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An exact method for the nonzero altitude transformation from geocentric to geodetic coordinates is derived. The method is mathematically general and should serve as a primary standard.
Formulas for the general-altitude (height above the ellipsoid) transformation from geocentric to geodetic coordinates and vice versa are derived. The set of four formulas is expressed in each of two useful forms: series expansions in powers of the earth's flattening and series expansions in powers of the earth's eccentricity. The error incurred in these expansions is of the order of one part in 30 million.-
The orientation of the reference frame of radio source catalogs relative to that of planetary ephemerides is uncertain by 30 mas (150 nrad). At this level of uncertainty this orientation offset, or 'frame tie', can be a major systematic error source for interplanetary spacecraft orbit determination. This work presents a method of determining the radio-planetary frame tie from a comparison of Very Long Baseline Interferometry (VLBI) and Lunar Laser Ranging (LLR) station coordinate and earth orientation parameter estimates. Preliminary results are presented which indicate that accuracies of 5 mas or better may be achieved with this method. An important by-product of this method of frame tie determination is a set of Deep Space Network (DSN) station locations with 10 cm per component accuracy. This station set is in a geocentric coordinate system with known orientation relative to the radio and planetary frames.
Geographic data, such as seismic event locations, station locations, etc., are generally given in geographic latitude Φ ’, longitude θ , and depth below sea level, ζ , using the WGS84 ellipsoid as a reference. In software systems that use this type of geographic data, it is necessary to manipulate the data mathematically in order to perform such tasks as finding the angular distance or azimuth from one point to another, to find an array of points along a great circle, to rotate a point about a pole of rotation, to move a point some angular distance in a specified direction, to find the intersections of two great circles or to find the intersections of a great circle and a small circle. In this paper, equations are presented that convert geographic locations first to geocentric coordinates and then to Earth-centered Cartesian coordinates where many mathematical manipulations can be performed conveniently and efficiently.
Geocentric coordinate determinations for station locations using optical observations of Pageos balloon satellites
Geodetic information is presented for NASA tracking stations and observation stations in the NASA geodetic satellites program. A geodetic data sheet is provided for each station, giving the position of the station and describing briefly how it was established. Geodetic positions and geocentric coordinates of these stations are tabulated on local or major geodetic datums, and on selected world geodetic systems when available information permits.
The directory documents geodetic information for NASA tracking stations and observation stations in the NASA Geodetic Satellites Program, including stations participating in the National Geodetic Satellite Program. Station positions of these facilities are given on local or preferred major datums, and on the Modified Mercury Datum 1968. A geodetic data sheet is provided for each station, giving the position of the station and describing briefly how it was established. Geodetic positions and geocentric coordinates of these stations are tabulated on local or major geodetic datums, and on selected world geodetic systems when available information permits.
Geodetic information for NASA tracking stations and for observation stations cooperating in NASA geodetic satellite programs is presented. A Geodetic Data Sheet is provided for each station, giving the position of the station and describing briefly how it was established. Geodetic positions and geocentric coordinates of these stations are tabulated on local or major geodetic datums and on selected world geodetic systems. The principal tracking facilities used by NASA, including the Spaceflight Tracking and Data Network, the Deep Space Network, and several large radio telescopes are discussed. Positions of these facilities are tabulated on their local or national datums, the Mercury Spheroid 1960, the Modified Mercury Datum 1968, and the Spaceflight Tracking and Data Network System. Observation stations in the NASA Geodetic Satellites Program are included along with stations participating in the National Geodetic Satellite Program. Positions of these facilities are given on local or preferred major datums, and on the Modified Mercury Datum 1968.
The extended sequential filter has been applied to the problem of dynamically determining the geocentric coordinates of two laser satellite tracking stations. This filter provides significant advantages over the classical batch methods through (1) fewer iterations required for convergence, (2) wider radius of convergence, and (3) availability of the parameter estimate evolution. Processing the data sequentially readily identifies the data arcs required to minimize the effects of geopotential model errors. By means of the Smithsonian standard earth 2 and the Goddard earth model 1 geopotentials to reduce laser range observations of the Beacon Explorer-C satellite, it is demonstrated that a two-pass arc is optimal for estimating the height of one station and all coordinates of the second station while minimizing the effect of geopotential model error. These two-pass estimates are in good agreement with other determinations that utilize considerably more data as well as different satellites.
The paper obtains a global representation of the geopotential in spherical harmonics with sufficient detail to determine both a satellite trajectory and the geocentric coordinates of all the tracking stations in a well-defined coordinate system to an accuracy of a few centimeters or better. Laser tracking data on nine satellites are combined with terrestrial gravimetry to obtain a spherical-harmonics representation of the geopotential complete through degree and order 24.
