Perturbations of satellite orbits by tesseral harmonics in the earth's gravitational potential

1963 ◽  
Vol 11 (7) ◽  
pp. 797-815 ◽  
Author(s):  
G.E. Cook
Keyword(s):  
Gravitational Potential ◽  
Satellite Orbits ◽  
Tesseral Harmonics

A discussion on orbital analysis - Odd zonal harmonics in the geopotential, determined from fourteen well-distributed satellite orbits

1967 ◽  
Vol 262 (1124) ◽  
pp. 144-147
Keyword(s):  
Gravitational Potential ◽  
Major Axis ◽  
Detailed Account ◽  
Satellite Orbits ◽  
Orbital Eccentricity ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
Zonal Harmonics ◽  
Distributed Satellite ◽  
Orbital Analysis

Coefficients of the odd zonal harmonics in the Earth’s gravitational potential are evaluated by analysing the oscillations in orbital eccentricity of fourteen satellites chosen to give the widest and most uniform possible distribution in orbital inclination and semi-major axis. The best representations of the odd zonal harmonics are found to be in terms of seven coefficients (J5, */15)) or ten coefficients (J 3,J 5, J 21) and values for these coefficients are given. A detailed account of this work is being published in Planetary and Space Science.

Evaluation of odd zonal harmonics in the Earth’s gravitational potential

1994 ◽  
Vol 446 (1926) ◽  
pp. 149-168
Keyword(s):  
Gravitational Potential ◽  
Satellite Orbits ◽  
Zonal Harmonics

Coefficients of the odd zonal harmonics in the Earth’s gravitational potential J 3 , J 5 , J 7 , . . . , have been evaluated by analysing the variations in eccentricity of 29 satellite orbits from near-equatorial to polar. The evaluation includes data recently derived from the analysis of two extremely sensitive orbits, those of Cos­mos 373 and Cosmos 185 rocket at inclinations to the Equator of 62.9° and 64.1°, respectively. The amplitude of the oscillation in perigee height arising from the influence of the odd zonal harmonics on each of these satellites is extremely large, amounting to approximately 60 km for Cosmos 373 and 30 km for Cosmos 185 rocket . New 8-, 14- and 18-coefficient sets have been obtained with standard de­viations up to 50% lower than before. The geoid profile and predicted amplitude of the oscillation in eccentricity are compared with those given by the two most recent models from other sources.

Perturbations of repeating groundtrack satellites by tesseral harmonics in the gravitational potential.

AIAA Journal ◽  
1966 ◽  
Vol 4 (7) ◽  
pp. 1281-1286 ◽  
Author(s):  
M. P. FRANCIS ◽  
G. S. GEDEON ◽  
B. C. DOUGLAS
Keyword(s):  
Gravitational Potential ◽  
Tesseral Harmonics

Evaluation of 14th-order harmonics in the geopotential from 18 resonant satellite orbits

1993 ◽  
Vol 442 (1915) ◽  
pp. 343-360
Keyword(s):  
Earth Model ◽  
Satellite Orbits ◽  
Earth’S Gravity Field ◽  
European Model ◽  
Geopotential Models ◽  
Lower Standard ◽  
Independent Test ◽  
Odd Degree ◽  
Standard Deviations ◽  
Tesseral Harmonics

The values of lumped harmonics from the analyses of 18 satellite orbits at 14th-order resonance are used to determine individual tesseral harmonics of order 14 in the Earth’s gravity field. Eight C and five S coefficients are determined for odd degree and six C , S pairs for even degree. The results are most useful in providing the only independent test of the values obtained in recent comprehensive geopotential models. The models of the 1980s are generally consistent with the resonance values, which have lower or comparable standard deviations. The new Goddard Earth Model, GEM-T3, and European model, GRIM4-C1 have much lower standard deviations and show significant differences from our values.

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

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