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NASA NTRS2019

Analysis of Mercury Laser Altimeter Crossovers with Improved Mercury and MESSENGER Ephemerides

Based on previous applications of laser altimetry to planetary geodesy at GSFC [Mazarico et al. (2014),(2016)] and taking advantage of new accurate Mercury and MESSENGER orbits by [Genova et al. (2019)], we analyze altimetric crossovers from the MESSENGER (Mercury Surface, Space Environment, Geochemistry and Ranging) Laser Altimeter (MLA) to solve for orbital and geodetic parameters (e.g., rotation and orientation). We present our results based on a new Python software package recently developed at GSFC that can simulate and process altimetry data in a closed-loop. Realistic simulations of MLA data, including an appropriate range noise from the instrument and realistic terrain roughness, are performed in order to fully characterize the robustness of the solution. The simulation results are then applied to our analysis of the full dataset acquired by the MLA instrument.

Bertone, Stefano↗
NASA NTRS2020

The Ultimate Solar Azimuth Formula: A Note on the Formula that Renders Circumstantial Treatment Unnecessary and an Update Of the Ephemerides to that of The Astronomical Almanac for the Year 2019

A conceptually and mathematically concise formula for computing the solar azimuth angle has been used by a subgroup of scientists, but for lack of documentation and publication, it has not been well circulated. This note introduces this formula which is based on the idea of a unit vector, 𝑺, originating from the observer’s location and pointing toward the center of the Sun. The vector is completely determined by the coordinates of the subsolar point and of the observer. The x-and y-components of the vector determine the solar azimuth angle, and their use along with the function atan2, which is available in a number of programming/scripting languages, including Fortran and Python, renders any circumstantial treatment absolutely unnecessary. The z-component of the vector, at the same time, determines the solar zenith angle.

Taiping Zhang↗
NASA NTRSDate not supplied

Perturbations, TTVs & the (Un)reliability of Ephemerides of Kepler Planets

Fractional uncertainties quoted for orbital periods of the vast majority of planet candidates listed in recent Kepler catalogs are $<10^{-5}$, with values $\sim 10^{-6}$ (corresponding to 2 minutes per 4 years) being typical. These small uncertainties suggest ephemeris predictions for most Kepler planets are robust for decades to come. Tabulated periods list formal uncertainties in the mean times between midpoints of successive transits during the time interval in which transits were observed. However, transit timing variations (TTVs) produce errors in estimates of some planets’ orbital periods that need to be accounted for in certain dynamical investigations and ephemeris predictions. Periodic TTVs with timescales short compared to the interval of Kepler observations largely average out and do not produce significant errors in estimates of orbital periods. TTVs with timescales comparable to the interval of Kepler observations have been fit for dozens of Kepler planet candidates to estimate long-term average orbital periods (Holczer et al. 2016, ApJS 225, 9), and more detailed dynamical models have been used to estimate long-term average periods of a small number of well-studied planets. Most Kepler planets that show large TTVs are near mean-motion orbital resonances with other planets. The largest effect for planets moderately close to two-body resonances are due to rotation of the forced eccentricity vector by resonant perturbations; the timescale for this precession is typically short, so the variations tend to average out. Libration of planets locked in resonances typically occurs on timescales longer than the Kepler baseline, but few Kepler planets appear to be resonantly-locked. The more general but smaller (during the era of Kepler observations) effect is caused by secular precession of the planets' free eccentricities usually has a period much longer than the baseline of the Kepler observations, so it is not accounted for in estimates of mean periods or uncertainties. This precession causes a discrepancy between Kepler era mean orbital period and long-term mean orbital period can exist even for planets having TTVs that are too small to be observable during the epoch of Kepler observations.

Kepler↗
NASA NTRS2021

Refining the Transit Timing and Photometric Analysis of TRAPPIST-1: Masses, Radii, Densities, Dynamics, and Ephemerides

We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST, and K2 transit-time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host starand the planet densities. We find that all seven planets’ densities may be described with a single rocky mass–radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition but enhanced in light elements,such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses toa precision of 3%–5%, equivalent to a radial-velocity(RV)precision of 2.5 cm s−1, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small, the orbits are extremely coplanar, and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers, which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations and speculate on possible implications of the planet densities forthe formation, migration, and evolution of the planet system.