The lunar laser range data taken at McDonald Observatory between Aug. 1969 and May 1980 has been analyzed. The simple rms residual for the 2954 ranges is 31 cm. Results of the analysis include GM(earth) = 398600.45 cu km/sec sq within 0.02 cu km/sec sq and a secular acceleration of the lunar orbital mean longitude of -23.8 arcsec/sq century within 1.5 arcsec, which yields a Q of 12.3 at semidiurnal frequencies. The lunar harmonic C30 is -8.7/1,000,000 within 0.000001 and the lunar rotational dissipation of 0.0047 within 0.0005 day. Also resulting from the solution are geocentric coordinates of McDonald accurate to 30 cm, including the first value for the longitude with the new IAU constants and a dynamical equinox.
This paper contains a collection of computational algorithms for determining geocentric ephemerides of Earth satellites, useful for both mission planning and data reduction applications. Special emphasis is placed on the computation of sidereal time, and on the determination of the geocentric coordinate of the center of the Sun, all to the accuracy found in the Astronomical Almanac. The report is completely self-contained in that no requirement is placed on any external source of information, and hence, these methods are ideal for computer application.
Prelaunch and postlaunch calibration plans for the APAFO magnetometer experiment are presented. A study of tradeoffs between boom length and spacecraft field is described; the results are summarized. The prelaunch plan includes: calibration of the Vector Fluxgate Magnetometer (VFM), Star Sensors, and Scalar Helium Magnetometer (SHM); optical bench integration; and acquisition of basic spacecraft field data. Postlaunch calibration has two phases. In phase one, SHM data are used to calibrate the VFM, total vector magnetic field data are used to calibrate a physical model of the spacecraft field, and both calibrations are refined by iteration. In phase two, corrected vector data are transformed into geocentric coordinates, previously undetected spacecraft fields are isolated, and initial geomagnetic field models are computed. Provided the SHM is accurate to the required 1.0 nT and can be used to calibrate the VFM to the required 3.0- nT accuracy, the tradeoff study indicates that a 12 m boom and a spacecraft field model uncertainty of 5 percent together allow the 1.0 nT spacecraft field error requirement to be met.
Data collected from a worldwide 1992 experiment have been processed at JPL to determine precise orbits for the satellites of the Global Positioning System (GPS). A filtering technique has been tested to improve modeling of solar-radiation pressure force parameters for GPS satellites. The new approach improves orbit quality for eclipsing satellites by a factor of two, with typical results in the 25- to 50-cm range. The resultant GPS-based estimates for geocentric coordinates of the tracking sites, which include the three DSN sites, are accurate to 2 to 8 cm, roughly equivalent to 3 to 10 nrad of angular measure.
The REST simulator includes many parameters: a) Inertial <-> Fix to Earth reference system; b) Geodetic <-> Geocentric coordinates; c) Rotational velocity of the Atmosphere; d) Effect of the rotation of the Earth; e) Bulge effect of the Earth; f) Spherical harmonic expansion for the Earth s gravitational potential, J2 (zonal); g) Heat flux, temperature in the wall; h) Drag coefficient for different regimes; i) Flow regime status; j) Density model NRLMSISE-00; k) Wind model HWM-93; l) G2S atmospheric model with the latest meteorological conditions and m) Landing area (Monte Carlo Simulations)
The processing of the GPS observations of the site survey at Sheshan 25-m radio telescope in August 2008 is reported. Because each session in this survey is only about six hours, not allowing the subdaily high frequency variations in the station coordinates to be reasonably smoothed, and because there are serious cycle slips in the observations and a large volume of data would be rejected during the software automatic adjustment of slips, the ordinary solution settings of GAMIT needed to be adjusted by loosening the constraints in the a priori coordinates to 10 m, adopting the "quick" mode in the solution iteration, and combining Cview manual operation with GAMIT automatic fixing of cycle slips. The resulting coordinates of the local control polygon in ITRF2005 are then compared with conventional geodetic results. Due to large rotations and translations in the two sets of coordinates (geocentric versus quasi-topocentric), the seven transformation parameters cannot be solved for directly. With various trial solutions it is shown that with a partial pre-removal of the large parameters, high precision transformation parameters can be obtained with post-fit residuals at the millimeter level. This analysis is necessary to prepare the follow-on site and transformation survey of the VLBI and SLR telescopes at Sheshan
The magnetopause electron layer in the distant magnetotail is an annular region encircling the magnetopause in which bursts of tailward-streaming energetic (E 200 keV) electrons are almost continuously present. Sunward-streaming electron bursts with time scales and energy spectral indices similar to those of layer bursts are sometimes observed in interplanetary space upstream of the Earth. Evidence is presented to show that the layer bursts and the interplanetary bursts have a common source. With the aid of a new coordinate system, geocentric interplanetary medium coordinates, appropriate for describing the access of energetic charged particles in the inner magnetosheath to a spacecraft located in interplanetary space, it is shown that the interplanetary bursts occur predominantly on the sunward extension of the field lines associated with the magnetopause electron layer.
A graphical procedure is provided for performing coordinate transformations between the geocentric-solar-equatorial, geocentric-solar-ecliptic and geocentric-solar-magnetospheric coordinate systems. The procedure is designed to facilitate intercomparison of previous studies of interactions between interplanetary and geomagnetic fields that made use of these coordinate systems. The interaction in the geocentric-solar-magnetosphere system has been shown to give the most consistent results.