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1.
The comparisons of the Earth gravity field models by the order of their harmonic coefficients, performed with the basic lumped coefficients (Planet. Space Sci.29, 653, 1981, Paper I) are here extended to cover all harmonic coefficients (both odd and even degree). The lumped coefficients (the “e-terms” and “longitudinal” terms), corresponding to 18 Earth models, are compared mutually (Figs. 2–15). The large differences, observed for various models and orders, are of particular interest: they are gathered into Table 1. The result of Paper I was a little pessimistic. The same is true here: various inhomogeneities, sometimes very large, in the accuracy of the harmonic coefficients must exist—even for low orders. Most of our comments and objections, however, relate to the older Earth models, which have only a historical value now. Our comparisons are only relative ones; an actual test of the accuracy of the models (their calibration) is possible via data with independent status (Kloko?ník, 1982, 1983).  相似文献   

2.
The method of collocations (LSC) has been compared with traditional least-squares adjustments (LSA) for determining the values of the individual harmonic coefficients in the expansion for the Earth gravitational potential from the lumped geopotential coefficients of order 30, accumulated from previous analyses of satellite orbits near the 15th-order resonance. The computations are based on the data from King-Hele and Walker (1982b), where the 30th-order harmonic coefficients were determined from the lumped values by means of the usual least-squares method. We take into account the correlation coefficients among the lumped coefficients; we do not omit higher degree harmonics but on the contrary, they are statistically estimated as the signal in LSC. Four groups of runs have been performed: from LSA (similar to that in King- Hele and Walker, 1982b) to as general LSC as possible. The resulting harmonic coefficients are compared mutually, with the resonant solution by King-Hele and Walker (1982b), with our older trials (Kostelecký and Kloko?ník, 1979) and with recent comprehensive Earth models (GEM 10 B(C), ‘Rapp 77’ and GRIM 3). The comparison by harmonic coefficients is in Tables 4 and 5 and on Fig. 1, that via lumped coefficients for arbitrary inclination is in Figs. 2–7. The first few pairs of the 30th-order harmonic coefficients, at least C?30, 30and S?30, 30, are now well determined. King-Hele and Walker (1982b) used better data than we had in our previous solution (Kostelecký and Kloko?ník, 1979), so that the LSC does not play so important a role in the determination as played in the older solution. Although our evaluations serve as an example where more complicated LSC is not necessary, LSC ought to be preferred in a situation where LSA does not achieve optimal utilization of the data base.  相似文献   

3.
The Earth's gravitational potential is usually expressed as an infinite series of tesseral harmonics, and it is possible to evaluate “lumped harmonics” of a particular order m by analyses of resonant satellite orbits—orbits with tracks over the Earth that repeat after m revolutions. In this paper we review results on 30th-order harmonics from analyses of 15th-order resonance, and results on 29th- and 31st-order harmonics from 29:2 and 31:2 resonance.The values available for 30th-order lumped harmonics of even degree are numerous enough to allow a solution for individual coefficients of degree up to 40. The best-determined coefficients are those of degree 30, namely
109C30,30= ?1.2±1.1 109S30,30= 9.6±1.3
The standard deviations here are equivalent to 1 cm in geoid height.For the 29th- and 31st-order harmonics, and for the 30th-order harmonics of odd degree, there are not enough values to determine individual coefficients, but the lumped values from particular satellites can be used for “resonance testing” of gravity field models, particularly the Goddard Earth Model 10B (up to degree 36) and 10C (for degree greater than 36). The results of applying these tests are mixed. GEM 10B/C emerges well for order 30, with s.d. about 3×10?9; for order 31, the GEM 10B values are probably good but the GEM 10C values are probably not; for order 29, the test is indecisive.  相似文献   

