using a spherical proof mass and a cam-guided caging mechanism. The caging mechanism controls the location of the proof mass for testing and constrains it during launch. Design requirements, design details, and hardware are described.
The use of estimators or observers is discussed as applied to satellite attitude control and the control of drag-free satellites. The practical problems of implementation are discussed, and the relative advantages of full and reduced state estimators are compared, particularly in terms of their effectiveness and bandwidth as filters. Three applications are used to illustrate the principles. They are: (1) a reaction wheel control system, (2) a spinning attitude control system, and (3) a drag-free satellite translational control system. Fixed estimator gains are shown to be adequate for these (and many other) applications. Our experience in the hardware realization of estimators has led to categorize the error sources in terms of those that improve with increased estimator gains and those that get worse with increased estimator gains.
Drag measuring requirements and comparison of accelerometer or drag-free satellite control systems usage for atmospheric density determination
The parameters and relations associated with optimal systems are examined, taking into account a quadratic performance index and a root square locus plot, including the characteristic roots of the optimal system and its adjoint system as a function of the cost function weights. The calculation of the locus is described and the employment of the considered relations in studies of a drag-free satellite is discussed. Attention is given to weights regarding the initial states, questions of rotating integral control, approaches for experimental verification, and the performance of various methods for the reduction of fuel consumption due to center of spin offsets.
The original motivation for studying control laws for pulse plasma systems was based on the improved life characteristics possible with pulse plasma jets. These pulse plasma units are relatively massive compared with cold gas thrustors. As a result, therefore, significant mass savings can be achieved by minimizing the the number of thrustors. The control laws, therefore, were developed for thrust available from two thrustors only. In a spinning satellite, these thrustors are sufficient to completely control the vehicle as long as the spin rate is sufficiently high for a given level of external disturbance. The thrustors are canted so that a component of each is along the plus and minus spin axis. The other component of each thrustor acts in the radial direction. It is sufficient to analyze the behavior in the plane of spin assuming a single thrustor.
The inner perturbing forces acting on sensors were analyzed, taking into account the technological limitations imposed on the proof mass position pickup and proof mass acquisition system. The resulting perturbing accelerations are evaluated as a function of the drag-free sensor parameters. Perturbations included gravitational attraction, electrical action, magnetic action, pressure effects, radiation effects, and action of the position pickup. These data can be used to study the laws of guidance, providing an optimization of the space probe as a whole.
A satellite configuration having two gyroscopes with axes parallel to the boresight of a telescope and two at right angles to the telescope and approximately parallel and perpendicular to the earth's axis is proposed for measuring geodetic precessions due to the earth's motion about the sun, higher order geodetic terms calculated from the earth's quadrapole mass moment (0.010 arc-sec/year in a 400 nautical mile polar orbit), and deflection by the sun of the starlight signal for the reference telescope. Data from the experiment also contain large periodic signals due to the annual and orbital aberrations of starlight which are useful in providing a built in reference signal of known amplitude for scaling the relativity signals, and should yield a singularly precise measurement of the parallax of the reference star. The development of the gyroscope and its readout system are discussed, as well as signal integration, drag-free control, and attitude control.
Zero gravity satellite concept feasibility and control system design evaluation using air cushion vehicle
The design of apparatus being built to measure the general relativistic precession of gyroscopes in earth orbit is discussed, with emphasis on the role of cryogenics. Operation with a superconducting rotor is crucial in that it provides the only known way of attaining the required angular resolution of 0.001 arc-sec. Operation at low temperatures also provides the star tracker, to which the gyros are referenced, with excellent null stability. The boil-off gas from the large helium dewar is used to operate the vehicle in a drag-free mode which is expected to improve the gyro performance by a factor of ten. The dewar system is compatible with a wide range of experiments requiring temperatures as low as 2K in space.
A typical Geopause satellite orbit has a 14 hour period, a mean height of about 4.6 earth radii, and is nearly circular, polar, and normal to the ecliptic. At this height only a relatively few gravity terms have uncertainties corresponding to orbital perturbations above the decimeter level. The orbit is at the geopotential boundary, the geopause. The few remaining environmental quantities which may be significant can be determined by means of orbit analysis and accelerometers. The Geopause satellite system also provides the tracking geometry and coverage needed for determining the orbit, the tracking system biases and the station locations. Five or more fundamental stations well distributed in longitude can view Geopause over the North Pole. Geopause also provides the basic capability for satellite-to-satellite tracking of drag-free satellites for mapping the gravity field and altimeter satellites for surveying the sea surface topography.
The design of a drag-free satellite and its application to measuring tidal interaction of the earth and tesseral harmonics are discussed. Principle areas of discussion are: (1) the feasibility of making geophysical measurements which are not possible with conventional satellites, and (2) design of attitude and translation control systems for spinning vehicle and possible coupling of attitude and translation control for gravity stabilized vehicles.
The translational and attitude control of a drag-free, rotating satellite are usually designed to be independent of each other. However, coupling may exist which can produce instability. The different types of coupling and the stability conditions are studied, using root locus type techniques. The resulting root loci have unusual shapes due to the nonlinearity of the characteristic polynomial in terms of the coupling parameters. It is possible, however, to use standard root loci techniques by appropriate factoring and subsequent superposition of loci. The effect of the main parameters upon the overall stability of the system is studied. Both, attitude and translation instabilities eventually arise - the former being more critical for typical satellite designs. An analytical expression for the stability boundary is developed.
Drag free spacecraft performance in deep space, examining inner residual disturbance forces for motion control systems