Eric Agol↗
NASA NTRS1995

Statistical Performance of TOPEX/POSEIDON Prime Mission Ground and On-Board Ephemerides and Consequences for the Extended Mission

TOPEX/POSEIDON is a joint American/French ocean topography experiment currently in the last year of its nominal mission and soon to enter a three year extended mission. To meet science requirements, the satellite must point the altimeter antenna at the ocean local nadir with good accuracy. This paper discusses the pointing accuracy of the Operational Orbit Ephemeris and its Fourier power series representation in the On-Board Computer. The consequences for the extended mission due to this performance are also discussed.

TOPEX/POSEIDON↗
NASA NTRS2017

Solar System Ephemerides, Pulsar Timing, Gravitational Waves, & Navigation

In-spiraling supermassive black holes should emit gravitational waves, which would produce characteristic distortions in the pulse time of arrival residuals from millisecond pulsars. There are multiple national and regional consortia that have constructed pulsar timing arrays by precise timing of different sets of millisecond pulsars. An essential aspect of precision timing is the transfer of the pulsar times of arrival to a (quasi-)inertial reference frame, conventionally taken to be the solar system barycenter. The solar system barycenter is determined from the knowledge of the planetary masses and orbits, which has been re ned over the course of the past 50 years by multiple spacecraft missions. Within the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), uncertainties on the solar system barycenter are emerging as an important element of the overall NANOGrav noise budget. We describe what is known about the solar system barycenter, touch upon how uncertainties in it affect gravitational wave studies with pulsar timing arrays, and consider future trends in spacecraft navigation.

Vallisneri, M.↗
NASA NTRS2000

Dynamical Reference Frame: Current Relevance and Future Prospects

Planetary and lunar ephemerides are no longer used for the determination of inertial space. Instead, the new fundamental reference frame, the International Celestial Reference Frame (ICRF), is inherently less susceptible to extraneous, non-inertial rotations than a dynamical reference frame determined by the ephemerides would be. Consequently, the ephemerides are now adjusted onto the ICRF, and they are fit to two modern, accurate observational data types: ranging (radar, lunar laser, spacecraft) and Very Long Baseline Interferometry (VLBI) (of spacecraft near planets). The uncertainties remaining in the inner planet ephemerides are on the order of 1 kilometer, both in relative positions between the bodies and in the orientation of the inner system as a whole. The predictive capabilities of the inner planet ephemerides are limited by the uncertainties in the masses of many asteroids. For this reason, future improvements to the ephemerides must await determinations of many asteroid masses. Until then, it will be necessary to constantly update the ephemerides with a continuous supply of observational data.

VLBI (VERY LONG BASELINE INTERFEROMETRY)↗
NASA NTRS1991

GPS orbit determination at the National Geodetic Survey

The National Geodetic Survey (NGS) independently generates precise ephemerides for all available Global Positioning System (GPS) satellites. Beginning in 1991, these ephemerides were produced from double-differenced phase observations solely from the Cooperative International GPS Network (CIGNET) tracking sites. The double-difference technique combines simultaneous observations of two satellites from two ground stations effectively eliminating satellite and ground receiver clock errors, and the Selective Availability (S/A) signal degradation currently in effect. CIGNET is a global GPS tracking network whose primary purpose is to provide data for orbit production. The CIGNET data are collected daily at NGS and are available to the public. Each ephemeris covers a single week and is available within one month after the data were taken. Verification is by baseline repeatability and direct comparison with other ephemerides. Typically, an ephemeris is accurate at a few parts in 10(exp 7). This corresponds to a 10 meter error in the reported satellite positions. NGS is actively investigating methods to improve the accuracy of its orbits, the ultimate goal being one part in 10(exp 8) or better. The ephemerides are generally available to the public through the Coast Guard GPS Information Center or directly from NGS through the Geodetic Information Service. An overview of the techniques and software used in orbit generation will be given, the current status of CIGNET will be described, and a summary of the ephemeris verification results will be presented.