4.
Cosmos 395 rocket (1971-13B) is moving in a near-circular orbit inclined at 74° to the equator. Its average height, near 540 km after launch in February 1971, slowly decreased under the action of air drag and on 24 March 1972 it experienced exact 15th-order resonance, with the successive equator crossings 24° apart in longitude. Its orbit has been determined at 21 epochs between September 1971 and September 1972 using 1100 observations, including 55 from the Malvern Hewitt camera: the mean S.D. in inclination is 0.001° and in eccentricity 0.00001.The variations in inclination i, eccentricity e, right ascension of the node Ω, and argument of perigee ω, near 15th-order resonance are analysed to determine values of lumped 15th-order harmonic coefficients in the geopotential. The inclination yields equations accurate to 4 per cent for coefficients of order 15 and degree 15,17,19..., which are in excellent agreement with those from Cosmos 387 (1970-111A) in an orbit of similar inclination but different resonant longitude. Analysis of the variations in e gives two pairs of equations for the coefficients of order 15 and degree 16, 18..., which are used to obtain tentative values of the (16,15) coefficients. For the first time the resonant variation of other elements (Ω and ω) has also been analysed with partial success.  相似文献   

5.
The analysis of variations in satellite orbits when they pass through 15th-order resonance (15 revolutions per day) yields values of lumped geopotential harmonics of order 15, and sometimes of order 30. The 15th-order lumped harmonics obtained from 24 such analyses over a wide range of orbital inclinations are used here to determine individual harmonic coefficients of order 15 and degree 15,16,…35; and the 30th-order lumped harmonics (from eight of the analyses) are used to evaluate individual coefficients of order 30 and degree 30,32,…40. The new values should be more accurate than any previously obtained. The accuracy of the 15th-order coefficients of degree 15, 16,…23 is equivalent to 1 cm in geoid height, while the 30th-order coefficients of degree 30, 32 and 34 are determined with an accuracy which is equivalent to better than 2 cm in geoid height. The results are used to assess the accuracy of the Goddard Earth Model 10B.  相似文献   

6.
The satellite 1971-10B passed through exact 15th-order resonance on 30 March 1981 and orbital parameters have been determined at 52 epochs from some 3500 observations using the RAE orbit refinement program, PROP, between September 1980 and October 1981. The variations in inclination and eccentricity during this time have been analysed, and six lumped 15th-order harmonic coefficients and two 30th-order coefficients have been evaluated. The 15th-order coefficients are the best yet obtained for an orbital inclination near 65°; and previously there were no 30th-order coefficients available at this inclination. The lumped coefficients have been used to test the Goddard Earth Model GEM 10B: there is good agreement for seven of the eight coefficients.  相似文献   

7.
C. Möstl  J. A. Davies 《Solar physics》2013,285(1-2):411-423
The NASA Solar TErrestrial RElations Observatory (STEREO) mission offered the possibility to forecast the arrival times, speeds, and directions of solar transients from outside the Sun–Earth line. In particular, we are interested in predicting potentially geoeffective interplanetary coronal mass ejections (ICMEs) from observations of density structures at large observation angles from the Sun (with the STEREO Heliospheric Imager instrument). We contribute to this endeavor by deriving analytical formulas concerning a geometric correction for the ICME speed and arrival time for the technique introduced by Davies et al. (Astrophys. J., 2012, in press), called self-similar expansion fitting (SSEF). This model assumes that a circle propagates outward, along a plane specified by a position angle (e.g., the ecliptic), with constant angular half-width (λ). This is an extension to earlier, more simple models: fixed-Φ fitting (λ=0°) and harmonic mean fitting (λ=90°). In contrast to previous models, this approach has the advantage of allowing one to assess clearly if a particular location in the heliosphere, such as a planet or spacecraft, might be expected to be hit by the ICME front. Our correction formulas are especially significant for glancing hits, where small differences in the direction greatly influence the expected speeds (up to 100?–?200 km?s?1) and arrival times (up to two days later than the apex). For very wide ICMEs (2λ>120°), the geometric correction becomes very similar to the one derived by Möstl et al. (Astrophys. J. 741, 34, 2011) for the harmonic mean model. These analytic expressions can also be used for empirical or analytical models to predict the 1 AU arrival time of an ICME by correcting for effects of hits by the flank rather than the apex, if the width and direction of the ICME in a plane are known and a circular geometry of the ICME front is assumed.  相似文献   

