Two-Body Problem with Drag and High Tangential Speeds

Carter, Thomas; Humi, Mayer

doi:10.2514/1.31482

Cited by 9 publications

(2 citation statements)

References 6 publications

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“…The accurate computation of satellites orbits has been the subject of numerous monographs [1][2][3][4][5][6] and research papers [7][8][9] (to name a few). In particular the effect of the Earth oblateness [6,17,18] and drag forces on satellite orbits [10,11,25] were the subject of some recent publications [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Satellite Orbits and Relative Motion in Levi-Civita Coordinates

Humi

2015

Preprint

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In this paper we consider satellite trajectories in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then unify these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits in which energy and and angular momentum are on equal footing and thus characterize the orbit by its two invariants. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two satellites whose trajectories are in the same plane. We carry out also a numerical verification of these equations.

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Section: Introductionmentioning

confidence: 99%

Satellite Orbits and Relative Motion in Levi-Civita Coordinates

Humi

2015

Preprint

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“…This limitation is caused by an approximation which is highly accurate when the radial speed is small compared with the tangential speed. This simplification has been used successfully by the authors in studies that involve atmospheric drag [24,25]. We replace the total characteristic velocity which is the original cost function by a related cost function which is useful near a nominal circular orbit, and present closed-form solutions to this related optimization problem.…”

Section: Introductionmentioning

confidence: 99%

A new approach to impulsive rendezvous near circular orbit

Carter

Humi

2012

Celest Mech Dyn Astr

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A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related characteristicvalue function and this related optimization problem can be solved in closed form. The solution of this problem is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity increments.Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are presented. If necessary these velocity increments could be calculated from a hand calculator containing trigonometric functions. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted.Optimal non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each category of solutions are presented. The region of the boundary values that admit each category of solutions of the related problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Some examples are simulated. Similar results are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions are not discussed in detail, but should be presented in a following study Although this approach is thought to provide simpler computations than existing methods, its main contribution may be in establishing a new approach to the more general problem.

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Perturbation Effects of Quadratic Drag on the Orbital Elements of a Satellite in a Central Force Field

2011

J of Astronaut Sci

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This paper presents the perturbation effects of quadratic drag on the orbital elements of satellites in a central force field. The author studied this subject by using the mixed-drag model, that is the Rumi-Carter drag model in terms of the exponential drag model. The solutions of the perturbation equations are represented by the Bessel function. The results show clearly that the semimajor axis and eccentricity exhibit secular variation, but the longitude of perigee exhibits no variation. As an example we calculated the secular variation of the semimajor axis, eccentricity, perigee and apogee distances, and height for three satellites and the obtained results are discussed.

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Two-Body Problem with Drag and High Tangential Speeds

Cited by 9 publications

References 6 publications

Satellite Orbits and Relative Motion in Levi-Civita Coordinates

Satellite Orbits and Relative Motion in Levi-Civita Coordinates

A new approach to impulsive rendezvous near circular orbit

Perturbation Effects of Quadratic Drag on the Orbital Elements of a Satellite in a Central Force Field

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