M. S. Schenewerk↗
NASA NTRS1982

The Seasat altimeter mean sea surface model

Gridding techniques are used to combine an 18-day set of Seasat altimeter data and two precisely-computed Seasat ephemerides, in order to arrive at global contour maps of the mean sea surface topography. The altimeter data have an rms agreement of 111 cm with the SS3 mean sea surface computed by means of the PGS-S3 ephemerides, and of 70 cm with the SS4 mean surface derived from the PGS-S4 ephemerides. While comparisons with the GEM 10B 1 x 1 deg gravimetric geoid have yielded rms differences of 2.8 m, those with a global mean sea surface derived from GEOS 3 altimeter data show rms differences of 1.3 m and 1.1 m for the cases of the SS3 and SS4 surfaces, respectively. An SS4 mean sea surface topograph is featured among the study findings presented. Further improvements in the representation of mean sea surface topography are expected with the development of more accurate gravity models for orbit computation.

Marsh, J. G.↗
NASA NTRS1983

The JPL 'long ephemeris', DE102/LE51

A number of applications exist in astronomical research for planetary and lunar ephemerides covering an extended length of time. This paper discusses such a set of ephemerides, DE102/LE51, produced at JPL, covering the time 1411 B.C. to 3001 A.D. The ephemerides are dynamically self-consistent, in that the equations of motion were integrated simultaneously. They also represent the most accurately known positions covering such a time span. They have already been used by a number of different users in a variety of different applications.

Standish, E. M., Jr.↗
NASA NTRS1998

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.↗
NASA NTRS2017

Precision Asteroid Astrometry

Among the methods used to guide spacecraft to their destinations, Optical Navigation (OpNav) remains an effective option. OpNav makes use of star fields and small body ephemerides to precisely locate spacecraft. To facilitate accurate OpNav, the small body ephemerides must be constantly updated; asteroid orbits accumulate errors each year of a few milliarcseconds. Through extended exposures, taken with strategic offsets, a least-squares solution can be found that determines updated ephemeris data. This updated data can also be used by occultation astronomers to gain further information about the small bodies, including their size and shape. Using the 24-inch telescope at the Caltech Table Mountain Observatory (TMO), we capture two or more 180 second exposures of each target. These images, combined with a file for the predicted background star field and two reference files, are then processed through a series of scripts and programs. Starting with a prediction file and two to five exposures of the asteroid, the data is processed. This original data is about 32MB per observation. Once the data are reduced to only Right Ascension and Declination for each target, the data are ready for delivery. This consists of text only, and for each target takes about 80 bytes; this resulting data reduction is about five orders of magnitude. This method produces observed positions that are refined by about 12 milliarcseconds, a refinement that is accomplished almost nowhere else. The occultation observations that are facilitated by the ephemerides being refined also produce results that are not possible in any other way from ground-based observations.

Dial, Jason↗
NASA NTRS1972

The BMW analytic aerodynamic drag method for the Vinti satellite theory

In order to retain separability in the Vinti theory of earth satellite motion when a non conservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which reproduces tabular values of static model atmospheric densities at all altitudes to within ninety-eight percent and simultaneously reduces the variational equations to indefinite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program. Results of the BMW (Bonavito, Mistretta, Watson) theory for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by the BMW theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time.

Watson, J. S.↗
NASA NTRS1981

Numerical integration of the satellites of the outer planets

The formulation of a numerical integration program, used to construct ephemerides for satellites of the outer planets, is described. The equations of motion are derived, including (1) n massive integrated satellites, (2) m massive perturbing planets, (3) J2, J4 oblateness coefficients of the primary and each satellite, and (4) a barycentric coordinate system. Variational equations are also found: (1) 6n initial states and n masses of the integrated satellites, (2) J2, J4 of the primary planet, (3) the mass of the system, and (4) right ascension and declination of the pole. The formulation was used to construct the satellite ephemerides of Saturn for the Voyager mission.

Peters, C. F.↗
NASA NTRS1982

A comparative study of atmospheric density models in the context of definitive and predictive earth satellite orbit determination

The results of a comparative orbit determination study of four global atmospheric density models (modified Harris-Priester, Jacchia-Roberts, Mass Spectrometer/Incoherent Scatter (MSIS), and Simple Exponential Model (SEM)) are presented. Utilizing these models, definitive orbit determination consistency and accuracy are evaluated using the maximum position differences that occur during 6-hour overlap periods between ephemerides generated from 30-hour data arcs. Propagated ephemerides are compared with definitive orbit solutions to evaluate predictive accuracy. The results indicate that, for satellites above 300 kilometers, all four atmospheric density models produce comparable orbit determination accuracies when an atmospheric drag scaling factor and the satellite state vector are estimated in the orbit determination process.

Shanklin, R. E., Jr.↗