8.
The orbit of 1970-47B passed very slowly through 14th-order resonance, and the changes in orbital inclination and eccentricity have been analysed over a 4-year period, from January 1977 to January 1981, using 208 U.S. Navy orbits. The analysis has yielded values for three pairs of lumped harmonic coefficients of 14th order, which have accuracies equivalent to 0.4, 1.5 and 2.0 cm in geoid height. Three pairs of values of 28th-order lumped harmonic coefficients were also obtained, and the best of these has a standard deviation (S.D.) corresponding to an accuracy of 0.7 cm in geoid height. The lumped harmonic coefficients have been compared with the corresponding values from the latest geopotential models, and agreement is satisfactory.  相似文献   

9.
Bistatic radar observations of Mars' north polar region during 1977–1978 showed surface rms slope σβ ranging from 1 to 6°; these values apply to horizontal scales of 1–100 m. Values of roughness tend to decrease with increasing latitude (especially over 65–80°N), but there are many exceptions. The smoothest surfaces (σβ≤1°) appear to be inclusions within generally rougher (σβ～3°) terrain, rather than broad expanses of very smooth material. The permanent north polar cap is relatively uniform with 2.5?σβ?3.0°. Considerable structure has been found in echo spectra, indicating a heterogeneous and perhaps anisotropic scattering surface. Echo spectra obtained from the same region, but several months apart (1°<LS<62°), show no significant differences in inferred roughness. Estimates of reflectivity and dielectric constant are systematically low in the polar region. This may indicate that surface material north of 65°N is less dense than that near the equator, but more study of these data is needed. Estimates of surface roughness and dielectric constant in the equatorial region are consistent with results from Earth-based measurements to the accuracy of our analysis.  相似文献   

10.
Further reduction of Doppler tracking data from Mariner 9 confirms our earlier conclusion that the gravity field of Mars is considerably rougher than the fields of either the Earth or the Moon. The largest positive gravity anomaly uncovered is in the Tharsis region which is also topographically high and geologically unusual. The best determined coefficients of the harmonic expansion of the gravitational potential are: J2 = (1.96 ± 10.01) × 10?3 ; C22 = ?(5.1 ± 0.2) × 10?5; and S22 = (3.4 ± 0.2) × 10?5. The other coefficients have not been well determined on an individual basis, but the ensemble yields a useful model for the gravity field for all longitudes in the vicinity of 23° South latitude which corresponds to the periapse position for the orbiter.The value obtained for the inverse mass of Mars (3 098 720 ± 70 M⊙?1) is in good agreement with prior determinations from Mariner flyby trajectories. The direction found for the rotational pole of Mars, referred to the mean equinox and equator of 1950.0, is characterized by α = 317°.3 ± 0°.2, δ = 52°.7 ± 0°.2. This result is in excellent agreement with Sinclair's recent value, determined from earth-based observations of Mars' satellites, but differs by about 0°.5 from the previously accepted value. Other important physical constants that have either been refined or confirmed by the Mariner 9 data include: (i) the dynamical flattening, f = (5.24 ± 0.02) × 10?3; (ii) the maximum principal moment of inertia, C = (0.375 ± 0.006) MR2; and (iii) the period of precession of Mars' pole, P ? (1.73 ± 0.03) × 105 yr, corresponding to a rate of 7.4 sec of arc per yr.  相似文献   

11.
The orbit of Cosmos 837 rocket (1976-62E) has been determined at 36 epochs between January and September 1978, using the RAE orbit refinement program PROP 6 with about 3000 observations. The inclination was 62.7° and the eccentricity 0.039. The orbital accuracy achieved was between 30m and 150m, both radial and crosstrack. The orbit was near 29:2 resonance in 1978 (exact resonance occurred on 14 May) and the values of orbital inclination obtained have been analysed to derive lumped 29th-order geopotential harmonic coefficients, namely:
109C0,229 = ? 10 ± 15
and
109S0,229 = ?76 ± 12
. These will be used in future, when enough results at different inclinations have accumulated, to determine individual coefficients of order 29. The values of lumped harmonics obtained from analysis of the values of eccentricity were not well defined, because of the high correlations between them and the errors in removing the very large perturbation (31 km) due to odd zonal harmonics.  相似文献   

