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Planetary Radar Astronomy

Radar is a powerful technique that has furnished otherwise unavailable information about solar system bodies for three decades. The advantages of radar in planetary astronomy result from: (1) the observer's control of all the attributes of the coherent signal used to illuminate the target, especially the wave form's time/frequency modulation and polarization; (2) the ability of radar to resolve objects spatially via measurements of the distribution of echo power in time delay and Doppler frequency; (3) the pronounced degree to which delay-Doppler measurements constrain orbits and spin vectors; and (4) centimeter-to-meter wavelengths, which easily penetrate optically opaque planetary clouds and cometary comae, permit investigation of near-surface macrostructure and bulk density, and are sensitive to high concentrations of metal or, in certain situations, ice. Planetary radar astronomy has primarily involved observations with Earth-based radar telescopes, but also includes some experiments with a spaceborne transmitter or receiver. In addition to providing a wealth of information about the geological and dynamical properties of asteroids, comets, the inner planets, and natural satellites, radar experiments have established the scale of the solar system, have contributed significantly to the accuracy of planetary ephemerides, and have helped to constrain theories of gravitation. This review outlines radar astronomical techniques and describes principal observational results.

Ostro, Steven J.↗

Simulation of Attitude and Trajectory Dynamics and Control of Multiple Spacecraft

Agora software is a simulation of spacecraft attitude and orbit dynamics. It supports spacecraft models composed of multiple rigid bodies or flexible structural models. Agora simulates multiple spacecraft simultaneously, supporting rendezvous, proximity operations, and precision formation flying studies. The Agora environment includes ephemerides for all planets and major moons in the solar system, supporting design studies for deep space as well as geocentric missions. The environment also contains standard models for gravity, atmospheric density, and magnetic fields. Disturbance force and torque models include aerodynamic, gravity-gradient, solar radiation pressure, and third-body gravitation. In addition to the dynamic and environmental models, Agora supports geometrical visualization through an OpenGL interface. Prototype models are provided for common sensors, actuators, and control laws. A clean interface accommodates linking in actual flight code in place of the prototype control laws. The same simulation may be used for rapid feasibility studies, and then used for flight software validation as the design matures. Agora is open-source and portable across computing platforms, making it customizable and extensible. It is written to support the entire GNC (guidance, navigation, and control) design cycle, from rapid prototyping and design analysis, to high-fidelity flight code verification. As a top-down design, Agora is intended to accommodate a large range of missions, anywhere in the solar system. Both two-body and three-body flight regimes are supported, as well as seamless transition between them. Multiple spacecraft may be simultaneously simulated, enabling simulation of rendezvous scenarios, as well as formation flying. Built-in reference frames and orbit perturbation dynamics provide accurate modeling of precision formation control.

Stoneking, Eric T.↗

MSFC Stream Model Preliminary Results: Modeling Recent Leonid and Perseid Encounters

The cometary meteoroid ejection model of Jones and Brown (1996b) was used to simulate ejection from comets 55P/Tempel-Tuttle during the last 12 revolutions, and the last 9 apparitions of 109P/Swift-Tuttle. Using cometary ephemerides generated by the Jet Propulsion Laboratory s (JPL) HORIZONS Solar System Data and Ephemeris Computation Service, two independent ejection schemes were simulated. In the first case, ejection was simulated in 1 hour time steps along the comet s orbit while it was within 2.5 AU of the Sun. In the second case, ejection was simulated to occur at the hour the comet reached perihelion. A 4th order variable step-size Runge-Kutta integrator was then used to integrate meteoroid position and velocity forward in time, accounting for the effects of radiation pressure, Poynting-Robertson drag, and the gravitational forces of the planets, which were computed using JPL s DE406 planetary ephemerides. An impact parameter was computed for each particle approaching the Earth to create a flux profile, and the results compared to observations of the 1998 and 1999 Leonid showers, and the 1993 and 2004 Perseids.

Cooke, William J.↗

Simultaneous solution for the masses of the principal planets from analysis of optical, radar, and radio tracking data.

The Jet Propulsion Laboratory has developed a set of computer programs known as the Solar System Data Processing System (SSDPS) which is employed in improving the ephemerides of the major planets and for improving the values of several associated astronomical constants. A group of solutions for the masses of the major planets, together with the AU and radii of Mercury, Venus, and Mars, is presented. These solutions based upon optical, radar, and spacecraft radio tracking data are preliminary. The relative power of radar and radio tracking data vis-a-vis purely optical data in a solution is shown. The problems which could arise by adopting solutions based upon a single data type are demonstrated.

