Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

2018 ◽  
Vol 130 (3) ◽  
Author(s):  
Bharat Mahajan ◽  
Srinivas R. Vadali ◽  
Kyle T. Alfriend
Keyword(s):  
Tesseral Harmonics

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.

scholarly journals III. On certain functions connected with tesseral harmonics, with applications

1894 ◽  
Vol 56 (336-339) ◽  
pp. 45-49
Keyword(s):  
Angular Distance ◽  
Zonal Harmonic ◽  
Physical Research ◽  
Tesseral Harmonics

The transformation of a zonal harmonic referred to a pole on a sphere to another pole on the same sphere, and its expression in a series containing the 2 n + 1 harmonics of the same order referred to this new pole, is an operation frequently employed in physical research. The purpose of this paper is the investigation of certain functions of the angular distance between the poles which occur when a general tesseral harmonic is transformed from one pole and plane to another pole and another plane of reference. If the coordinates of any point on the sphere when referred to the first pole are β' and γ' ; β' denoting the colatitude, and γ' the longitude.

Modified long-period behavior due to tesseral harmonics.

AIAA Journal ◽  
1968 ◽  
Vol 6 (7) ◽  
pp. 1229-1234 ◽  
Author(s):  
J. VAGNERS
Keyword(s):  
Long Period ◽  
Tesseral Harmonics

The orbits of Ariel 4 and Prospero

1975 ◽  
Vol 343 (1633) ◽  
pp. 257-264 ◽  
Keyword(s):  
Gravitational Field ◽  
Orbital Parameters ◽  
Zonal Harmonics ◽  
Earth’S Gravitational Field ◽  
Tesseral Harmonics ◽  
Visual Observations

Orbital parameters for Ariel 4 and Prospero have been determined at the Royal Aircraft Establishment and made available for use with the respective telemetry analysis programs. Ariel 4 orbit determinations were based on N.A.S.A. Minitrack observations, and Prospero orbit determinations on U.S. Navy observations and a small number of visual observations. Both orbits are near polar (inclination 83° for Ariel 4 and 82° for Prospero) but not otherwise similar. The initial perigee and apogee heights were, respectively, 500 and 600 km for Ariel 4, as against 550 and 1600 km for Prospero. Hence Ariel 4 has experienced much more drag than Prospero and orbital parameters had to be determined at much closer intervals for the former than for the latter, 3 days as against 7 days. The Ariel 4 orbit is being analysed to study the effects of 15th-order tesseral harmonics in the Earth’s gravitational field, and the Prospero orbit has been used in a recent determination of odd zonal harmonics.

scholarly journals Precise Analytical Computation of Frozen-Eccentricity, Low Earth Orbits in a Tesseral Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Martin Lara ◽  
Juan F. San-Juan ◽  
Luis M. López-Ochoa
Keyword(s):  
Model Design ◽  
Zonal Model ◽  
Period Effects ◽  
Short Period ◽  
Orbit Analysis ◽  
Low Earth Orbits ◽  
Tesseral Harmonics ◽  
Earth Orbits ◽  
Eccentricity Orbit

Classical procedures for designing Earth’s mapping missions rely on a preliminary frozen-eccentricity orbit analysis. This initial exploration is based on the use of zonal gravitational models, which are frequently reduced to a simpleJ2-J3analysis. However, theJ2-J3model may not be accurate enough for some applications. Furthermore, lower order truncations of the geopotential are known to fail in describing the behavior of elliptic frozen orbits properly. Inclusion of a higher degree geopotential, which also takes into account the short-period effects of tesseral harmonics, allows for the precise computation of frozen-eccentricity, low Earth orbits that show smaller long-period effects in long-term propagations than those obtained when using the zonal model design.

scholarly journals The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Jarbas Cordeiro Sampaio ◽  
Rodolpho Vilhena de Moraes ◽  
Sandro da Silva Fernandes
Keyword(s):  
Dynamical System ◽  
Numerical Integration ◽  
Lyapunov Exponents ◽  
Orbital Dynamics ◽  
Zonal Harmonics ◽  
Chaotic Orbits ◽  
The Earth ◽  
Tesseral Harmonics ◽  
Final System

The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonicsJ20andJ40and the tesseral harmonicsJ22andJ42are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.

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