12.
M. Noland  J. Veverka 《Icarus》1977,30(1):212-223
At least three large areas on the surface of Phobos are covered by a dark material of complex texture which scatters light according to the Hapke-Irvine Law. The average 20° to 80° intrinsic and disc-integrated phase coefficients of this material are βi = 0.020 ± 0.001 mag/deg and β = 0.033 mag/deg, respectively. These values are slightly greater than the values found for Deimos in Paper II (preceding article). On the largest scale the surface of Phobos is rougher than the surface of Deimos, perhaps accounting for the slightly greater phase coefficients. Contrary to the situation on Deimos, no definite regions of intrinsically brighter material are apparent on Phobos. This difference could account for the slightly lower average reflectance of Phobos relative to Deimos. No evidence for large exposures of solid rock has been found in the three areas studied.  相似文献   

13.
Samos 2, 1961 α 1, launched on 31 January 1961, was the first satellite to enter a sun-synchronous orbit at an inclination of 97.4°. The initial perigee and apogee heights were 474 km and 557 km respectively, the initial period was 94.97 min and the satellite decayed on 21 October 1973 after more than 12 years in orbit.Samos 2 passed through the condition of 31 : 2 resonance in June 1971 and orbital parameters have been determined at 22 epochs from 1674 observations using the RAE orbit refinement program, PROP, between mid-April and Mid-September 1971. The variations of inclination and eccentricity during this time have been analysed and values for six lumped 31st-order harmonic coefficients in the geopotential have been obtained. These have been compared with those derived from the individual coefficients, of order 31 and appropriate degrees, from the most recent Goddard Earth Model, GEM 10C.The decrease in inclination between launch and 1971 has been examined: it is found to be caused mainly by a near-resonant solar gravitational perturbation.  相似文献   

14.
The orbit of China 2 rocket, 1971-18B, has been determined at 114 epochs throughout its 5-yr life, using the RAE orbit refinement program PROP 6, with more than 7000 radar and optical observations from 83 stations.The rocket passed slowly enough through the resonances 14:1, 29:2, 15:1 and 31:2 to allow lumped geopotential harmonic coefficients to be calculated for each resonance, by least-squares fittings of theoretical curves to the perturbation-free values of inclination and eccentricity. These lumped coefficients can be combined with values from satellites at other inclinations, to obtain individual harmonic coefficients.The rotation rate of the upper atmosphere, at heights near 300 km, was estimated from the decrease in orbital inclination, and values of 1.15, 1.05, 1.10 and 1.05 rev/day were obtained between April 1971 and January 1976. From the variation in perigee height, 25 values of density scale height were calculated, from April 1971 to decay. Comparison with values from the COSPAR International Reference Atmosphere 1972 shows good agreement between April 1971 and October 1975, but the observational values are 10% lower, on average, than CIRA thereafter.A further 1400 observations, made during the final 15 days before decay, were used to determine 15 daily orbits. Analysis of these orbits reveals a very strong West-to-East wind, of 240 ± 40 ms?1, at a mean height of 195 km under winter evening conditions, and gives daily values of density scale height in the last 7 days before decay.  相似文献   

15.
The effect of the Earth??s compression on the physical libration of the Moon is studied using a new vector method. The moment of gravitational forces exerted on the Moon by the oblate Earth is derived considering second order harmonics. The terms in the expression for this moment are arranged according to their order of magnitude. The contribution due to a spherically symmetric Earth proves to be greater by a factor of 1.34 × 106 than a typical term allowing for the oblateness. A linearized Euler system of equations to describe the Moon??s rotation with allowance for external gravitational forces is given. A full solution of the differential equation describing the Moon??s libration in longitude is derived. This solution includes both arbitrary and forced oscillation harmonics that we studied earlier (perturbations due to a spherically symmetric Earth and the Sun) and new harmonics due to the Earth??s compression. We posed and solved the problem of spinorbital motion considering the orientation of the Earth??s rotation axis with regard to the axes of inertia of the Moon when it is at a random point in its orbit. The rotation axes of the Earth and the Moon are shown to become coplanar with each other when the orbiting Moon has an ecliptic longitude of L ? = 90° or L ? = 270°. The famous Cassini??s laws describing the motion of the Moon are supplemented by the rule for coplanarity when proper rotations in the Earth-Moon system are taken into account. When we consider the effect of the Earth??s compression on the Moon??s libration in longitude, a harmonic with an amplitude of 0.03?? and period of T 8 = 9.300 Julian years appears. This amplitude exceeds the most noticeable harmonic due to the Sun by a factor of nearly 2.7. The effect of the Earth??s compression on the variation in spin angular velocity of the Moon proves to be negligible.  相似文献   

