Orbital Targeting Based on Hodograph Theory for Improved Rendezvous Safety

Thompson, B.; Choi, Kevin K.; Piggott, Scott; Beaver, Stefanie R.

doi:10.2514/1.47858

Cited by 23 publications

(19 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To improve rendezvous safety, Thompson et al [3] require that two tangent orbits share only a single common point (i.e., the tangent point) and the flight-path angles at that point match. Then the transfer orbit and the final/initial orbit can be noncoplanar for the specified arrival/departure flight-directionangle problem.…”

Section: Problem Statementmentioning

confidence: 99%

“…Although the solutions to all these three tangent orbit problems defined before have been obtained by using the hodograph theory in [3], a numerical iterative technique is required to solve the cotangent orbit problem. This section will provide closed-form solutions to these problems by an approach independent of the orbital hodograph theory.…”

Section: Closed-form Solutions For Tangent Orbit Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Study of Tangent Orbit and Conditions for Its Solution Existence

Zhang

Zhou

Mortari

et al. 2012

Journal of Guidance, Control, and Dynamics

View full text Add to dashboard Cite

This paper presents an analytical study of the two-body tangent orbit technique by providing solution-existence conditions. The flight-direction angle is used to describe and solve this problem. Closed-form solutions are obtained for three classic problems: specified arrival flight-direction angle, specified departure flight-direction angle, and cotangent transfers. Not all of the problems admit solutions; thus, closed-form conditions for solution existence are provided by imposing a positive semilatus rectum constraint and a negative transfer-orbit energy (elliptic orbit transfer) constraint. The final solution-existence condition is then provided in terms of the true anomaly range for initial or final orbit. The singularity problem of 180 deg orbit transfer is also analyzed. Several examples are provided to verify the proposed analytical methods.

show abstract

Section: Problem Statementmentioning

confidence: 99%

Section: Closed-form Solutions For Tangent Orbit Problemsmentioning

confidence: 99%

Analytical Study of Tangent Orbit and Conditions for Its Solution Existence

Zhang

Zhou

Mortari

et al. 2012

Journal of Guidance, Control, and Dynamics

View full text Add to dashboard Cite

show abstract

“…The numerical solution was obtained based on the orbital hodograph theory. 10 Moreover, the closed-form solution was obtained by using the geometric characteristics 11 and by the flight-direction angle, 12 respectively. The latter reference also gave the closed-form solution for the solution-existence condition.…”

Section: Introductionmentioning

confidence: 99%

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

Zhang

Cao

2014

Chinese Journal of Aeronautics

View full text Add to dashboard Cite

The two-body orbital transfer problem from an elliptic parking orbit to an excess velocity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. Firstly, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse orbit.

show abstract

“…After the completion of the Apollo program interest waned in relative motion research as the U.S. space program focused heavily on mission architectures centered on large monolithic spacecraft with a multitude of capabilities, e.g., the Space Transportation System (shuttle) platform [2]. Recent interest in low-cost, rapid call-up mission architectures structured around fractionated systems [3], small satellites (i.e., pico-, nano-, micro-satellites), and constellations has spurred renewed efforts in the relative motion problem [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Position Extrema in Keplerian Relative Motion: A Gröbner Basis Approach

2012

View full text Add to dashboard Cite

This paper analyzes the relative motion between two spacecraft in orbit. Specifically, the paper provides bounds for relative spacecraft position-based measures which impact spacecraft formation-flight mission design and analysis. Previous efforts have provided bounds for the separation distance between two spacecraft. This paper presents a methodology for bounding the local vertical, horizontal, and cross track components of the relative position vector in a spacecraft centered, rotating reference frame. Three metrics are derived and a methodology for bounding them is presented. The solution of the extremal equations for the metrics is formulated as an affine variety and obtained using a Gröbner basis reduction. No approximations are utilized and the only assumption is that the two spacecraft are in bound Keplerian orbits. Numerical examples are included to demonstrate the efficacy of the method. The metrics have utility to the mission designer of formation flight architectures, with relevance to Earth observation constellations.

show abstract

Orbital Targeting Based on Hodograph Theory for Improved Rendezvous Safety

Cited by 23 publications

References 13 publications

Analytical Study of Tangent Orbit and Conditions for Its Solution Existence

Analytical Study of Tangent Orbit and Conditions for Its Solution Existence

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

Position Extrema in Keplerian Relative Motion: A Gröbner Basis Approach

Contact Info

Product

Resources

About