Lieske, J. H.↗

Graphical Planning Of Spacecraft Missions

Mission Planning Graphical Tool (MPGT) computer program provides analysts with graphical representations of spacecraft and environmental data used in planning missions. Designed to be generic software tool configured to analyze any specified Earth-orbiting spacecraft mission. Data presented as series of overlays on top of two-dimensional or three-dimensional projection of Earth. Includes spacecraft-orbit tracks, ground-station-antenna masks, solar and lunar ephemerides, and coverage by Tracking Data and Relay Satellite System (TDRSS). From graphical representations, analyst determines such spacecraft-related constraints as communication coverage, infringement upon zones of interference, availability of sunlight, and visibility of targets to instruments.

Jeletic, J. F.↗

Trilogy, A Planetary Geodesy Mission Concept for Measuring the Expansion of the Solar System

The scale of the solar system is slowly changing, likely increasing as a result of solar mass loss, with additional change possible if there is a secular variation of the gravitational constant, G. The measurement of the change of scale could provide insight into the past and the future of the solar system, and in addition a better understanding of planetary motion and fundamental physics. Estimates for the expansion of the scale of the solar system are of order 1.5 cm year(exp -1) AU(exp -1), which over several years is an observable quantity with present-day laser ranging systems. This estimate suggests that laser measurements between planets could provide an accurate estimate of the solar system expansion rate. We examine distance measurements between three bodies in the inner solar system -- Earth's Moon, Mars and Venus -- and outline a mission concept for making the measurements. The concept involves placing spacecraft that carry laser ranging transponders in orbit around each body and measuring the distances between the three spacecraft over a period of several years. The analysis of these range measurements would allow the co-estimation of the spacecraft orbit, planetary ephemerides, other geophysical parameters related to the constitution and dynamics of the central bodies, and key geodetic parameters related to the solar system expansion, the Sun, and theoretical physics.

David E Smith↗

Radar studies in the solar system

A study of the solar system by means of ground based radar is presented. Emphasis was on developing the ephemerides needed to acquire radar data at Arecibo Observatory. Concentration was also on analyzing the resultant data to: test fundamental laws of gravitation; determine the size, shape, topography, and spin vectors of the targets; and study the surface properties of these objects, through their scattering law and polarization characteristics.

Shapiro, Irwin I.↗

Radar Studies in the Solar System

We aid in a study of the solar system by means of ground-based radar. We have concentrated on (1) developing the ephemerides needed to acquire radar data at Arecibo Observatory and (2) analyzing the resultant data to: test fundamental laws of gravitation; determine the size, shape, topography, and spin vectors of the targets; and study the surface properties of these objects, through their scattering law and polarization characteristics.