16.
The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars’ tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J2. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10−4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10−4 in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration.  相似文献   

17.
M. Noland  J. Veverka 《Icarus》1976,28(3):405-414
We have used the integrated brightnesses from Mariner 9 high-resolution images to determine the large phase angle (20° to 80°) phase curves of Phobos and Deimos. The derived phase coefficients are β = 0.032 ± 0.001 mag/deg for Phobos and β = 0.030 ± 0.001 mag/deg for Deimos, while the corresponding phase integrals are qPhobos = 0.52 and qDeimos = 0.57. The predicted intrinsic phase coefficients of the surface material are βi = 0.019 mag/deg and βi = 0.017 mag/deg for Phobos and Deimos, respectively. The phase curves, phase coefficients and phase integrals are typical of objects whose surface layers are dark and intricate in texture, and are consistent with the presence of a regolith on both satellites. The relative reflectance of Deimos to Phobos is 1.15±0.10. The presence of several bright patches on Deimos could account for this slight difference in average reflectance.  相似文献   

18.
Results of a harmonic analysis of the arrival directions for primary cosmic-ray particles with energies E 0 ? 1017 eV and zenith angles θ ? 45° recorded on the Yakutsk array over 29 years of its continuous operation (1983–2012) are presented. These events are shown to have different global anisotropies in different time intervals: the phase of the first harmonic φ 1 = 119° ± 18° and its amplitude A 1 = 0.030 ± 0.014 in the 1983–1994 samples changed into φ 1 = 284° ± 13° and A 1 = 0.033 ± 0.010 in 1998–2010. All of this could be caused by a considerably increased flux of heavy nuclei from the exit of the Galaxy’s local arm after 1996.  相似文献   

19.
UBV observations of asteroid 433 Eros were conducted on 17 nights during the winter of 1974/75. The peak-to-peak amplitude of the lightcurve varied from about 0.3 mag to nearly 1.4mmag. The absolute V mag at maximum light, extrapolated to zero phase, is 10.85. Phase coefficients of 0.0233 mag/degree, 0.0009 mag/degree and 0.0004 mag/degree were derived for V, B-V, and U-B, respectively. The zero-phase color of Eros (B?V = 0.88, U?B = 0.50) is representative of an S (silicaceous) compositional type asteroid. The color does not vary with rotation. The photometric behavior of Eros can be modeled by a cylinder with rounded ends having an axial ratio of about 2.3:1. The asteroid is rotating about a short axis with the north pole at λ0 = 15° and β0 = 9°.  相似文献   

20.
We performed for the first time stereoscopic triangulation of coronal loops in active regions over the entire range of spacecraft separation angles (?? sep??6°,43°,89°,127°,and 170°). The accuracy of stereoscopic correlation depends mostly on the viewing angle with respect to the solar surface for each spacecraft, which affects the stereoscopic correspondence identification of loops in image pairs. From a simple theoretical model we predict an optimum range of ?? sep??22°??C?125°, which is also experimentally confirmed. The best accuracy is generally obtained when an active region passes the central meridian (viewed from Earth), which yields a symmetric view for both STEREO spacecraft and causes minimum horizontal foreshortening. For the extended angular range of ?? sep??6°??C?127° we find a mean 3D misalignment angle of ?? PF??21°??C?39° of stereoscopically triangulated loops with magnetic potential-field models, and ?? FFF??15°??C?21° for a force-free field model, which is partly caused by stereoscopic uncertainties ?? SE??9°. We predict optimum conditions for solar stereoscopy during the time intervals of 2012??C?2014, 2016??C?2017, and 2021??C?2023.  相似文献   

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