Effectiveness of KS elements in satellite orbit prediction using earth's gravity, drag and solar radiation pressure

Satellite moving under the gravitational field of Earth deviates from its two-body elliptic orbit, due to the combined effects of the gravitational field of Earth, atmospheric drag, solar radiation pressure, third-body gravitational effects, etc. This paper utilizes the KS regular element equations to solve Newtonian equations of motion to obtain numerical solution with respect to perturbing forces, like, Earth's gravity (includes zonal, sectorial and tesseral harmonics terms), atmospheric drag and solar radiation pressure. Effectiveness of the theory is illustrated by comparing the results with some of the existing theories in literature.

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

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.

Averaging Tesseral Effects: Closed Form Relegation versus Expansions of Elliptic Motion

Longitude-dependent terms of the geopotential cause nonnegligible short-period effects in orbit propagation of artificial satellites. Hence, accurate analytical and semianalytical theories must cope with tesseral harmonics. Modern algorithms for dealing analytically with them allow for closed formrelegation. Nevertheless, current procedures for the relegation of tesseral effects from subsynchronous orbits are unavoidably related to orbit eccentricity, a key fact that is not enough emphasized and constrains application of this technique to small and moderate eccentricities. Comparisons with averaging procedures based on classical expansions of elliptic motion are carried out, and the pros and cons of each approach are discussed.

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

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.

Planetary Satellite Orbiters: Applications for the Moon

Low-altitude, near-polar orbits are very desirable as science orbits for missions to planetary satellites, such as the Earth's Moon. In this paper, we present an analytical theory with numerical simulations to study the orbital motion of lunar low-altitude artificial satellite. We consider the problem of an artificial satellite perturbed by the nonuniform distribution of the mass of the Moon (J2–J5,J7, andC22). The conditions to get frozen orbits are presented. Using an approach that considers the single-averaged problem, we found families of periodic orbits for the problem of an orbiter travelling around the Moon, where frozen orbits valid for long periods of time are found. A comparison between the models for the zonal and tesseral harmonics coefficients is presented.

NMR shim coil design utilising a rapid spherical harmonic calculation method

A rapid spherical harmonic calculation method is used for the design of Nuclear Magnetic Resonance shim coils. The aim is to design each shim such that it generates a field described purely by a single spherical harmonic. By applying simulated annealing techniques, coil arrangements are produced through the optimal positioning of current-carrying circular arc conductors of rectangular cross-section. This involves minimizing the undesirable harmonics in relation to a target harmonic. The design method is flexible enough to be applied for the production of coil arrangements that generate fields consisting significantly of either zonal or tesseral harmonics. Results are presented for several coil designs which generate tesseral harmonics of degree one.