Shapiro, Irwin I.↗

Radar Studies in the Solar System

We aid in study of the solar system by means of ground-based radar. We have concentrated on: (1) developing the ephemerides needed to acquire radar data at Arecibo Observatory and (2) analyzing the resultant data to: test fundamental laws of gravitation; determine the size , shape, topography, and spin vectors of the targets; and study the surface properties of these objects, through their scattering law and polarization characteristics. We are engaged in radar observations of asteroids and comets, both as systematically planned targets and as "targets of opportunity." In the course of the program, we have prepared ephemerides for about 80 asteroids and three comets, and the radar observations have been made or attempted at the Arecibo Observatory, in most cases successfully, and in some cases on more than one apparition. The results of these observations have included echo spectra for the targets and, in some cases, delay - Doppler images and measurements of the total round-trip delay to the targets. Perhaps the most dramatic of these results are the images obtained for asteroids (4179) Toutatis and 1989PB (Castalia), which were revealed to be double-lobed objects by the radar images. Besides these direct results, the radar observations have furnished information on the sizes and shapes of the targets through analysis of the Doppler width of the echoes as a function of time, and on the surface properties (such as composition, bulk density, and roughness) through analysis of the reflectivity and of the polarization state of the echoes. We have also refined the orbits of the observed asteroids as a result of the Doppler (and in some cases delay) measurements from the radar observations. Although the orbits of main-belt asteroids accessible to ground-based radar are quite well known from the available optical data, some near-Earth objects have been seen by radar very soon after their optical discovery (for example, 199OMF, just eight days after discovery). In such cases. the radar results ensure that the object in question can be anticipated and identified at the next apparition. We have also participated in radar studies of the terrestrial planets. The results of these studies have included both planetary topography profiles from the analysis of round-trip delays to points along the target Doppler equator and determinations of the target spin state. The latter is of special interest in the case of Venus, which is very close to, but not on, a multi-body spin-orbit resonance such that Venus rotates 12 times for every 8 Earth orbits and 13 Venus orbits. As a result, Venus presents nearly the same face toward Earth at each inferior conjunction. Our latest results confirm that the spin state of Venus is slightly off the resonance. The delay measurements from planetary 2 ranging have also been used in combination with other types of range data in testing general relativity with increasing accuracy. We have also been engaged in radar studies of planetary satellites. Using our ephemerides, Arecibo made radar observations of the Galilean satellites of Jupiter and of Mars' satellite Phobos during the favorable opposition seasons (1988-1992 for Jupiter and 1990 for Mars). An attempt was also made to observe Deimos, but without detecting an echo. In 1997, an attempt was made to observe Saturn's satellite Titan, using the newly upgraded Arecibo radar system for transmitting and the Goldstone radar for receiving, but no echo was detected. The study of satellites by radar is in many ways similar to that of asteroids. The results from these observations have included characterization of the surface properties from the reflectivity and polarization ratio, as well as (in the case of the large satellites of Jupiter) the variation of reflectivity with incidence angle.

Shaprio, Irwin I.↗

Analyze satellite-tracking laser data in order to study satellite ephemerides, solid-Earth and ocean tides and laser system performance

The decrease in the semimajor axis of Lageos is considerably larger than expected. Gravitational effects, reference system effects, solar radiation pressure, Earth albedo pressure, neutral atmospheric drag, the Poynting Robertson Effect, and electrodynamic effects were used in explaining the observations. Quick look data provided are used to determine the Earth's polar motion and length of day. This process is routine, and provides these geophysical data every five days.

Gaposchkin, E. M.↗

Occultations of stars by solar system objects. VII - Occultations of catalog stars by asteroids in 1988 and 1989

Predictions are given for 102 occultations of stars by minor planets occurring in 1988 and 1989. The predictions are based on a computerized comparison of asteroid ephemerides with star positions given in eight major astrometric catalogs. The search is completed for all numbered asteroids whose orbits are accurately known and that reach an angular diameter of at least 0.08 arcsec during the search years. Preliminary information sufficient for planning is given for each occultation.

Wasserman, L. H.↗

Lifetime predictions for the Solar Maximum Mission (SMM) and San Marco spacecraft

Lifetime prediction techniques developed by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) are described. These techniques were developed to predict the Solar Maximum Mission (SMM) spacecraft orbit, which is decaying due to atmospheric drag, with reentry predicted to occur before the end of 1989. Lifetime predictions were also performed for the Long Duration Exposure Facility (LDEF), which was deployed on the 1984 SMM repair mission and is scheduled for retrieval on another Space Transportation System (STS) mission later this year. Concepts used in the lifetime predictions were tested on the San Marco spacecraft, which reentered the Earth's atmosphere on December 6, 1988. Ephemerides predicting the orbit evolution of the San Marco spacecraft until reentry were generated over the final 90 days of the mission when the altitude was less than 380 kilometers. The errors in the predicted ephemerides are due to errors in the prediction of atmospheric density variations over the lifetime of the satellite. To model the time dependence of the atmospheric densities, predictions of the solar flux at the 10.7-centimeter wavelength were used in conjunction with Harris-Priester (HP) atmospheric density tables. Orbital state vectors, together with the spacecraft mass and area, are used as input to the Goddard Trajectory Determination System (GTDS). Propagations proceed in monthly segments, with the nominal atmospheric drag model scaled for each month according to the predicted monthly average value of F10.7. Calibration propagations are performed over a period of known orbital decay to obtain the effective ballistic coefficient. Progagations using plus or minus 2 sigma solar flux predictions are also generated to estimate the despersion in expected reentry dates. Definitive orbits are compared with these predictions as time expases. As updated vectors are received, these are also propagated to reentryto continually update the lifetime predictions.

Smith, E. A.↗

Planetary ephemerides approximation for radar astronomy

The planetary ephemerides approximation for radar astronomy is discussed, and, in particular, the effect of this approximation on the performance of the programmable local oscillator (PLO) used in Goldstone Solar System Radar is presented. Four different approaches are considered and it is shown that the Gram polynomials outperform the commonly used technique based on Chebyshev polynomials. These methods are used to analyze the mean square, the phase error, and the frequency tracking error in the presence of the worst case Doppler shift that one may encounter within the solar system. It is shown that in the worst case the phase error is under one degree and the frequency tracking error less than one hertz when the frequency to the PLO is updated every millisecond.

Sadr, R.↗

Occultations of stars by solar system objects. VIII - Occultations of catalog stars by asteroids, planets, Titan, and Triton in 1990 and 1991

Predictions are given for occultations of catalog stars by asteroids, planets, Titan, and Triton in 1990 and 1991. The predictions are based on a computerized comparison of the occulting bodies' ephemerides and nine major star catalogs. The search is complete for all numbered asteroids whose angular diameters exceed 0.08 arcsec during the search years. Preliminary ground tracks are shown for the more favorable occultations.

Wasserman, L. H.↗

SDO Onboard Ephemeris Generation

The Solar Dynamics Observatory (SDO) spacecraft is a sun-pointing, semi-autonomous satellite that will allow nearly continuous observations of the Sun with a continuous science data downlink. The science requirements for this mission necessitate very strict sun-pointing requirements, as well as continuous ground station connectivity through high gain antennas (HGAs). For SDO s onboard attitude control system to successfully point the satellite at the Sun and the HGAs at the ground stations with the desired accuracy, in addition to the need for accurate sensors it must have good onboard knowledge of the ephemerides of the Sun, the spacecraft, and the ground station. This paper describes the minimum force models necessary for onboard ephemeris generation in support of an attitude control system. The forces that were considered include the Sun s point mass, Moon s point mass, solar radiation pressure (SRP), and the Earth s gravity with varying degree and order of terms of the geopotential.

Berry, Kevin E.↗

Tracking and Data Relay Satellite (TDRS) tracking and orbit determination

Analysis results were derived using the Goddard Trajectory Determination System to determine the orbit of TDRS-East. A batch weighted least-squares algorithm is used to fit the Bilateration Ranging Transponder system tracking measurements. Six state parameters (position and velocity components) and the solar radiation pressure coefficient are estimated. The solutions are obtained by fitting the data over 34 hr arcs that overlap by 10 hr. Ephemerides are generated over the 34 hr arcs and then compared over the overlapping regions. The position differences indicate the consistency of the solutions and give a measure of their accuracy. The effect of the modeling of perturbative forces (solar radiation pressure, nonspherical geopotential field) on these results are studied. Error analysis is performed using the ORAN program to estimate the effect of force-model errors and measurement-related errors on the TDRS-East ephemeris.

Teles, J.↗

Ephemeris errors of GPS satellites

Numerical models are developed to examine the potential effects of solar radiation, the terrestrial gravitational field, and the estimated initial state of the Global Positioning System (GPS) satellites, along with the capability of current models to account for the effects on the ephemeris of the GPS constellation. Of particular interest is the accuracy of the satellite position predictions for applications in geodesy. The main characteristics of the GPS orbits are reviewed and linear combinations of possible errors for 3 day ephemerides are examined. It is shown that the effects of the forces on the GPS orbits will be dynamic, yet can be expressed simply enough to maintain positioning accuracy to 1 percent. The calculations can also take into consideration solar wind pressure on the solar panels.

Colombo, O. L.↗

JPL Development Ephemeris number 96

The fourth issue of JPL Planetary Ephemerides, designated JPL Development Ephemeris No. 96 (DE96), is described. This ephemeris replaces a previous issue which has become obsolete since its release in 1969. Improvements in this issue include more recent and more accurate observational data, new types of data, better processing of the data, and refined equations of motion which more accurately describe the actual physics of the solar system. The descriptions in this report include these new features as well as the new export version of the ephemeris. The tapes and requisite software will be distributed through the NASA Computer Software Management and Information Center (COSMIC) at the University of Georgia.

Standish, E. M., Jr.↗